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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptNIH Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Epidemics. Author manuscript; available in PMC Jun 1, 2013.
Published in final edited form as:
PMCID: PMC3405853
NIHMSID: NIHMS374786

Agent-based and phylogenetic analyses reveal how HIV-1 moves between risk groups: injecting drug users sustain the heterosexual epidemic in Latvia

Abstract

Injecting drug users (IDU) are a driving force for the spread of HIV-1 in Latvia and other Baltic States, accounting for a majority of cases. However, in recent years, heterosexual cases have increased disproportionately. It is unclear how the changes in incidence patterns in Latvia can be explained, and how important IDU are for the heterosexual sub-epidemic. We introduce a novel epidemic model and use phylogenetic analyses in parallel to examine the spread of HIV-1 in Latvia between 1987 and 2010. Using a hybrid framework with a mean-field description for the susceptible population and an agent-based model for the infecteds, we track infected individuals and follow transmission histories dynamically formed during the simulation.

The agent-based simulations and the phylogenetic analysis show that more than half of the heterosexual transmissions in Latvia were caused by IDU, which sustain the heterosexual epidemic. Indeed, we find that heterosexual clusters are characterized by short transmission chains with up to 63% of the chains dying out after the first introduction. In the simulations, the distribution of transmission chain sizes follows a power law distribution, which is confirmed by the phylogenetic data. Our models indicate that frequent introductions reduced the extinction probability of an autonomously spreading heterosexual HIV-1 epidemic, which now has the potential to dominate the spread of the overall epidemic in the future. Furthermore, our model shows that social heterogeneity of the susceptible population can explain the shift in HIV-1 incidence in Latvia over the course of the epidemic. Thus, the decrease in IDU incidence may be due to local heterogeneities in transmission, rather than the implementation of control measures. Increases in susceptibles, through social or geographic movement of IDU, could lead to a boost in HIV-1 infections in this risk group. Targeting individuals that bridge social groups would help prevent further spread of the epidemic.

Keywords: Agent-based model, Social structure, Transmission chain, Evolution, Phylodynamics

1. Introduction

Although the total number of new infections caused by human immunodeficiency virus 1 (HIV-1) infections worldwide is decreasing since 1997, the current UNAIDS report estimates that in 2010 around 2.7 million people became newly infected with HIV (UNAIDS, 2011). Most of these HIV-1 infections occur in Sub-Saharan Africa with some countries showing a HIV-1 prevalence of up to 25% in the adult population (UNAIDS, 2011). Another focus of high transmission is in Eastern Europe, where elevated incidence rates, especially among specific risk groups, are observed. While the spread of HIV-1 in Sub-Saharan Africa is mostly driven by heterosexual contacts, the epidemics in several Eastern European countries are mainly spreading through injecting drug users (IDU) (UNAIDS, 2011). In particular, the Baltic countries of Estonia and Latvia are dealing with a large HIV-1 epidemic in their IDU population, resulting in some of the highest HIV-1 prevalences in Central and Eastern Europe (UNAIDS, 2010; Hamers and Downs, 2003; Uuskula et al., 2008; Laisaar et al., 2011).

One of the most important factors influencing the spread of an epidemic is the ability of an infected individual to establish a sufficient number of contacts with susceptible individuals during its infectious period. A major focus of previous research was on the importance of super spreaders, individuals with a high number of social contacts, for the spread of the epidemic (Hyman et al., 2001; Metzger et al., 2011). However, the social and geographical structure of the susceptible population also determine these contact rates. Small groups of people sharing the same transmission risks (e.g. IDU, men who have sex with men (MSM)) could increase locally the spread of the epidemic, as these small groups enhance the probability of infected individuals finding contacts for transmission. However, to maintain and to spread the epidemic more widely, infected individuals have to leave the local clusters and interact with other people.

The composition and interactions among these different social groups might influence the overall dynamics of the epidemic, as well as the virus diversification patterns. Conversely, observed viral diversity may tell us something about epidemiological clusters. Indeed, there is a growing interest to infer relationships between the spread of virus in a population (epidemiology) and the evolution of that virus (phylogenetics) (Grenfell et al., 2004; Pybus and Rambaut, 2009). For example, we have recently studied the relation between the rate of spread of HIV-1 and the virus rate of evolution (Maljkovic Berry et al., 2007, 2009). Several groups have studied epidemiological characteristics of different diseases based on viral sequence data, such as HIV-1 (Stadler et al., 2011; Kouyos et al., 2010; Volz et al., 2009; Skar et al., 2011; Leigh Brown et al., 2011; Leventhal et al., 2012), hepatitis C (Pybus et al., 2001), infection by paramyxoviridae (Pomeroy et al., 2008), or rabies virus (Talbi et al., 2010) to name just a few (for more general discussions and reviews see O’Dea and Wilke (2011); Rasmussen et al. (2011); Holmes and Grenfell (2009); Grenfell et al. (2004)).

Here, we present a framework to follow both HIV-1 spread and evolution in a population using an agent-based model (Schmid et al., 2010). The modeling approach distinguishes between susceptible and infected individuals to capture the full infection history, including contact tracing data for infected individuals. However, following each individual of the susceptible population would require detailed information on the social contact network between them, which is difficult to obtain. Thus in our model uninfected individuals are modeled at a population level, stratified by transmission risk and social group. The social network in our model forms and can change during the simulation. The model is in between a mean-field approximation of the HIV-epidemic as done by regular SIR-models based on ordinary differential equations (Keeling and Rohani, 2007; Anderson and May, 1979; May and Anderson, 1979), and the computational intensive simulation of a complete network of susceptible and infected individuals (Volz et al., 2010). Our model includes vital dynamics, as well as disease dynamics of the infected population, within host viral dynamics, and considers social structure of the susceptible population as e.g. given by geographical or economical aspects. Values from the literature are used to parameterize the model.

In this study, we focus on the epidemiological characteristics of our modeling framework. We use the model to study epidemiological data from Latvia, obtained from the Infectology Center of Latvia (Balode et al., 2004, 2011). These data capture the HIV-1 epidemic in Latvia from 1987 to 2010 and include information on the diagnoses of HIV-1 by transmission route. We also have access to a large number of HIV-1 sequences of this epidemic (Balode et al., 2004, 2011). Our objective is to approximately track the epidemiological data with our model and study the social structure of the susceptible population that can explain features of the data, such as the increasing importance of heterosexual transmissions in the spread of HIV-1 in this country. Furthermore, without including phylogenetics directly in our model yet, we analyze the consistency between our model results and phylogenetic inference based on the sequence data.

2. Materials and Methods

2.1. Epidemiological and phylogenetic data

Epidemiological data from Latvia including information on diagnoses and transmission routes of HIV between 1987 and 2010 were obtained from the Infectology Center of Latvia. We assume that the number of diagnoses is a proxy for new HIV-1 cases in Latvia, but see e.g. Bezemer et al., 2008. Data were collected as previously described (Balode et al., 2004, 2011). The Latvian HIV reporting practice follows the requirements of ECDC and WHO/Euro surveillance program, and on average 80,000 diagnostic HIV tests are performed per year (UNGASS, 2010). Briefly for the phylogenetic data, HIV-1 env V3 sequences were derived from 315 Latvian individuals of different risk groups (heterosexuals, HET; injecting drug users, IDU; men-who-have-sex with men, MSM; and unknown, UNK) representing all geographical regions of Latvia. Previous studies had shown that the vast majority of infections occurred in IDU after approximately year 2000 (Balode et al., 2004). Thus to get a more complete picture of the entire epidemic we made an effort to include early samples, as well as samples from other risk groups (Balode et al., 2011). We especially focused on HET transmission sequences to get a detailed understanding of this sub-epidemic, oversampling this population with regard to the occurrence among all HIV-1 diagnoses. The majority (n = 232) of the sequences were HIV-1 subtype A1, as expected since this is the subtype spread among IDUs.

2.2. Ethical approval

The study was approved by Los Alamos National Laboratory Human Subjects Research Review Board (Study No. LANL 09-01). The generation of sequence data and epidemiological analyses was previously approved by the Latvian Ethical Committee (19.06.1998. Nr.2 and 24 March, 2005, A-4, decision nr.4), and the Regional Medical Ethics Board in Stockholm (Dnr. 2004/4:6 and Dnr 2008/4:1) (Balode et al., 2004, 2011).

2.3. Phylogenetic analysis

The phylogeny of HIV-1 subtype A1 in Latvia was inferred by maximum likelihood (ML) analyses using PhyML version 3.0 (Guindon et al., 2005) and Bayesian Markov Chain Monte Carlo (BMCMC) phylogenetic reconstruction using MrBayes version 3.1.2 (Ronquist and Huelsenbeck, 2003). The substitution model (GTR+I+G) was identified using FindModel (www.hiv.lanl.gov) with parameter values optimized during the phylogenetic inference. The robustness of the ML tree was investigated using aLRT and non-parametric bootstrap analyses (500 pseudo-replicates) available in PhyML. The BMCMC search was conducted with two separate chains with 106 generations, initially sampled every 100 generation. After discarding the first 25% of samples (even though convergence was reached within <5%), we randomly subsampled 104 trees to describe the subtype A1 epidemic. To investigate number of IDU-to-HET introductions, trees were rooted at the first sampled IDU cases, ladderized and the paraphyletic order and length of risk group taxa-labels were analyzed. Recall that the sequence data was collected to include as many HET (and other than IDU) samples as possible so that the IDU samples would not overwhelm the phylogenetic representation (Balode et al., 2011). Even so, sampling of rare transmission chains may be underrepresented. However, our approach to estimate the number of IDU-to-HET introductions accounts for the oversampling of HET sequences compared to IDU in the phylogenetic sample. To assess statistical significance, 104 random bifurcating trees with the same label distributions were analyzed. Automation and analysis were conducted using R scripts (R-Development-Core-Team, 2006).

2.4. Heuristic model of HIV-1 in Latvia

In Figure 1A we show the number of new HIV-1 diagnoses in Latvia from 1987 to 2010. Based on the observed peak of HIV-1 diagnoses in Latvia in the year 2001, one could assume that the cumulative number of cases, I(t), is characterized by a bi-phasic increase. To test statistically whether there is such a bi-phasic increase, we formulate a heuristic model for the number of new cases, I(t). Let β1 and β2 denote the rates at which new infected individuals are diagnosed during the two phases, tT and t > T, with β1 ≥ β2. The change in the cumulative number of cases is then described by

dIdt=𝟙[tT]β1I+𝟙[t>T]β2I
(1)
Figure 1
HIV-1 Epidemic in Latvia from 1987 to 2010. New HIV-1 diagnoses per year (A) and cumulative number of HIV-1 diagnoses (B) stratified by risk group. The lines in panel B show the best fit of Eq. (2) to the data.

Here, [mathematical double-struck 1][tT] defines the indicator function with [mathematical double-struck 1][tT] = 1 if tT and 0 otherwise. Solving Eq. (1) leads to

I(t)=I0 exp (𝟙[tT]β1(tt0)+𝟙[t>T](β1(Tt0)+β2(tT)))
(2)

where I0 denotes the number of index cases at t0, the time of the onset of the epidemic, meaning the first year with an infected individual for each risk group (t0All=1987,t0IDU=1995,t0MSM=1987,t0HET=1990). Data were fitted to Eq. (2) using a non-linear least-squares method. All analyses were performed using the R language of statistical computing (R-Development-Core-Team, 2006).

2.5. Agent-based model and events

To simulate the dynamics of the HIV-1 epidemic, we developed an agent-based model consisting of two types of actors (infected and susceptible individuals) and, in the basic setting presented here, three types of events (infection, developing AIDS and death). Each infected individual is represented by an individual agent while susceptibles are followed on a population level. That is, they are divided into social and risk groups, but do not have any other properties or associated events.

Infected individuals are characterized by different traits describing their individual, social, virological and behavioral properties. The population is divided into n social groups, S, which represent potential local contact networks, but could also represent different geographical regions (eg., urban areas vs. rural areas). Additionally, we distinguish between four different risk groups, R, for HIV-1 transmission: (i) injecting drug-users (IDU), (ii) men who have sex with men (MSM), (iii) heterosexuals (HET), and (iv) sex-workers (SW). Each infected individual is characterized by a vector G = (R, S,C) defining the risk group(s) for HIV transmission, R; all the social group(s) that the individual can belong to, S; and the current social group(s), C [subset or is implied by] S, i.e., the social group(s) the individual is currently interacting with. In addition, infected individuals are characterized by their age, sex, risk behavior, the time they became infected, viral load, and AIDS and treatment status (Figure 2). For simplicity, in the current study, we assume that the viral load of each individual is given by a common profile that depends only on the time since infection (Figure S1). Newly infected agents start with an age of at least 15 years, as we do not assume younger people to contribute much to the epidemic. The time step of the simulation is one day. The agent-based model was implemented in the R language of statistical computing (R-Development-Core-Team, 2006). In the following, we will give a detailed description of the different events as well as a motivation for the different parameters used in the simulations.

Figure 2
Schematic of the modeling framework. Infected individuals are followed on an individual level characterized by different traits, e.g. the age of the individual or the viral load. The susceptible population is stratified into different risk groups according ...

2.5.1. Infection

The probability of an infected agent, i, to infect a susceptible individual, s, is calculated based on the risk of HIV transmission per contact, β, and the gender of the interacting individuals. The transmission-matrices for β based on appropriate values from the literature (Boily et al., 2009; Jin et al., 2010; Grebely and Dore, 2011; White et al., 2007) are shown in Figure S2. Furthermore, the probability to infect a susceptible individual depends on the viral load, incorporated by a factor DV, as well as the effective number of contacts, nEC, an individual has during a specific time period. With these parameters, the probability of at least one susceptible individual s in risk group Rs and social group Ss being infected by individual i in risk group Ri and current social group Ci is defined by:

piinf (Rs,Ss)={0if    (RsRi)(SsCi)1(1min{DVβ,1})nECotherwise
(3)

Here, an infected individual can only infect susceptibles which share the same risk group(s) and current social group(s) as the infected agent. The probability of transmission upon contact, i.e., needle sharing or sexual intercourse, is given by DV β, where DV denotes a factor accounting for increased transmissibility given higher viral loads. If DV β becomes very large, a susceptible gets infected with probability 1. The effective number of contacts an individual has per time step, nEC, is given by an assumed basic number of contacts, nC, which is additionally influenced by factors related to the age (Da) and the behavior (Db) of the infecting agent, as well as the frequency of appropriate susceptibles in the corresponding social group, f (e.g. frequency of heterosexual females given an infected heterosexual male). We assume a linear relationship between these factors, defining nEC = DaDbfnC.

Parameterization of Eq. (3)

Quinn et al. (2000) showed that the risk of HIV-transmission per contact depends on the viral load of the transmitting partner. In their study, following 415 heterosexual couples in rural Uganda in which one of the partners was HIV-positive while the other one was initially HIV-negative, the authors observed that for each log10 increase in viral load the relative risk for HIV transmission increased by a factor of 2.45. Therefore, we assume that the baseline transmission rate β (Figure S2) is calculated for a viral load of V = 104 HIV-1 RNA copies/ml (Quinn et al., 2000), and define DV as the factor changing infectiousness due to the individual’s viral loads, thus DV = 2.45log10(V)−log10(104). We use the same factor for sexual and needle-sharing transmission, although this could be changed. We assume that the viral load of each infected agent follows the same profile (Figure S1): After reaching a peak of 106 RNA copies/ml around day 25 after infection, the viral load will drop to a set-point viral load of V = 104 HIV-1 RNA copies/ml. It remains constant on this level for the asymptomatic phase of the disease until the individual has progressed to AIDS, upon which the viral load increases again. Here, we are only interested in the generic shape of the viral load, including the potential for increased transmission during primary infection due to higher viral load. Therefore, we do not vary the set-point viral load between different individuals.

The number of effective contacts, nEC, of an individual, is parameterized as follows: Based on previous studies investigating sexual behavior (Schmid et al., 2010; Wawer et al., 2005; Rothenberg et al., 2000; Wellings et al., 2006; Volz et al., 2010), we assume a basic rate of nC = 5 sexual contacts per month for a heterosexual or MSM individual. For sex workers, this contact rate is estimated to be around 6 times higher, giving 30 contacts per month Elmore-Meegan et al., 2004). One study involving IDUs reported a rate of needle-sharing of ~ 5 times per month (Rothenberg et al., 2000), and so we use nC = 5 also for IDUs. However, the risk of HIV transmission, in particular for sexual transmission, decreases with age (Quinn et al., 2000; Davenport et al., 2004), likely due to decreased contact rates. Therefore, nEC is influenced by an age-related factor Da, reducing the number of sexual contacts nC with age (see Davenport et al. 2004 and Table S1 for a parameterization). In addition, as individual behavior also alters the risk of infection, for example by leading to more contacts than the baseline, we include a factor characterizing the individual’s behavior, Db. If Db > 1, the individual has more contacts than the standard contacts described above, making it more likely to spread the epidemic. We allow for different profiles of behavior for each risk group, by assuming that Db follows a beta-distribution on the interval (0,3) characterized by two shape parameters, α and β (the scale parameter is 3). Without loss of generality, we fixed β = 5 and allowed α to vary between the different risk groups. We chose α for each risk group to roughly reproduce the Latvian epidemic. At the time of infection, Db for the new infected agent is sampled from these distributions (see Figure S3). With our parameterization, an infected individual of the youngest age class (15–19 years) has on average [n with macron]EC = 3.75 sexual contacts per month. This decreases to [n with macron]EC = 1.25 contacts per month for the age class 35–39 (note that these are random contacts which might also be with the same person, and not necessarily new sex partners). With the risk behavior distribution for IDU, an individual in this risk group will perform on average [n with macron]EC = 11.7 risky injections practices per month.

For each combination of risk group (R) and social group (S) that the infected individual belongs to, there is a potential infection event with probability piinf (Rs,Ss) (Eq. (3)). At each time step of the simulation, we assume that at most one infection event occurs, which is chosen according to a multinomial distribution out of the potential infection events piinf (Rs,Ss), ∀Rs [set membership] R, ∀Ss [set membership] S. The actual occurrence of an infection is then determined by a binomial distribution with the corresponding probability piinf (s,s). Upon infection, a new agent, i + 1, is created with the same risk group and social group determined by the infection event, Gi+1 = (Ri+1, Si+1,Ci+1) where Ri+1 = Rs and Si+1 = Ci+1 = Ss. Additional risk and social groups for the newly infected individual, besides its main risk and social group, are sampled randomly according to the corresponding frequencies in the population. Additional risk groups are sampled based on the prevalence of the different risk groups in the main social group and vice versa. This allows the epidemic to spread to different risk and social groups (see the Appendix A for a detailed description of this process).

2.5.2. Developing AIDS

An individual infected with HIV-1 can progress to AIDS. The time between the infection and the development of AIDS varies between patients with an average of 10–11 years and ranging from progression within a couple of years up to more than 20 years of AIDS free survival (Munoz et al., 1989, 1995). In addition to several other factors, the time of progression to AIDS correlates with the set-point viral load, i.e., the viral load at the onset of the chronic phase of the infection (Mellors et al., 1996). Based on the study by Mellors et al. (1996), we calculate the hazard λ(V) of individuals to progress to AIDS depending on the set-point viral load, V (see Table S2). We assume a constant hazard for progression to AIDS throughout the course of infection and that there is no progression to AIDS during the acute phase. That is, if an individual has been infected for the time Δ, then for Δ < Δ(V), where Δ(V) defines the time of the beginning of the chronic phase (60 days after infection), the probability of progression is negligible. Thus, an individual will develop AIDS at each time step with the probability piAIDS (Δ,) given by

piAIDS (Δ,)={0if Δ<Δ()1exp(λ())otherwise
(4)

Additionally, in the simulations shown here we assumed that when the viral load of a subject increases by one log10 compared to its set-point viral load, the infected individual progresses to AIDS. With the viral course shown in Figure S1, the average duration of the chronic phase is around 10–12 years. We assume a constant hazard for the progression to AIDS dependent on the set-point viral load of the infected individual. However, using an individual progression hazard λ parameterized according to CASCADE (2000), which is population based and depends on the time since infection, did not change our results. We also assume that infected individuals in the AIDS-phase do not contribute to the epidemic. The sensitivity of our results with regard to this assumption is examined as well.

2.5.3. Death

The probability of an infected individual dying, pideath, depends on two factors: (i) an age-related mortality and (ii) a disease related mortality. We calculated the age-specific mortality rates μ(a) per year separately for males and females based on the lifetables for the US (CDC, 1999) as an example for a developed country. The disease associated mortality rates, ν(Δ) dependent on the duration of infection Δ, were obtained from the CASCADE study, in which disease related survival was analyzed (CASCADE, 2000; Davenport et al., 2004) (see Table S3). At each time step, the probability of the infected individual i to die is calculated by:

pideath (a,Δ)=1exp (μ(a)365) exp (ν(Δ)365)
(5)

Note that μ(a) and ν(Δ) were converted into rates per day for our simulations.

2.6. Susceptible population

We applied our model to epidemiological data of the HIV epidemic in Latvia from 1987–2010. The total population of Latvia is around 2.22 × 106 people with a male to female ratio for the age of 15–65 years of r = 0.95 (CIA-Factbook, 2011). As a large fraction of the total population is rather unlikely to be directly exposed to HIV during the observed epidemical time period of 22 years, we define 25% of the total population as susceptible (=exposed to HIV), comparable to the highest prevalence of HIV observed in Sub-Saharan Africa (UNAIDS, 2010). For computational efficiency, we model 20% of the susceptible population, corresponding to NS = 1.11 × 105 susceptible individuals in total.

To distribute the susceptibles over the different risk groups we make the following assumptions: (i) The prevalence of IDU in Latvia is estimated at about 0.0066 (Aceijas et al., 2004) and all IDUs are assumed to be susceptible to HIV infection. (ii) Estimates of lifetime prevalence of homosexual contacts in men ranged from 6–15% in Eastern Europe with around half of them having had male partners in the past year (Wellings et al., 2006; Caceres et al., 2006), which we use as a defining criterium for MSM. As most of the studies reporting these estimates were performed in high-risk populations (Caceres et al., 2006), we use the minimum prevalence of MSM, 3%, in our susceptible population, which is comparable to estimates for Western Europe (Wellings et al., 2006). Furthermore, we assume 50% of the total MSM population to be susceptible (i.e., with potential exposure) to HIV infection. (iii) The number of female sex workers was considered to be 0.1% of the total female population. All of these sex workers are assumed to be susceptible to HIV infection. (iv) The rest of the susceptible population belongs to the heterosexual risk group. Table 1 shows the number of susceptible males and females in the different risk groups in our simulations. We used the same male to female ratio for all different risk groups with r = 0.95. Therefore, we also considered a risk group comprising homosexual females. However, there is no transmission among those individuals (Figure S2, β = 0) and they do not contribute to the epidemic at all.

Table 1
The number of susceptible males and females distributed by the different risk groups for HIV transmission as considered in the simulations. We assume the same male/female ratio (0.95) for each risk group. Homosexual contacts between females do not contribute ...

One of the objectives of this study was to investigate the social structure of the susceptible population giving rise to the observed distribution of cases through time. Our basic scenario assumes separation of the susceptible population into three different social groups as indicated in Table 2A. This separation is based on phylogenetic analysis of the actual data: Phylogenetic analysis revealed that the epidemic in the Latvian MSM population was dominated by strains of HIV-1 subtype B, while viral strains in IDU were of subtype A1, indicating limited mixing between these two different risk groups (Balode et al., 2004, 2011). Heterosexual individuals mixed with both risk groups, but with ~90% of heterosexual cases belonging to the subtype A1 epidemic (Balode et al., 2004, 2011), indicating marginal mixing with the MSM population. Therefore, we considered the MSM population as a separate social group (S=“b”) without any possible mixing with other social groups, while IDU and HET are able to interact with IDU in one social group (S=“a”) and HET divided between social groups “a” and “c”. Later on, we allow for more heterogeneous grouping scenarios as defined in Table 2B.

Table 2
Different grouping scenarios for the distribution of susceptibles by social groups. Numbers denote the percentage of male/female susceptible individuals of the risk group in the corresponding social group. (A) Homogenous grouping scenario. (B) Heterogenous ...

3. Results

3.1. The HIV-1 epidemic in Latvia from 1987-2010: epidemiological data

As in most Eastern European countries, Latvia‘s HIV-1 epidemic is mainly driven by injecting drug users (Hamers and Downs, 2003). Especially in the early years of the 21st century, the number of new HIV-1 diagnoses among injecting drug users in Latvia increased dramatically (Figure 1), comparable to the situation in neighboring countries, e.g. the Russian Federation and especially Estonia (Hamers and Downs, 2003; Uuskula et al., 2008). However, in recent years the number of diagnosed HIV-1 infections among IDUs seems to be decreasing while the number of new diagnoses caused by heterosexual transmission is accelerating. In 2009, there were approximately two times more new HIV-1 infections caused by heterosexual transmission than by IDU (135 HET vs. 74 IDU). As the number of HIV-1 tests performed per year in Latvia is relatively constant (between 2001 and 2006 around ~85.000 – 89.000 tests per year) (UNGASS, 2010), we take the number of new HIV-1 diagnoses as an approximation for the number of HIV-1 cases in our model.

To quantify the dynamics of the total epidemic and the individual sub-epidemics stratified by risk group, we fitted an empirical model to the data (see Eq. (2) in Materials and Methods). This model assumes that the cumulative number of cases between 1987 and 2010 increases bi-phasicly, at rates β1 and β2, with the switch between the two rates occurring at time T. For IDU, we estimated the switch to occur in 2001, corresponding to the peak of new HIV-1 cases in this risk group. Before 2001, the number of new HIV-1 infections among IDU increased with a rate of β1 = 1.21 year−1 [1.18, 1.25], and after with a much smaller rate of β2 = 0.05 year−1 [0.037, 0.064]. The number of new HIV-1 infections caused by heterosexual transmission increased with a rate of β1 = 0.46 year−1 [0.44, 0.47] before 2002. After 2002, the increase is estimated to be β2 = 0.18 year−1 [0.17, 0.19]. Comparing these rates, we find that before 2002, the increase in IDU cases is approximately three times faster than in heterosexual cases, but the opposite is true after 2002. Results for all fits are shown in Table S4 in the Supplemental Material. A model with a bi-phasic increase fits the data significantly better than a model with a constant rate over the whole period (F-test, p < 10−15); and there is no significant improvement in the fits of the individual sub-epidemics assuming a tri-phasic increase (F-test, p > 0.05). Thus, these results suggest that a shift in transmission rates could explain the changing pattern of HIV-1 infections among IDU and heterosexuals in Latvia.

We wanted to investigate if this shift can be accounted for by the social structure of the susceptible population without having to assume drastic changes, for example in viral infectivity or people’s behavior. To this end, we used the agent-based model described in Materials & Methods.

3.2. Structure of the sub-epidemics: Insights from the agent-based model

Before studying the influence of social structure on the dynamics of the epidemics, we examined the development of each sub-epidemic (IDU, MSM, HET) in the agent-based model. An important contributor for the spread of HIV infection is the individual behavior that may increase or decrease risk of transmission. There are different types of behavior to be considered, such as the number of different partners, the frequency of contacts (sexual or needle sharing), the use of protective measures, etc. We combine all these factors in one behavioral parameter Db, which scales the number of risky contacts an individual has compared to the assumed baseline number, nC.

The HIV-1 epidemics in the MSM and IDU sub-populations can be considered more or less self-contained, because most of the infections occur within the corresponding risk groups (Balode et al., 2004, 2011). This allowed us to estimate the α shape parameter for the Beta distributions of Db for these two risk groups (see Materials & Methods and Supplemental Material), by choosing a value such that the model approximately predicts the right number of cumulative cases for each risk group in 2010 (Figure S3). The simulations to adjust this parameter were run separately for each of the two risk groups, and α was kept constant in all further simulations.

Applying the same strategy to the heterosexual risk group, we found that with a single introduction into this population, in the vast majority of runs the epidemic dies out even if we assume a risk behavior higher than in the IDU group, which seems very unlikely. Even with a contact rate in the HET group 10 times higher than in MSM, we found that only ~ 30% of the simulations generated an epidemic maintained over at least 20 years (see Figure S4(a)). This is perhaps not surprising given the low transmission probability for heterosexual contacts compared to MSM or IDU contacts, which have 20–40 times higher transmission rates (Figure S2). In contrast, introducing a HIV infection into a MSM population leads to ~ 77% of runs establishing a sustained epidemic, with on average ~ 180 cumulative cases in total compared to the 204 cases in the data.

While a general higher contact rate of heterosexuals compared to other risk groups is quite unrealistic, it is possible that a heterosexual subgroup, characterized by high contact rates, e.g. female sex workers, could provide a reservoir to constantly feed the heterosexual epidemic. Estimates for the fraction of the male population visiting female sex workers are difficult to obtain and vary between 1%–14% (Wellings et al., 2006). To examine how this additional risk group might influence the size of a heterosexual HIV-1 epidemic, we investigated the upper limit as a conservative scenario that promotes the sustainability of the epidemic. We assumed a social group which contained 100% of the female sex workers and 40% of the heterosexual susceptible population in which the infection was introduced by different index cases. However, the inclusion of female sex workers as an additional risk group does not substantially affect the outcome of the epidemic, whether the epidemic is started by a male or female individual. Once a female sex worker is infected, an epidemic is more likely to be observed, as can be seen from the introduction of an infected female sex worker into the susceptible population. Nevertheless, given reasonable contact rates for heterosexuals (say, similar to those of MSM), this additional risk group is not sufficient to reproduce the size of the heterosexual HIV sub-epidemic in the Latvian population (Figure S4(c)–(d)).

Altogether, our model suggests that the magnitude of the sub-epidemic in Latvia in the heterosexual risk group is difficult to explain by a single introduction into this risk group. Either the Latvian epidemic corresponds to the occurrence of an event with very low probability or several introductions are needed to lead to an epidemic of the observed size. The simplest explanation, which is also compatible with the phylogenetic data, is then that the IDU and HET risk groups are linked epidemiologically. In Table 2A, we show our basic scenario for a possible distribution of the susceptible population into different social groups, with some IDU and HET sharing a common social group (“a”), where they interact. In Figure 3A, we show the evolution of the different sub-epidemics for such a structure of the susceptible population. As expected, the simulations are compatible with the MSM subepidemic in Latvia, because we chose the risk behavior in this population to approximately match the total number of cases. Assuming all IDU to randomly interact in one social group leads to an epidemic with on average all susceptible IDU infected after 22 years. Moreover, due to the possibility of frequent interactions between IDU and heterosexuals, it also gives rise to a large heterosexual sub-epidemic (see below). Both of these lead to much larger numbers of infected than seen in the actual data, which lie outside the 2.5- and 97.5-percentiles of the simulations at later times. In particular, these simulations do not recover the slowing down of the IDU sub-epidemic after 2001 (Figure 1).

Figure 3
Cumulative incidence curves for the sub-epidemics of MSM, IDU and HET transmission given the different social structures for the total susceptible population shown in Table 1. Panel A (upper row) shows the results for a scenario close to a well-mixed ...

3.3. Social structure and the change in HIV-1 incidence among IDUs in Latvia

The majority of cases in the HIV-1 epidemic in Latvia between 1987 and 2010 are related to IDU transmissions (Figure 1). However, in this risk group, a decrease in the number of new diagnoses is obvious after 2001 Figure 1 and Table S3). There are two main hypotheses to explain this decrease: (i) the transmissibility of IDU has decreased due to changes in risk behaviour or the application of treatment programs, or (ii) the number of susceptible IDU in the population was reduced around this time. Evidence for the first hypothesis is lacking, as we argue in the Discussion. The second hypothesis assumes that the decrease in new HIV-1 cases among IDU is due to a reduction in the susceptible population. While we find no evidence for reduction in the total number of IDU around 2001 (Aceijas et al., 2004, 2006), a local decrease in susceptible individuals is possible. Groups of IDU might form clusters of different sizes with limited interaction between them.

To test this hypothesis, we examined how a heterogeneous social grouping structure among the IDU and heterosexual population, with different degrees of mixing between the social groups, might affect the spread of the two sub-epidemics.

We ran many simulations with different grouping structures for the susceptible population to understand what possible scenarios could explain the overall epidemic in Latvia. While it is still theoretically possible to infect the whole susceptible population, the assumption of different social groups impairs the interaction between individuals, and slows the spread of the epidemic. In general we found that having more, smaller groups led to the possibility of saturation in the IDU epidemic. For example, keeping the same total number of susceptible individuals as in our baseline scenario, but distributing them through many small social groups, as indicated in Table 2B, leads to much smaller epidemics.

The fast early increase in the IDU population, similar to the one observed in the data, is due to the spread of HIV in social group “a”, which comprises the largest susceptible sub-population of IDU. When the number of cases in this social group approaches saturation, the incidence decreases overall, but the epidemic continues to spread in the other IDU groups. Thus, this grouping structure allows the model to reproduce in a reasonable way the observed data (Figure 3B). Moreover, this grouping structure is to some extent comparable to the geographical distribution of the Latvian population. Most HIV infections occur in Riga, the capital and largest city, which also comprises the largest number of susceptible individuals (e.g. IDU (Aceijas et al., 2004; UNGASS, 2010)). We also analyzed a situation where we allow for an explicit decrease in the IDU susceptible population with a reduction in the total number of IDU after 2002, e.g., due to emigration. Such a scenario also leads to reductions in the number of new cases in the IDU population, like our assumption of different social groups. However, with this decrease in susceptibles, we do not see a saturation in the IDU epidemic as observed in the data. In addition, the reduction in incidence is highly dependent on the magnitude of the reduction (e.g. 20% or 50%) in IDU (not shown). The similar effect of both assumptions, either social separation or a decreasing IDU population, indicates that both scenarios are to some extent comparable. The separation of the total number of susceptible IDU into different social groups represents a dynamic IDU population. Due to mixing between social groups, the number of available susceptible IDUs increases dynamically as infections are introduced into different social groups. In later years, it becomes more and more difficult to reach further IDU, i.e. introductions into smaller groups, mimicking a decrease in the number of IDU.

In summary, the course of the HIV epidemic caused by IDU transmission in Latvia can be explained by clustering of the susceptible population, without needing to invoke changes in individual behavior, which are not currently supported by epidemiological studies.

Another important result from dividing the population in smaller social groups is that the increase in the number of heterosexual infections is substantially reduced. Indeed, the range defined by the 2.5- and 97.5-percentile of the runs in the simulation now includes the observed data. To understand this result in more detail, we analyzed the effect of the IDU epidemic on the spread of HIV in the heterosexual population.

3.4. The role of IDU in sustaining the heterosexual epidemic

As mentioned above, it is difficult to observe a sustained heterosexual epidemic without continued input from an “outside” reservoir. Due to the stochastic nature of our model, there is a high probability of the epidemic going extinct in the initial stages (Jacquez and O’Neill, 1991; May et al., 2001). With our model, we are able to follow the transmission events among the different groups (and indeed each infected agent). This enables us to examine the importance of HIV transmission from IDU to heterosexual partners in overcoming this initial high probability of extinction in the heterosexual sub-epidemic. In Figure 4, we show the proportion of heterosexual cases introduced by individuals infected by intravenous drug use among all new heterosexual cases. We see that the median fraction of IDU related transmission increases up to year 10, corresponding to ~ 50 − 60% of all new heterosexual cases (Figure 4). For the heterogeneous mixing depicted in Table 2B this fraction then decreases, as the IDU sub-epidemic saturates and more and more infections only within the heterosexual risk group can be observed.

Figure 4
Fraction of IDU related heterosexual transmissions among all new heterosexual cases. The median of 100 epidemics for a homogenous (solid line) and heterogenous (dashed line) grouping scenario are shown referring to the heterosexual sub-epidemics depicted ...

As a consistency check for these results, we analyzed sequence data from the Latvian epidemic. The infections of the Latvian HIV-1 epidemic are driven mainly by HIV-1 subtype B amongst MSM and subtype A1 amongst IDU (Balode et al., 2004). Most of the HET infections also involve subtype A1, likely introduced from the IDU sub-epidemic. Consequently, a phylogenetic tree of Latvian HIV-1 subtype A1 shows mixing of the IDU and HET risk groups (Figure 5A). The number of HIV-1 introductions into the heterosexual risk group was estimated from the phylogeny by counting the number of HET-labeled taxa runs in a ladderized tree. Because a single maximum likelihood tree had poor support (aLRT and non-parametric bootstrap), we investigated trees sampled from a Bayesian Markov Chain Monte Carlo (BMCMC) phylogenetic reconstruction (Huelsenbeck and Ronquist, 2001). We sampled 10,000 trees after burn-in from the BMCMC set of likely trees, and estimated that HIV-1 was introduced ~45 (sd=2.8) times into the HET group (Figure 5B). To further test if we had enough signal to estimate the number of introductions, we sampled 10,000 random trees with the same frequency of HET, IDU, MSM and UNK (=unknown) labels. This showed that our estimate was highly significant (p < 0.001, Wilcoxon rank sum test with continuity correction). Hence, although there was some uncertainty in the phylogeny, our estimate of the number of introductions of HIV-1 subtype A1 into the HET risk group was robust. Thus, the phylogenetic data suggests about 66% (45/68) introductions from the IDU into the HET risk group. This fraction is in reasonable agreement with our simulations described above.

Figure 5
Phylogenetic analysis of the mixing between IDU and HET. A Phylogenetic tree of the HIV-1 subtype A1 epidemic based on 232 samples in total (68 HET, 131 IDU, 4 MSM, 29 unknown) with black circles denoting the HET taxa. B Distribution of the number of ...

In the model we can look in more detail at this process. In Figure 6, we show the transmissions between different social groups and different risk groups. We find that the proportion of heterosexual transmissions from individuals infected by intravenous drug use among all new heterosexual cases varies in the different social groups. Early in the epidemic, this proportion in social group “a”, where the most mixing between HET and IDU occurs, is even higher than the overall estimate of 50 − 60% (Figure 6A). If our sequence sample is biased towards this larger group (presumably Riga) then the agreement between model and phylogenetic results is reinforced. Additionally, Figure 6 shows the transmission profiles between different social groups. Here, we found that the transmission balance between any two social groups depends mainly on the ratio of the prevalence of IDU in those groups. Groups with higher prevalences of IDU among their susceptible population are more likely spreader groups, causing more infections in other groups than vice versa.

Figure 6
Fraction of HIV infected individuals in each social group and transmission links between the groups: The dynamics for one representative simulation of an epidemic in a susceptible population structured as in Table 2B is shown after 10 years (A) and after ...

3.5. Heterosexual transmission chains in data and simulation

Another way to look at the effect of an infected IDU as the source of heterosexual transmissions is to study the length of heterosexual transmission chains started by an IDU. In Figure 5C, we show that in the simulations the vast majority of introductions were dead ends, i.e. the infected heterosexual did not infect anyone else. But some introductions resulted in a chain of transmissions. Indeed, we found that the distribution of chain lengths, k, in our simulation is consistent with a power law distribution, P(k) ~ k−γ, with exponent γ = 2.01 and 95% CI (1.70, 2.49). We next verified these simulation results in the phylogenetic data which included 68 HET taxa. We found that about 20% (9/45) of the introductions correspond to dead ends, and chains rarely involve more than 3 consecutive transmissions (Figure 5C). We used the sample of 10,000 BMCMC trees to estimate the distribution of chain sizes implied by the data. This distribution was also consistent with a power law distribution with exponent γ = 2.43, and 95% credible interval (2.0, 3.01) (Figure 5C). We hypothesized that the higher power law coefficient in the phylogenetic data compared to the simulated epidemic could be due to the phylogenetic data representing only a subsample of the full heterosexual epidemic. Thus, we next repeated these calculations for our simulations but sampling only 68 HET. The resulting smaller chain sizes leads to a higher power law coefficient (and more uncertainty) than in the full epidemic (γ = 2.67 (1.46, 3.83)), consistent with the hypothesis that sample effects lead to larger coefficients in the phylogenetic data (Stumpf et al., 2005).

4. Discussion

Each observed and documented HIV-epidemic is the result of specific dynamics shaped by the structure of the susceptible population and individual behavior. Phylogenetic analysis may be useful to infer the interaction between individuals and to rebuild the social network underlying the resulting epidemic (Grenfell et al., 2004). However, the sampled phylogenetic sequences might only reflect a fraction of the real epidemic and, even if complete sampling was possible, it will not cover the whole population exposed to the virus as the sample only includes those who got infected. Therefore, it is important to study the influence of heterogeneity of the susceptible population on the epidemic dynamics in order to reveal specific patterns of spread, and to establish links between this spread and phylogenetic observations.

To study these phylodynamics issues, we developed an agent-based model for epidemiology and evolutionary dynamics of HIV. The model framework is in between a well-mixed assumption of susceptible and infected individuals and a fully detailed contact network model. In contrast to a well-mixed model as e.g. described by a SIR-model (Keeling and Rohani, 2007), our model allows the tracking of infected individuals in terms of their HIV disease progression and vital dynamics. Additionally, the model considers heterogeneity in the population as e.g. mediated by spatial or social aspects. However, our model neglects the detailed description of a prior social contact network in the susceptible population as described in other studies (Volz et al., 2010). Construction of a reliable social network requires enormous amounts of information, which is difficult to obtain, hard to trust and difficult to generalize. Even when available, this information represents a biased sample of the overall population network, because these studies typically only follow high-risk groups (Rothenberg et al., 2000; Volz et al., 2010). Furthermore, a predefined social network model restricts the analysis to very specific situations. Rather than being predetermined, the social network in our model develops and may change during the simulation, due to infections. One particular aspect that is difficult to ascertain is the number of sexual contacts between individuals. General studies on sexual behavior address this value only insufficiently (Wellings et al., 2006), while more detailed inquiries are usually obtained among specific social groups, e.g. HIV infected individuals, which are not representative for the behavior of the general susceptible population (Caceres et al., 2006; Rothenberg et al., 2000). To overcome this problem we included a parameter describing the risk behavior of different individuals and calibrated it by applying our model to epidemiological data.

Our simulations show that it is highly unlikely to observe an HIV-1 epidemic in the heterosexual population as in Latvia with only a single or a few introductions of index cases. Given the typical number of sexual contacts (Wellings et al., 2006), the early stochastic extinction probability is high (Jacquez and O’Neill, 1991; May et al., 2001). Even with the unrealistic assumption of contact rates that are more than 20 times higher than those assumed for MSM individuals, it is very unlikely to reproduce the number of cases observed in the heterosexual sub-epidemic in Latvia. Also the additional consideration of female sex workers (i.e., super-spreaders, Figure S4) or frequent longterm-partnerships between individuals in our model (data not shown), both of which may be associated with more frequent sexual contacts, do not influence the observable average size of the epidemic substantially. The heterosexual sub-epidemic in Latvia, at least in the beginning, had to be constantly seeded from the outside. The most likely explanation for this outside source is introductions by IDUs through their sexual partners (Hamers and Downs, 2003). As reasonable values for the frequency of needle sharing between IDUs ensure a self-sustaining HIV-1 epidemic with a high prevalence within the IDU population, this risk population works as a reservoir for the heterosexual sub-epidemic. This hypothesis was confirmed in our model as well as by phylogenetic analysis of the Latvian epidemic. Phylogenetic analysis revealed that ~90% of heterosexual cases belong to subtype A, which is the dominant subtype in the IDUs (Balode et al., 2004, 2011). In fact, we estimated that in our sample of 68 taxa related to heterosexual cases, on average 45 (~ 66%) were introduced by people previously infected due to IDU contact. A similar percentage was found in our agent-based model during the fast growing phase of the epidemic. However, once a certain number of infected heterosexual individuals is reached, the extinction probability of an autonomously spreading HIV-1 epidemic in this sub-population decreases (Jacquez and O’Neill, 1991; May et al., 2001; Britton, 2010; Tuckwell and Williams, 2007). This could explain why the recent observations in Latvia show an increase in heterosexual cases (Figure 1 and Table S4), even as the number of new HIV-1 diagnoses among IDU seems to be decreasing. Without any interventions, our models predict a potential for a fast growing number of heterosexual cases, dominating the total spread of the epidemic in the near future.

The question of whether IDU can trigger a generalized epidemic has also been discussed elsewhere (Wiessing and Kretzschmar, 2003; Saidel et al., 2003; Grassly et al., 2003). While Saidel et al. (2003), who used a mathematical model to study the spread of HIV-1 among IDU, sex-workers and the general population in Asia, predict a very large effect of IDU on a generalized epidemic among heterosexuals; Grassly et al. (2003) find almost no effect studying a similar question for Russia. Possible explanations for these obvious different findings have been discussed (Wiessing and Kretzschmar, 2003). Our simulations show that an autonomous heterosexual HIV-1 epidemic can be “triggered” by IDU without requiring behavioral changes among heterosexuals: Frequent HIV-1 transmissions from IDU to their sexual partners reduce the early extinction probability of an autonomous heterosexual HIV-1 epidemic (Jacquez and O’Neill, 1991; May et al., 2001; Britton, 2010; Tuck-well and Williams, 2007), leading to a maintained sub-epidemic. Several studies show the importance of targeting IDU as a bridge population spreading HIV to several other risk groups (Kretzschmar and Wiessing, 2008; Sutton et al., 2012; Brown and Peerapatanapokin, 2004; Ruxrungtham et al., 2004). Our analyses support these results. Signs for a generalized epidemic in Latvia seem to be rare (UNGASS, 2010), although its potential should be taken into account in future health policy implementations.

We found that the structure of the susceptible population has an influence on the epidemiological dynamics (Watts et al., 2005). Clustering of the susceptible population with limited interactions among the groups can limit the spread of the epidemic. While the same number of people is still susceptible, social separation lowers the overall transmission, thereby slowing down the spread of the epidemic. This social clustering can explain the observed shift in the number of HIV-1 diagnoses among IDU in Latvia after 2001. Another possible explanation would be the assumption of a changing susceptible IDU population, i.e., a reduction in the overall numbers of IDU after 2001. While we find no evidence for a decrease in the total number of IDU in Latvia (Aceijas et al., 2004, 2006), such a situation is analogous to our clustering hypotheses. As each social group becomes saturated in turn there is an effect of fewer and fewer susceptible IDU. Indeed, we ran simulations where we introduced an ad hoc reduction of 20% and 50% in IDU in 2001, and confirmed that this could lead to a decrease in the number of new HIV-1 diagnoses among IDU (data not shown). Intervention methods, such as treatment or needle exchange programs are other possible explanations for the shift in HIV-1 transmission rates among IDU. Evidence for these explanations is lacking as efficient antiretroviral treatment (ART) is not common in Latvia. Even as recently as 2009 only a small fraction of infected individuals had access to ART (~ 300 people), and only one third of those people are related to IDU transmission (de Joncheere et al., 2009). Furthermore, although Latvia introduced pilot needle exchange programs for IDU at the end of 1997 (UNGASS, 2010), those programs seem to provide an effective coverage of only 1–3% of the IDU population per year (Aceijas et al., 2007). The total budget for needle exchange programs in 2009 would only allow an effective coverage of ~ 100 IDU per year (UNGASS, 2010). In addition, several high risk groups, as e.g. prisoners, are excluded from those programs.

The clustering of social groups also implies that targeting individuals that bridge groups would be beneficial to prevention. Note that these bridging individuals do not need to be traditional “super-spreaders” but rather “facilitator-spreaders”. Recently, outbreaks among IDU in Sweden and Finland appear to have started by introductions of HIV in otherwise stable groups (Skar et al., 2011). Additional data from the Infectology Center of Latvia show that the epidemic started out in Riga, the capital of Latvia, which is by far the largest city as well as the largest HIV cluster in Latvia. After around 10 years, the epidemic spread to other, smaller regions. While the number of new infected cases seems to have decreased in Riga in recent years, the number of new infected individuals in the countryside is still at a stable level. These observations correspond approximately to the grouping structure that led to a better description of the epidemic in our model (Table 2B), and no change in the individual’s risk behavior is necessary to explain the slower increase in the number of IDU related HIV transmissions. This would also mean that, due to the limited prevention and treatment efforts (de Joncheere et al., 2009), it is possible for the epidemic to regain momentum if enough new susceptibles e.g. move to Riga.

We have to emphasize that we did not intend to perfectly match the HIV-1 epidemic in Latvia with our agent-based model. We are rather interested in possible scenarios that explain the dynamics observed in the Latvian epidemic. For instance, our models do not perfectly explain the late phase of the heterosexual epidemic where we on average predict more HIV-1 infections than actually occurred. Additional factors that are not considered in the model so far, e.g. treatment which reaches mostly the HET risk group (de Joncheere et al., 2009), can reduce this number. Thus, although we could tweak the social grouping structure to better reflect the actual number of cases, we do not believe that we would obtain any extra useful information.

Our agent-based model relies on estimated parameter values published in the literature. Many of these quantities vary between different studies, but we try to choose those that best reflect the situation in Latvia. Moreover, we chose those parameters before adjusting our model to the data and kept them fixed throughout the study. In addition, we studied a simplified model, with fewer parameters, by excluding additional events such as the introduction of therapy, the establishment of longterm partnerships or dynamical changes in individual risk behavior. While the model is prepared to incorporate these issues, we neglected these points in the analysis so far, as they do not apply to the Latvian epidemic (e.g. treatment) or are subject to future study. For example, the importance of longterm sexual partnerships on HIV epidemic dynamics is currently subject to an intense debate in the literature (see e.g. Sawers and Stillwaggon, 2010; Epstein and Morris, 2011) requiring a careful analysis on its own, which is beyond the scope of this study.

For simplicity, in our model we assumed that infected individuals who have developed AIDS do not contribute to the epidemic anymore. While this might be true for sexual transmission (MSM,HET) due to reduced contact rates given illness, this assumption might be inaccurate for IDU, who may not change their injection practices. We examined how this assumption affects the outcome of our model. While allowing for transmissions in the AIDS-phase, where transmission rates are even higher than during the asymptomatic phase due to increased viral load, increases the number of sexual HIV-1 transmissions (MSM,HET) in our heterogeneous grouping scenario, the total number of infected IDU remains unchanged. This is due to the fact that IDU, with their higher transmission rates and more frequent contacts, get more easily infected. Therefore, the longer infectious period does not contribute significantly to the epidemic.

An important property of our model is the ability to integrate epidemiological and phylogenetic data. For instance, we found both in the simulations and the phylogenetic data that the distribution of transmission chain sizes, k, for heterosexual transmission follows a power law distribution given by P(k) ~ kγ (Barabasi and Albert, 1999). The coefficient γ estimated from the model and the phylogenetic data is comparable to the one found for heterosexual HIV-transmission clusters in the UK (Hughes et al., 2009), and those generally observed for sexual contact networks (Liljeros et al., 2001; Amaral et al., 2000). Based on our analyses we conclude that the phylogenetic data provide a representative picture of the heterosexual transmission network in the Latvian epidemic.

In summary, we presented a novel modeling framework appropriate to study the epidemics and evolution of HIV. Applying our model to data of the HIV-1 epidemic in Latvia from 1987 to 2010 we show that the epidemiological scenario predicted by the model agrees with results obtained by phylogenetic analyses. Using this modeling approach to study in detail how epidemiological parameters and evolutionary data are related is the subject of our ongoing work.

Highlights

  • We develop an agent-based model to study HIV-1 transmission dynamics
  • We analyze epidemical data of Latvia using the agent-based model and phylogenetics
  • Injecting drug users sustained the heterosexual HIV-1 sub-epidemic in Latvia
  • Heterosexual transmission chain sizes follow a power law distribution
  • Social structure of susceptible population explains observed epidemical dynamics

Supplementary Material

supplement

Acknowledgements

We thank Helena Skar and Tim Wallstrom for helpful discussions. Portions of this work were done under the auspices of the U.S. Department of Energy. Funding support from NIH through grants 5R01AI08752002 and AI028433 and the National Center for Research Resources and the Office of Research Infrastructure Programs (ORIP) through grant 8R01-OD011095-21. RMR received partial funding from the European Union 7th Framework Programme under grant PCOFUND-GA-2009-246542 and from the Foundation for Science and Technology of Portugal. The funding agencies had no role in study design, analysis of data and the preparation of the manuscript.

Appendix A

Determining newly infected individuals

If an infected individual infects a susceptible, the attributes of this newly infected individual are determined as follows: the risk group and social group are defined by the mode of transmission and the social group of the infecting agent. Additional risk and social groups for the newly infected agent are sampled based on the occurrence probability of other risk groups in the transmitting social group and the distribution of the transmitting risk group among other social groups.

As people mainly tend to socialize and interact with people of the same age, the age of the newly infected individual is sampled according to a normal distribution defined by N(āi, 3), where āi is the age of the infecting individual at the time of the infection, but at least 15 years. Because contacts with sex workers are of commercial nature, the age of an individual infected by a sex worker is sampled according to the age distribution of men in Latvia which have a median age of 35 years.

There are different types of behavior such as the number of different partners or the frequency of contacts or sexual intercourse, which influence the susceptibility of an individual to HIV. We combine all these factors in the behavioral parameter Db, which scales the number of contacts an individual has compared to the assumed average number nC. We assume that the risk behavior of each risk group follows a beta-distribution which is a continuous probability distribution on the interval [0,3] characterized by two shape parameters, α and β. While β is kept fixed, we allow α to vary between the different risk groups. The risk behavior of a newly infected agent is then sampled from these different probability distributions. If an individual belongs to several risk groups, the highest risk behavior is applied to all risk groups as this parameter is assumed to describe the behavior of the person.

Footnotes

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