In normal influenza seasons, resistant viruses develop in several percent of individuals who receive oseltamivir treatment [8]. Resistant strains have also arisen in treated hosts infected with avian strains of influenza A/H5N1 [7,9]. Mathematical models designed to consider resistance to the adamantanes (M2 inhibitors) [10] or NIs [11,12] predict that if resistant strains suffer little or no fitness deficit (reductions in transmissibility) relative to sensitive strains, then resistant strains could spread, reducing the effectiveness of antiviral use by a degree that depends mainly on the magnitude of this fitness cost. In such models, the rate of emergence of resistance in individuals who receive treatment or prophylaxis affects the rate at which resistant strains first appear. Once resistant strains have appeared, their ability to spread to many other hosts in the population depends on whether antiviral use provides a sufficiently strong selective force to offset the ”fitness cost” of resistance [13,14].

Mathematical models analyzed to date [11,12] predict that the impact of resistance to NIs on the overall course of the epidemic is largely independent of the probability of de novo emergence of resistance in treated patients, at least for the range of probabilities considered. In contrast, practical discussions of measures to minimize resistance to NIs have focused largely on the need to reduce de novo emergence by appropriate dosing [15,16] and by use of prophylaxis, which is thought to lead to de novo emergence of resistance less often than treatment [17]. One possible reason for this focus on de novo acquisition of resistance is the view that significant transmission of resistant strains is unlikely. Most oseltamivir-resistant viruses appear compromised in replication, infectivity, and/or transmissibility [18]. As frequently noted before, strains bearing such “fitness costs” would be unlikely to spread much beyond the host in whom they first arise [11,12,15]. We believe that these findings, while encouraging, do not settle the issue. In response to a pandemic, developed countries propose to use NIs on up to a quarter or more of the population, potentially upwards of 100 million courses if such use were undertaken just in the United States and the United Kingdom. This would be a dramatic increase over the worldwide use of around 3.2 million courses in the 2001–2002 influenza season [19]. Such increased use of NIs would provide unprecedented opportunities for novel resistant variants to emerge, perhaps including strains with lower fitness costs than previously observed; moreover, widespread use may create selection pressure that could permit spread of a resistant strain despite a significant fitness cost of resistance.

Furthermore, data from interpandemic influenza strains and experience with other pathogens suggest that high fitness costs of resistance are not inevitable. Although two common NI-resistant influenza mutations cause significant fitness deficits in vitro and in vivo, a third (E119V), so far found only in N2 viruses [18], has no detectable fitness cost [20]. In other infections such as HIV and tuberculosis, the frequent presence of fitness costs in resistant mutants [21–23] does not prevent transmission of resistant variants in the population[21,24]. Moreover, compensatory mutations may mitigate any fitness costs incurred by resistant strains [25,26]. Recently published surveillance data show that novel resistance mutations in N1 and N2 neuraminidases continue to appear, including those for which in vitro and in vivo fitness is unknown. Four such novel strains were isolated from individuals with no known history of NI use, suggesting that transmission of resistant strains may have occurred [19]. In summary, it is prudent in pandemic planning to consider the possibility that resistant strains with modest or no fitness cost might emerge at some point during the pandemic, even if most strains observed to date have shown substantial fitness costs [27].

The basic model (Figure 1) is a standard susceptible-infectious-recovered (SIR) model [28], with compartments representing the number of individuals in each state. All are susceptible at the outset, and births and deaths are neglected on the time scale of interest. The infected/infectious (Y) compartment is divided into three categories: infected with sensitive virus and untreated (Y_SU), infected with sensitive virus and treated (Y_ST), or infected with resistant virus (Y_R). In the absence of prophylaxis, transmission occurs at a rate proportional to the number of infectious hosts, with transmission rate constants β_SU, β_ST, and β_R from untreated and treated hosts infected with sensitive virus, and hosts infected with resistant virus, respectively. Infectiousness is assumed to be exponentially distributed with a mean duration of 1/v days.

A fraction (f_p) of susceptible hosts (X) exposed to infection receive prophylaxis. A prophylaxed host who is exposed to infection with the sensitive strain (who would have been infected absent prophylaxis) may have one of three outcomes. With probability e_p (equivalent to AVE_S of Longini et al. [3], the reduction in hazard of infection for an individual on prophylaxis), transmission is blocked. Of those blocked infections, a proportion a_p are only partially blocked, so that the prophylaxed individual becomes immune, but does not become sick or infectious to others [17]; such individuals move directly to the recovered (Z) category. With probability c_p, the prophylaxis causes de novo resistance, so the individual is infected with drug-resistant virus. In the remaining 1 − c_p − e_p of cases, prophylaxis fails, and the individual is infected with the sensitive virus, but follows a natural history like that of a treated patient [3]. Prophylaxis has no effect on an individual's risk of infection upon exposure to the resistant strain.

Of those persons who become infected but have not been on prophylaxis, a fraction f_p are treated. In a fraction c_T of treated persons infected with the sensitive strain, the strain acquires de novo resistance, turning them (we assume instantaneously) into Y_R. In the remainder, treatment reduces infectiousness to β_ST (versus β_SU) per day, and/or reduces duration of infectiousness from 1/v to 1/v_T days. In model runs presented here, the effect is assumed to be only on β_ST; the code allows the effect to be partitioned arbitrarily between infectiousness and duration, and this distinction has almost no effect on the results. Treatment has no effect on individuals infected with the resistant strain. At the end of the infectious period, individuals enter the removed (Z) category; this includes both death and recovery with immunity.

Taken together, these arguments suggest it is important to consider the possibility that resistant strains with modest fitness costs (say 20% or less) can emerge at even extremely low frequencies de novo in hosts receiving antiviral drugs. The model suggests that, if this is the case, resistant strains may well may make a significant contribution to a pandemic. Although this conclusion is pessimistic, it is balanced to some degree by the model's prediction that, even if resistant strains do spread widely, the use of antivirals will likely reduce the magnitude and delay the peak of a pandemic. The extent of this delay depends on the exact magnitude of the fitness cost (higher cost equals more delay), the amount of antiviral use (more use equals more delay), and the effectiveness of other, nondrug interventions (better interventions/less transmissibility equals more delay).

One of the more surprising results obtained here is that (except for the unlikely case in which antiviral use can stop the epidemic before a resistant strain appears) the benefit of antiviral use in reducing the attack rate is greatest for intermediate levels of antiviral use. The reason for this prediction can be seen by imagining two extremes: Case A, in which no antiviral use occurs, so the epidemic simply unfolds without hindrance from antivirals but without resistance, and Case B, in which every individual is treated and prophylaxed throughout the epidemic. Assuming that a resistant strain capable of transmission emerges in Case B, the epidemic will essentially be all resistant, but again (because the antivirals are ineffective against the resistant strain), the resistant epidemic will pass unhindered by treatment. If we further assume that the fitness cost of resistance is 0 or minimal, then Case A and Case B will be almost identical in terms of attack rate, since each will be an epidemic of an essentially identical virus (from the point of view of transmission). Now consider Case C, with an intermediate level of antiviral use, which is not enough to stop transmission of the sensitive strain. Then there will be an epidemic of the sensitive strain, smaller than in Case A because antivirals slow its spread, but followed (at some interval, longer if emergence of resistance is rare) by an epidemic of the resistant strain. Because the resistant strain will be spreading in a population that is already partially immune (thanks to prior exposure to the sensitive strain), it will spread less successfully than in Case B, and in particular will “overshoot” less in the total number of people it infects. Here, overshoot refers to the standard property of epidemics in closed populations of peaking when they have reduced the number of susceptibles to a level that can no longer maintain growth of the epidemic (in simple models, to 1/R₀), but continue to infect more as the epidemic declines, so that the proportion of the population that escapes infection by the end of the epidemic is less than 1/R₀. The precursor epidemic of the sensitive strain reduces this overshoot and thereby results in a smaller attack rate. This phenomenon is explained more generally and more quantitatively in Protocol S1.

Another surprising result obtained here is that resistance reaches higher levels in the epidemic when more-successful nondrug interventions are in place, or equivalently when the baseline transmissibility of the infection is lower. This phenomenon, considered more quantitatively in Protocol S1, can be understood intuitively as follows. When transmission is highly efficient (due to a high baseline reproductive number or ineffective nondrug interventions), the epidemic happens so fast that resistance does not have time to reach very high levels; if, instead, the epidemic is slower, due to a less transmissible virus or better nondrug interventions, resistance has time to take off before the epidemic is over. More quantitatively, the prevalence of resistance in the population increases approximately by a factor proportional to R_R − R_S in each epidemic “generation” (the time from infection of one person to infection of his contact, which is on average 1/ν). When more-effective nondrug interventions are in place, this increase is somewhat smaller per generation (since R_R and R_S are reduced), but that reduction is more than offset by an increase in the number of generations of transmission in the epidemic (note that in Figure 4, the mean time to infection, a measure of the number of generations in the epidemic, can be two or more times as long when the reproductive number is reduced by 25% from 2.0 to 1.5). As an extreme limiting case, imagine an infection that had a basic reproductive number comparable to the population size, so that nearly the entire population was infected by the first index case. Even if everyone were prophylaxed and the index case treated, resistance would occur only in those who acquired it de novo; the epidemic would be over after one (or slightly more) generations, before resistance had time to increase much above its de novo emergence rate through repeated transmission over several epidemic generations.

The simple model used here enables evaluation in a general way of the potential impact of resistance on an influenza control program, to assess the relative contributions of different factors (parameters) contributing to the epidemic. It uses a simplified, exponentially distributed natural history; however, since most of the conclusions (except for those about the magnitude of delays) are about the final state of the population, and all terms in the equations can be nondimensionalized by dividing by the generation time, this simplification does not have a major effect on outcomes. This model does not account for saturation of contacts due to transmission within families and other small groups, and therefore predicts higher attack rates than more complex, agent-based models [4,5] for a given value of R₀. Given the simplifications inherent in any model and the large uncertainties about the properties of a potential pandemic strain and its resistant variants, we emphasize the qualitative predictions of the model—supported by analytical reasoning in Protocol S1—rather than the exact quantitative predictions. Important predictions that we believe to be robust to model structure are that (1) antiviral use will favor the spread of resistance even if such use rarely generates de novo resistant strains; (2) despite the spread of resistance, prophylaxis and treatment can both delay and reduce the size of the epidemic; (3) nondrug interventions (if effective) and antiviral use—which will likely be used together in the response to a pandemic [1,4,5]—generally have synergistic benefits, despite the fact that nondrug interventions may promote resistance; and (4) relatively minor differences in fitness cost may make large differences in outcomes, even when emergence probabilities are low (Figure 4). These results extend those of previous models, which showed (like our model) that the fitness cost of resistance strongly influences the ability of resistant strains to spread during an epidemic [10–12].

It may be possible to reduce the risk of amplifying resistant viral subpopulations within a treated host [7,8,15,32] by adequate dosing and greater emphasis on prophylaxis than treatment [16]. However, our results suggest that once resistant strains are present in the population, as they likely will be [7,33], heavy use of antivirals even for prophylaxis will promote their spread by inhibiting the drug-sensitive strain that competes with them. Thus, even a highly effective antiviral regimen with little or no risk of producing de novo antiviral resistance will, when used population-wide, promote the spread of resistant strains. Similar phenomena are observed in models of Mycobacterium tuberculosis [34], Streptococcus pneumoniae [35], and hospital-acquired infections [36], and are of concern when considering preventive treatment of tuberculosis [37] and malaria [38].

The conclusions described here are specifically relevant to NIs; prospects for the use of M2 inhibitors (adamantanes) in a pandemic are considered far less promising. Adamantane resistance is very widespread in some populations of H5N1, though rare in others [39]. The resistance profile of a strain causing the next pandemic is, of course, unknown. However, even if the pandemic were initially susceptible to adamantanes, widespread use these agents would likely select for resistance extremely rapidly [10], because rates of de novo emergence are considerably higher [8] for these agents than for NIs, whereas fitness costs for adamantane resistance are unmeasurable [40].

Although adamantane monotherapy is unlikely to be effective, combination chemotherapy with both NIs and adamantanes might have some benefits against a pandemic strain initially susceptible to both classes, just as combination therapy has been useful in other infections [41]. First, the rate of de novo emergence of resistance within hosts might be reduced. Second, and perhaps more importantly, the spread of mutant strains resistant to only one of the drugs might be curtailed in the population, because treatment and prophylaxis with the drug combination might reduce susceptibility and/or infectiousness even if only one of the drugs is effective. Finally, it is at least theoretically possible that dually resistant strains would suffer a greater fitness cost than singly NI-resistant strains, although this benefit may be negligible given the high fitness of adamantane-resistant strains.