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# Mathematical models to characterize early epidemic growth: A review.

### Author information

- 1
- School of Public Health, Georgia State University, Atlanta, GA, USA; Division of International Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD, USA. Electronic address: gchowell@gsu.edu.
- 2
- Department of Anthropology, University of Missouri, Columbia, MO, USA.
- 3
- Department of Biology, Georgetown University, Washington DC, USA; Division of International Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD, USA.
- 4
- Division of International Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD, USA.

### Abstract

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.

#### KEYWORDS:

Epidemic growth patterns; Epidemic modeling; Individual-based model; Reproduction number; Spatial models; Sub-exponential epidemic growth

### Comment in

- Power law incidence rate in epidemic models: Comment on: "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al. [Phys Life Rev. 2016]
- On parameter estimation in compartmental epidemic models: Comment on "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al. [Phys Life Rev. 2016]
- The need for data science in epidemic modelling: Comment on: "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al. [Phys Life Rev. 2016]
- Understanding apparently non-exponential outbreaks Comment on "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al. [Phys Life Rev. 2016]
- A general theory of early growth?: Comment on: "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al. [Phys Life Rev. 2016]
- Effects of clustered transmission on epidemic growth Comment on "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al. [Phys Life Rev. 2016]

- PMID:
- 27451336
- PMCID:
- PMC5348083
- DOI:
- 10.1016/j.plrev.2016.07.005

- [Indexed for MEDLINE]