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Infectious disease models are tools that are increasingly used to inform public health and preventive medicine research, policy, and practice. Although implementing infectious disease models requires a certain level of theoretical background and computational experience, the basic principles are easy to grasp. This chapter is a first introduction to infectious disease models and is intended to demystify models and the modeling process. In this chapter, we first highlight some uses and limitations of infectious disease models. Next, we discuss some of the main concepts underlying infectious disease modeling. Then, we introduce the foundational infectious disease model, the SIR model (or susceptible, infectious, recovered model) and its compartmental model extensions. We next discuss network and agent-based models, which are used to explore the importance of individual-level characteristics (such as superspreading). Finally, we briefly discuss the connection between data and models. After reading this chapter, you will understand the basics of infectious disease modeling, allowing you to engage with and interrogate the assumptions and conclusions of infectious disease modeling research.


Why Use Mathematical Models?

Patterns of health and disease arise from complex interactions of biological, social, and environmental factors. Disentangling these factors to understand the underlying causal processes is difficult, particularly as these factors often involve feedback loops playing out over time (and space). For instance, when a new respiratory pathogen is introduced in a population, it will first propagate freely without interference, but once discovered, interventions, such as social distancing and decontamination of surfaces, and changes in human behavior will affect how the pathogen continues to propagate, perhaps slowing transmission. This in turn might affect how the risk of infection is perceived, eventually leading to a return to business as usual, which might again facilitate the propagation of the pathogen. To make sense of these complex systems, we use models—simplifications of the real world that help us make sense of what we see. Models take many forms, from cartoon diagrams and verbal descriptions of a process (“if this, then that…”), to complex simulation models. We reason about the rules and processes that underlie health all the time—whether it’s reasoning about a possible diagnosis or the likely transmission modes in an outbreak, we rely on mental models of the system in question. Mathematics and statistics provide a way to formalize this kind of reasoning and to interrogate the processes and mechanisms that drive disease spread, thereby helping to improve public health responses. For instance, models were used to help quantify the potential impact of social distancing measures in slowing the rate of transmission of pH1N1 during the 2009 pandemic (see shaded box in section “The Basic Reproduction Number”).

Mathematical models and statistical models are not truly distinct classes (as many models are both mathematical and statistical), but there are some broad general distinctions between the two. Statistical models are typically used to examine associations and ...

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