Abstract
Mathematical models of the dynamics of infectious disease transmission are used to forecast epidemics and assess mitigation strategies. In this article, we highlight the analogy between the dynamics of disease transmission and chemical reaction kinetics while providing an exposition on the classic Susceptible–Infectious–Removed (SIR) epidemic model. Particularly, the SIR model resembles a dynamic model of a batch reactor carrying out an autocatalytic reaction with catalyst deactivation. This analogy between disease transmission and chemical reaction enables the exchange of ideas between epidemic and chemical kinetic modeling communities.
Highlights
INTRODUCTIONMathematical models of the dynamics of infectious disease transmission (Brauer, 2017; Hethcote, 2000) are useful for forecasting epidemics, evaluating public health interventions, and inferring properties of diseases
Mathematical models of the dynamics of infectious disease transmission (Brauer, 2017; Hethcote, 2000) are useful for forecasting epidemics, evaluating public health interventions, and inferring properties of diseases.In compartmental epidemic models (Brauer, 2008), each member of the population is categorized based on their disease status in addition to, possibly, their attributes and/or the treatment they received
The dynamics of disease transmission are typically modeled with differential equations that describe the flow of individuals between the compartments as the population mixes, the disease spreads, infected individuals progress through the stages of the disease, and public health interventions are implemented
Summary
Mathematical models of the dynamics of infectious disease transmission (Brauer, 2017; Hethcote, 2000) are useful for forecasting epidemics, evaluating public health interventions, and inferring properties of diseases. The dynamics of disease transmission are typically modeled with differential equations that describe the flow of individuals between the compartments as the population mixes, the disease spreads, infected individuals progress through the stages of the disease, and public health interventions are implemented. We highlight the analogy between the dynamics of disease transmission and chemical reaction kinetics while formulating and analyzing the SIR epidemic model. The SIR dynamic model of infectious disease transmission and its analogy with chemical kinetics.
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