Infection Modeling Case Study: Discrete Spatial Susceptible-Infected-Recovered Model

The susceptible-infected-recovered (SIR) model is used in epidemiology to simulate the transmission of infectious diseases. The continuous formulation of the SIR model is represented by a set of three coupled differential equations that can be solved numerically. Due to the dynamics of the simulation, the SIR model is best when simulating diseases that confer a lasting immunity. More complex models for disease transmission are typically derived from this base model and can include features such as additional infectious stages, stochastic frameworks, vaccines, and finite immunity. In this case study, I first examine the features of the continuous model. Then, I create a discrete model, which simulates individuals that transmit the disease based on proximity. With this basic framework established, one can examine strategies that change the spread of the infection, such as social distancing.