Modeling Infectious Disease Spread: Comparison of the Agent-Based-Modeling and Differential-Equation Approaches

In epidemiology, the SIR model is commonly used to describe the population dynamics ofinfectious diseases. It divides the population into three categories: Susceptible, Infected, and Recovered. We consider two approaches to describe its population dynamics. In the Ordinary Differential Equation (ODE) approach, we solve a set of differential equations that describe the rate of change of the fraction of each category. In the Agent-Based Model (ABM), we keep track of the state of each person and its position in a two-dimensional lattice. The ODE model has two model parameters, the infection strength b and the recovery rate k, whereas the ABM has three model parameters describing the diffusion, infection, and recovery rates. Our research aims to compare the two approaches and to establish a relationship between the ODE and ABM parameters. To find the optimal values of the b and k parameters that give matching results to the ABM simulation results, we employ two methods. In the first method, we determine the optimal b and k values by minimizing the differences between the curves generated by the ODE and ABM approaches. In the second method, we use an established relation between the end-state ratio of uninfected people and the contact number b/k. Our results show that these two estimation methods give consistent results and explain the fast-diffusion limit situation.