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A new SIR model with mobility.

by Ciana Applegate

Institution:	University of Louisville
Department:
Degree:	PhD
Year:	2022
Keywords:	SIR; mathematical modeling; stochastic processes; Ordinary Differential Equations and Applied Dynamics; Other Applied Mathematics
Posted:	3/25/2025
Record ID:	2291966
Full text PDF:	https://ir.library.louisville.edu/etd/3961

Abstract

In this paper, a mobility-based SIR model is built to understand the spread of the pandemic. A traditional SIR model used in epidemiology describes the transition of particles among states, such as susceptible, infected, and recovered states. However, the traditional model has no movement of particles. There are many variations of SIR models when it comes to the factor of mobility, the majority of studies use mobility intensity or population density as a measure of mobility. In this paper, a new dynamical SIR model, including the spatial motion of three-type particles, is constructed and the long-time behavior of the first and second moments of this dynamical system are studied. The intermittency and Lyapunov exponents are derived and analyzed as well.