SIR model with random diffusion, reinfection, and random transmission: exponential attractors and spread of the disease

TL;DR

This paper develops a stochastic SIR model with random factors, proving the existence of attractors and analyzing conditions for disease eradication or persistence.

Contribution

It introduces a novel stochastic PDE SIR model with random diffusion and transmission, establishing attractors and disease outcome conditions.

Findings

Existence of random and exponential attractors for the model

Construction of a disease-free global solution

Conditions for disease eradication or endemic persistence

Abstract

We introduce a stochastic SIR-type partial differential equation model incorporating random diffusion, reinfection, vital dynamics, and a randomly varying transmission rate. For the associated random dynamical system, we prove the existence of both random and exponential attractors. We construct a non-stationary, random disease-free global solution, which serves to localize the random attractor. Furthermore, we analyze the mean value of the random transmission coefficient to establish conditions under which the disease may either be eradicated or persist in an endemic state, depending on the system's parameters.