A nonlocal model of epidemic network with nonlimited transmission: Global existence and uniqueness

TL;DR

This paper analyzes a nonlinear nonlocal SIS epidemic model on networks with nonlimited transmission, proving existence, uniqueness, and stability of solutions, and characterizing conditions for disease eradication.

Contribution

It establishes local and global existence results, analyzes the asymptotic stability of the disease-free equilibrium, and extends understanding of epidemic dynamics on networks with nonlimited transmission.

Findings

Global existence for equal diffusion coefficients

Stability of disease-free equilibrium when population is small

Solutions converge to disease-free state over time

Abstract

Following \cite{ipel1}, we consider a nonlinear SIS-type nonlocal system describing the spread of epidemics on networks, assuming nonlimited transmission, We prove local existence of a unique solution for any diffusion coefficients and global existence in the case of equal diffusion coefficients. Next we study the asymptotic behaviour of the solution and show that the disease-free equilibrium (DFE) is linearly and globally asymptotically stable when the total mean population is small. Finally, we prove that the solution of the system converge to the $DFE$.