On degenerate reaction-diffusion epidemic models with mass action or standard incidence mechanism

TL;DR

This paper investigates how restricting movement in reaction-diffusion epidemic models affects disease spread, revealing that outcomes depend on transmission mechanisms, parameters, and population size.

Contribution

It introduces degenerate reaction-diffusion models with zero dispersal for susceptible or infected groups and analyzes their global dynamics using Lyapunov functions.

Findings

Limiting susceptible movement impacts disease transmission differently than limiting infected movement.

Transmission mechanism influences the effect of population movement restrictions.

Model parameters and population size significantly affect epidemic outcomes.

Abstract

In this paper, we consider reaction-diffusion epidemic models with mass action or standard incidence mechanism and study the impact of limiting population movement on disease transmissions. We set either the dispersal rate of the susceptible or infected people to zero and study the corresponding degenerate reaction-diffusion model. Our main approach to study the global dynamics of these models is to construct delicate Lyapunov functions. Our results show that the consequences of limiting the movement of susceptible or infected people depend on transmission mechanisms, model parameters, and population size.