Wave propagation for a discrete diffusive vaccination epidemic model with bilinear incidence

TL;DR

This paper investigates the existence of traveling wave solutions in a discrete diffusive vaccination epidemic model with bilinear incidence, linking mathematical results to epidemiological insights.

Contribution

It establishes conditions for the existence of traveling wave solutions based on the basic reproduction number and constructs Lyapunov functionals to connect different equilibria.

Findings

Traveling wave solutions exist when >1 and wave speed exceeds a critical value

Lyapunov functionals are used to connect different epidemiological equilibria

Results provide biological insights into epidemic spread and control

Abstract

The aim of the current paper is to study the existence of traveling wave solutions (TWS) for a vaccination epidemic model with bilinear incidence. The existence result is determined by the basic reproduction number $\Re_0$. More specifically, the system admits a nontrivial TWS when $\Re_0>1$ and $c \geq c^*$, where $c^*$ is the critical wave speed. We also found that the TWS is connecting two different equilibria by constructing Lyapunov functional. Lastly, we give some biological explanations from the perspective of epidemiology.