Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model

TL;DR

This paper analyzes a reaction-convection-diffusion PDE model for cholera, demonstrating that the basic reproduction number determines whether the disease persists or dies out globally, with conditions for stability and persistence.

Contribution

It establishes the global stability criteria and persistence conditions for the cholera model based on the basic reproduction number, extending understanding of epidemic dynamics.

Findings

Reproduction number predicts disease persistence or extinction.

Disease-free equilibrium is globally attractive when below threshold.

Persistent infection occurs if initial infection is non-zero.

Abstract

We study the global stability issue of the reaction-convection-diffusion cholera epidemic PDE model and show that the basic reproduction number serves as a threshold parameter that predicts whether cholera will persist or become globally extinct. Specifically, when the basic reproduction number is beneath one, we show that the disease-free-equilibrium is globally attractive. On the other hand, when the basic reproduction number exceeds one, if the infectious hosts or the concentration of bacteria in the contaminated water are not initially identically zero, we prove the uniform persistence result and that there exists at least one positive steady state.