The Dynamics of a Vertically Transmitted Disease

TL;DR

This paper presents a comprehensive analysis of a vertically transmitted disease using an SIRS model, identifying key thresholds that determine disease persistence, population growth, and stability, thus extending previous research in the field.

Contribution

It generalizes prior results by providing a complete global analysis with explicit thresholds for disease dynamics and population effects.

Findings

Identification of three explicit threshold parameters

Conditions for disease endemic equilibrium and stability

Insights into population growth influenced by disease dynamics

Abstract

An SIRS epidemiological model for a vertically transmitted disease is discussed. We give a complete global analysis in terms of three explicit threshold parameters which respectively govern the existence and stability of an endemic proportion equilibrium, the increase of the total population and the growth of the infective population. This paper gereralize the results of Busenberg and van den Driessche.