A Dynamic Model for Infectious Diseases: The Role of Vaccination and Treatment

TL;DR

This paper introduces a new infectious disease model incorporating incubation delays and relapse, analyzing how vaccination and treatment influence disease dynamics and stability, highlighting the importance of treatment rates in disease control.

Contribution

The study presents a novel model that includes incubation delays and relapse, providing new insights into the roles of treatment and vaccination in disease containment.

Findings

Treatment rate significantly controls disease spread.

Incubation delays affect system stability even with vaccination.

Global stability analyzed for a key case.

Abstract

Understanding dynamics of an infectious disease helps in designing appropriate strategies for containing its spread in a population. Recent mathematical models are aimed at studying dynamics of some specific types of infectious diseases. In this paper we propose a new model for infectious diseases spread having susceptible, infected, and recovered populations and study its dynamics in presence of incubation delays and relapse of the disease. The influence of treatment and vaccination efforts on the spread of infection in presence of time delays are studied. Sufficient conditions for local stability of the equilibria and change of stability are derived in various cases. The problem of global stability is studied for an important special case of the model. Simulations carried out in this study brought out the importance of treatment rate in controlling the disease spread. It is observed that incubation delays have influence on the system even under enhanced vaccination. The present study has clearly brought out the fact that treatment rate in presence of time delays would contain the disease as compared to popular belief that eradication can only be done through vaccination.