Cross-Regional Dynamics of Disease Spread: A Coupled SIRS Model

Abstract

Understanding the dynamics of infectious disease transmission in different populations is a key aspect of public health. In this thesis, the dynamics of infectious disease spread in and between two different regions are examined. Emphasis is given to how the disease dynamics of one region relate to the external infection rates of another region. The stability and dynamics of the disease are further examined via mathematical modelling and phase portrait analysis under different conditions-agent settings.

We have attempted to study the critical role played by fundamental parameters like transmissibility, recovery, and migration rates between regions in the dynamic of disease transmission. We present an unconventional method for determining the basic reproduction number, most appropriate for the specific case under consideration, possible only because of the underlying characteristics. It allows us to determine and identify the circumstances in which the disease-free equilibria is either stable or unstable. Furthermore, we ponder potential travel constraints and their impact on disease spread and any possible outbreaks.

In summary, this study helps us understand how different populations and outside factors interact, which helps us see how diseases spread. This knowledge can help us create and carry out plans to control infectious diseases better. Also, by explaining how diseases move from one place to another, this research helps us understand diseases better and how they can affect public health.