Vaccination Dynamics and Stability Insights: A SIR Model Approach to Epidemic Control

Abstract

In this paper, the standard susceptible, infectious, recovered (SIR) model of epidemic dynamics is considered to examine how vaccination in newborn affects equilibrium stability and infectious spread dynamics. This work includes the analysis of local and global stability at disease-free and endemic equilibrium points. Analytical and numerical methods are employed to demonstrate the increase in vaccination rate reduce infectious disease transmission. Our work addresses a literature gap and leads to better epidemic control methods.  An in-depth investigation of the model's local and global stability will help policymakers and health workers build immunization plans by revealing how the illness behaves in different situations. In summary, this work provides a straightforward, brief, and informative analysis of epidemic mobility with vaccination, essential for optimizing vaccination tactics to manage epidemics.