Stability and Local Bifurcation Analysis of a Measles SVIR Model with Waning Vaccine-Induced Immunity

Abstract

This study presents a mathematical model to investigate the transmission dynamics of measles in a population following the introduction of vaccination. The population is divided into four epidemiological compartments: Susceptible , Vaccinated , Infected  and Recovered  A key feature of the model is the inclusion of waning immunity induced by vaccination over time. A thorough mathematical analysis is performed to establish the positivity and boundedness of the model solutions, along with the existence and local stability of equilibrium points. Furthermore, the model is analyzed for the occurrence of local bifurcations, including Hopf bifurcations, to identify potential complex dynamical behaviors. Numerical simulations are conducted to validate the analytical findings and assess the influence of key parameters on the system dynamics