Modelling and analysing the spread of infectious diseases: the role of vaccination and public awareness

This paper presents and evaluates a nonlinear mathematical model designed to assess the impact of vaccination programs on the transmission dynamics of infectious diseases. The model categorizes the population into three compartments: susceptible individuals ( ), infected individuals ( ), and vaccinated individuals ( ). Employing both analytical approaches and numerical simulations, the study demonstrates that effective media campaigns promoting vaccination, coupled with an adequate vaccine supply, can substantially mitigate the spread of infections. The stability of the model is analyzed using the stability theory of differential equations, and numerical simulations are conducted to validate and reinforce the analytical results.