Modeling the impact of vaccination efficacy and awareness programs on the dynamics of infectious diseases

This study presents a pioneering deterministic mathematical model to explore the complex dynamics of infectious diseases, focusing on the synergy between vaccination efficacy and awareness programs in disease control. Within an SVIQR framework encompassing susceptible, vaccinated, infected, quarantined, and removed compartments. The model employs nonlinear differential equations to analyze disease-free and endemic equilibrium. Key analyses include calculating the basic reproduction number ( \(R_{0}\) $R_0$ ) and stability assessments using the Gershgorin Circle Theorem. Numerical simulations demonstrate the profound impact of vaccination and awareness programs, highlighting their crucial role in reducing disease transmission. The study underscores the societal implications, showing how effective vaccination strategies and enhanced awareness can significantly lower infection rates, thereby informing public health policies and fostering communities.