Stability analysis and quantification of effects of partial and full vaccination using fractional order SVIR model

An infectious disease such as COVID-19 posed a threat to public health worldwide due to its high infection rate and its further mutation into novel variants. Vaccination serves as a vital tool to interrupt its transmission cycle and far-reaching effects. However, the effectiveness of vaccination depends upon a well-planned strategy. This study explores the comparison between full and partial vaccination strategies using a novel fractional SVIR mathematical model with Caputo fractional derivative. The model categorizes vaccinated individuals into two groups: partially and fully vaccinated class. To account for limited medical resources and virus reemergence, we adopt the Holling type III saturated treatment function for treatment rate. In the analysis, we first show well posedness of model solutions. Further, we discuss the stability of the two equilibria exhibited by the system: DFE (Disease Free Equilibrium) and EE (Endemic Equilibrium). It is shown that the DFE is locally asymptotically stable when R0 < 1, and EE is locally asymptotic stable by Routh-Hurwitz criterion. Moreover, both the equilibrium points are proved to be globally asymptotically stable under certain conditions with the help of appropriate Lyapunov function. Numerical simulations are also performed to validate the analytical findings using MATLAB. The quantification of effects of partial and full vaccination reveals that full vaccination results in higher percentage of recovered population, making it evident that policymakers and professionals should focus on the implications of effective full vaccination among susceptible individuals.