Dynamics of Caputo fractional-order SIRV model: The effects of imperfect vaccination on disease transmission

Though vaccination protects individuals against many infectious diseases, such protection does not always last forever since a few vaccinated individuals could lose their lifelong immunity and eventually become infected. This study, therefore, determines the effects of imperfect vaccination and memory index on the spread of diseases through the Caputo fractional-order SIRV (Susceptible-Infected-Recovered-Vaccinated) epidemic model. Vital properties of the new model - including the conditions for the existence of a unique solution determined through the fixed-point theory and the conditions for the existence of a positive solution of the model obtained via the Mittag-Leffler function along with the Laplace transformation - are thoroughly studied. Consequently, our simulation results report that an increase in the imperfect vaccination force increases the population of infected individuals. For the memory effect, the higher "memory" the epidemic system has of past states (which corresponds to decreasing values of fractional-order parameter), the greater the peaks and magnitudes of infection shaping the epidemiological system dynamics.