Stability Analysis of a Fractional Epidemic Model Involving Vaccination Effect

This paper, by constructing a fractional epidemic model, analyzes the transmission dynamics of some infectious diseases under the effect of vaccination, which is one of the most effective and common control measures. In the model, with reference that antibody formation by vaccination may not cause permanent immunity, it has been taken into account that the protection period provided by the vaccine may be finite in addition the fact that this period may change according to individuals. The model differs from other SVIR models given in the literature in terms of its progressive process with a distributed delay in losing of the protective effect provided by the vaccine. To explain this process, the model has been constructed by using a system of distributed delay nonlinear fractional integro-differential equations. Thus, the model aims to present a realistic approach to following the course of the disease.