Stability Analysis with Bifurcation of an SVIR Epidemic Model Involving Immigrants

There are many factors effect on the spread of infectious disease or control it, some of these factors are (immigration and vaccination). The main objective of this paper is to study the effect of those factors on the dynamical behavior of an SVIR model. It is assumed that the disease is spread by contact between members of populations individuals. While the recovered individuals gain permanent immunity against the disease. The existence, uniqueness and boundedness of the solution of this model are investigated. The local and global dynamical behaviors of the model are studied. The local bifurcations and Hopf bifurcation of the model are investigated. Finally, in order to confirm our obtained results and specify the effects of model’s parameters on the dynamical behavior, numerical simulation of the SVIR model is performed.