Modeling And Analysis Of An SVIRS Epidemic Model Involving External Sources Of Disease
Raid Kamel Naji, Ahmed Ali Muhseen
Keywords: Epidemic models, Stability, Vaccinated, Immigrants, external sources, Local and Hopf bifurcation.
Abstract: In this paper a mathematical model that describes the flow of infectious disease in a population is proposed and studied. It is assumed that the disease divided the population into four classes: susceptible individuals (S), vaccinated individuals (V), infected individuals (I) and recover individuals (R). The impact of immigrants, vaccine and external sources of disease, on the dynamics of SVIRS epidemic model is investigated. The existence, uniqueness and boundedness of the solution of the model are discussed. The local and global stability of the model is studied. The occurrence of local bifurcation as well as Hopf bifurcation in the model is investigated. Finally the global dynamics of the proposed model is studied numerically.
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