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Backward bifurcation of an Sir-Si model with vaccination and treatment
EDWIN SETIAWAN NUGRAHA,NUNING NURAINI,JANSON NAIBORHU 장전수학회 2019 Advanced Studies in Contemporary Mathematics Vol.29 No.1
In the presence of treatment, most epidemic models demon- strate behavior of backward bifurcation. This is important in epidemiol- ogy because it provides signicant information for disease control. How- ever, most models consider only one single population. In this paper, an extended model of two populations in the form SIR-SI involving vaccina- tion and treatment is analyzed. The analysis of local and global stability of equilibria is discussed. By using the center manifold theorem, this model has backward bifurcation behavior when the number of infected people exceeds the treatment capacity. Vaccination decreases the basic reproduction number, but does not aect the backward bifurcation be- havior. This study also showed that under vaccination and treatment, an endemic equilibrium always occurs when R0 > 1.