Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis

Abstract

The effect of vaccination on the dengue fever epidemic described by an age structured modified SIR (Susceptible-Infected-Retired) model is studied using standard stability analysis. The chimeric yellow fever dengue tetravalent dengue vaccine (CYD-TDV™) is a vaccine recently developed to control this epidemic in several Southeast Asian countries. The dengue vaccination program requires a total of three injections, 6 months apart at 0, 6, and 12 months. The ages of the recipients are nine years and above. In this paper, we analyze the mathematical dynamics SIR transmission model of the epidemic. The stability of the model is established using Routh–Hurwitz criteria to see if a Hopf Bifurcation occurs and see when the equilibrium states are local asymptotically stable or global asymptotically stable. We have determined the efficiency of CYD-TDV by simulating the optimal numerical solution for each age range for this model. The numerical results showed the optimal age for vaccination and significantly reduced the severity and severity of the disease.

Keywords

• dengue fever
• local stability
• global stability
• vaccination