Impact of Humoral Immune Response and Absorption Effect on Dynamics of Dengue Virus

Abstract

Dengue infection represents a global threat causing 50-100 million infections per year and placing half of the world’s population at risk. Even though how infection is controlled and cured rather remains a mystery, antibodies are thought to play a major role in clearing the virus. In this paper, we study the dynamics of dengue virus with humoral immune response and absorption effect. The proposed model incorporates a time delay in production of antibodies. The basic reproduction number R0 is computed and a detailed stability analysis is done. It was found that the model has 3 steady states, namely, infection free equilibrium, no immune equilibrium and the endemic equilibrium. Conditions for R0 were developed for the local stability of these 3 equilibrium states. The global stability was studied using appropriate Lyapunov function and LaSalle’s invariance principle. We then established a condition for which the endemic equilibrium point is globally asymptotically stable. Also it was observed that the virus count goes to negligible levels within 7-14 days after the onset of symptoms.