Mathematical analysis of within-host dengue dynamics with innate and adaptive immune responsess

Dengue is among the most prevalent arboviral disease in humans worldwide. Infection with dengue can cause a wide spectrum of disease indications, from clinically inapparent infection to life threatening severe disease. Despite the increasing burden of dengue, development of an effective vaccine has rather remained elusive. One reason is the complex immunopathogenesis involved during an infection. To understand the viral dynamics and immune responses during dengue, we develop a mathematical model which describes the dynamics of healthy cells, infected cells and pathogens in the presence of innate and adaptive immune responses. A detailed analysis of the model was done and the most important model parameters were identified. The analytical findings were demonstrated by numerical simulations. It was observed that the model has five equilibria, namely, the disease free equilibrium, immunity induced viral clearance, no immune equilibrium, virus persistence in the absence of adaptive immune response and no antibody equilibrium. A detailed stability analysis of each equilibrium was implemented. It was observed that no antibody immune equilibrium is unstable for some parameter values. Thus it can be inferred from the detailed analysis, that the introduction of immune response strongly affects the stability of the system and antibodies plays a very important role in shaping dengue dynamics.