Mathematical modeling on T-cell mediated adaptive immunity in primary dengue infections.

At present, dengue is the most common mosquito-borne viral disease in the world, and the global dengue incidence is increasing day by day due to climate changing. Here, we present a mathematical model of dengue viruses (DENVs) dynamics in micro-environment (cellular level) consisting of healthy cells, infected cells, virus particles and T-cell mediated adaptive immunity. We have considered the explicit role of cytokines and antibody in our model. We find that the virus load goes down to zero within 6 days as it is common for DENV infection. From our analysis, we have identified the important model parameters and done the numerical simulation with respect to such important parameters. We have shown that the cytokine mediated virus clearance plays a very important role in dengue dynamics. It can change the dynamical behavior of the system and causes essential extinction of the virus. Finally, we have incorporated the antiviral treatment for dengue in our model and shown that the basic reproduction number is directly proportional to the antiviral treatment effects.