Analysis of the dengue disease model with two virus strains

Dengue fever (DF) and dengue haemorrhagic fever (DHF) are the disease caused by the dengue virus which is transmitted to the human by infected female mosquitoes. The disease is endemic in more than 100 countries over the world. Dengue virus has four distinct serotypes which are closely related to each other antigenically. A person who infected by the dengue virus will never be infected again by the same serotype, but he looses immunity from the three other serotypes. Infection with one serotype does not provide cross-protective immunity against to others. Here we assume that there are two serotypes exist in the population. Someone who has recovered from one serotype become susceptible to the other serotype and can be reinfected. In this paper we analyze the model of dengue fever with two infections from the different serotype by linear analysis. Then we study the effect of vaccination to the model. In numerical simulation, we use Runge-Kutta order 4 to integrate the solution of the system.