Mathematical model for 4 serotypes of dengue virus with vaccination

In this study, we formulate the SIR model to consider the transmission cycle between two population groups; Human and mosquito populations. We are interested in the cases of unvaccinated and vaccinated where human populations are infected from DEN1, DEN2, DEN3 and DEN4. For mosquito population, we divided it into susceptible and infected populations. The model is analyzed by using dynamical modeling method. The basic reproductive number is obtained from next generation matrix. If the basic reproductive number is less than one, the solutions of our model converge to the disease free steady state. The solutions of our model oscillate to the endemic steady state for the basic reproductive number is greater than one. The numerical solutions are found to support our analytical results.