Mathematical Model of Dengue Infectious Diseases with Vector Control and Vaccination

This paper present a mathematical model of ASEI-SEVIR type for dengue transmission with two attentions were considered, mosquito control and imperfect random mass vaccination. Next step is analysis of fixed point and its stability of the fixed point by considering the basic reproduction number (R₀), to obtain the time evolution of the effective reproduction number (R_(t)) and simulation. The result of the analysis show that there is a single fixed point of model, namely disease-free equilibrium (E₀), which is stable if R₀ < 1. If R₀ < 1., all compartments in model is going to fixed point E₀ with establish parameters in simulation. In simulation, mosquito control and imperfect random mass vaccination can be show from a fraction of susceptible human was vaccinated (ψ), the infection rate of vaccinated members (σ), control to the aquatic phases of the mosquito (c_α) and control to the terrestrial phases of the mosquito (c_m) in generaly giving strong contribution to reduce population human and mosquito infectious including values of R₀ and R_(t), except for parameter σ.