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This paper presents a mathematical model for dengue disease to understand its dynamics by using a set of differential equations to describe the effects between human and mosquito populations. In this model, the human population is divided into fi ve types of individuals: susceptible vaccination fi rst infectious second infectious and recovered and the mosquitoes population is divided into three types of individuals: larva mosquitoes uninfected female mosquitoes and infected female mosquitoes The epidemic and endemic analysis have also presented along with numerical simulations to verify our model. Our results suggested that the prevention and control of dengue outbreaks can be implemented in an optimal way.
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