In this work, we propose a non-linear system of differential equations that models the dynamics of transmission of dengue fever. Then, we perform a stability analysis of this model. In particular, we prove that when the threshold of the model called the basic reproduction ratio is less than unity, the disease-free equilibrium is globally asymptotically stable. Furthermore, when this value is greater than unity, under suitable conditions, the endemic equilibrium is globally asymptotically stable. Some numerical simulations are provided to illustrate the obtained theoretical results. We also propose a global sensitivity analysis of the basic reproduction ratio.

dengue general incidence function mathematical analysis basic reproduction number Lyapunov function stability analysis sensitivity