Resumen de Global Dynamics and Optimal Control of Multi-Age Structured Vector Disease Model with Vaccination, Relapse and General Incidence

Sheng-Fu Wang, Lin-Fei Nie

• Vaccine effectiveness, disease recovery and recurrence are important issues that must be faced in the prevention and control of vector-borne infectious diseases. We develop, in this paper, a dynamical model of vector disease with multi-age-structure to describe the transmission of parasites (or bacteria) between vectors and hosts, where vaccination, relapse and general incidence are introduced to study how these factors influence the spread and control of disease. First, the accurate formulation of the basic reproduction number is gained, which determines the existence and local asymptotic stability of the disease-free and endemic steady states. Further, by utilizing the fluctuation theorem and the method of Lyapunov function, we verify that the disease-free steady state is globally asymptotically stable if the basic reproduction number is less than one. In addition, we also prove that the endemic steady state of this model without relapse is globally asymptotically stable if the basic reproduction number is greater than one.

  Moreover, the optimal control problem for our model is formulated and analyzed.

  Finally, some numerical simulations are conducted to explain these analytical results.