Control óptimo de un modelo de Malaria con retraso en la variable de control

Abstract

In this work, we propose an optimal control model governed by ordinary differential equations, for the transmission of Malaria in which we use a delay in the control variable. The control scheme that we use is the intervention over the larval population, with the aim of minimize the number of infected human. Also, we have considered the time from which a healthy human host is infected with the parasite until the person shows the first symptoms of the disease and become infectious. This incubation time was incorporated in the model through a delay, included in the system of differential equations that governing the optimal control problem. We prove the existence of an optimal control and for characterize it we use the Pontryagin minimum principle for delayed optimal control problems. A method of Runge Kutta of third order was implemented to solve the state system. Also, an explicit Euler method was used for the adjoint system and finally we implemented a projected gradient method to solve the problem of optimization