OPTIMAL CONTROL FOR A VECTOR-BORNE INFECTION WITH IMMIGRATION OF INFECTIVE: MALARIA IN NIGERIA AS A CASE STUDY

Due to comparatively low level of border control in Africa, immigration of infectious individualis an important factor for triggering and persistence of epidemics. In this paper we consider a 7-dimensional non-linear differential equations model of a malaria disease that includes constantimmigration of infective individual into a population. For this model, we consider the optimalcontrols aimed at the reduction of both the level of infection; (the number of infected humans) aswell as the level of danger (the abundance of infected vectors). Specifically, we consider threecontrols in this model, namely (i) screening of the immigrants (ii) the use of prophylactic drugs onthe susceptible humans and (iii) the use gametocytes destroying drugs on the infected humans. ThePontryagin’s Maximum Principle allows us to reduce the problem to a boundary value problem;the optimal control problem then can be solved numerically using an iterative method. Finally,numerical simulations of the optimal control problem are carried out to investigate theeffectiveness of the proposed control measures.