Mathematical models and optimal control in mosquito transmitted diseases

Abstract

Malaria is a life threatening disease, entirely preventable and treatable, provided the currently recommended interventions are properly implemented. These interventions include vector control through the use of insecticide-treated nets (ITNs). However, ITN possession does not necessarily translate into use. Human behavior change interventions, including information, education, communication (IEC) campaigns and post-distribution hang-up campaigns are strongly recommended. Here we consider a mathematical model for the effects of ITNs on the transmission dynamics of malaria infection, which takes into account the human behavior. We introduce in this model a supervision control, representing IEC campaigns for improving the ITN usage. Then we propose and solve an optimal control problem where the aim is to minimize the number of infectious humans while keeping the cost low. Numerical results are provided, which show the effectiveness of the optimal control interventions.