Regional Control for Spatially Structured Mosquito Borne Epidemics: Part II: Computational Issues

This paper is a continuation of a previous paper by the first two authors to appear in the same IWR Special Issue for Scientific Computing. We are concerned with an optimal regional control problem for spatially structured vector borne epidemic system, considering malaria as a case study. A conceptual reduced mathematical model of malaria had been presented consisting of a two-component reaction-diffusion system. Three actions (controls) had been included: killing mosquitoes, treating the infected humans and reducing the contact rate mosquitoes-humans. The problem which is faced concerns the optimal choice of the region of intervention, by introducing a cost functional which takes into account the total cost of the damages produced by the disease, of the controls and of the intervention in a certain subdomain, for a finite time horizon case. A gradient algorithm had been proposed for the search of a minimal value of the cost functional, with respect to both the control parameters and the region of intervention. The scope of the present paper concerns the numerical implementation of such an algorithm. The level set method has played a major role for the mathematical description of the subregion of intervention. The outcomes of a series of numerical simulations are reported, under a variety of parameter scenarios.