Regional control for spatially structured mosquito borne epidemics. II: Computational issues. (English) Zbl 1464.35351
Summary: This paper is a continuation of a previous paper by the first two authors [Vietnam J. Math. 49, No. 1, 21–35 (2021; Zbl 1464.35350)] 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.
For Part I, see [S. Aniţa and V. Capasso, Vietnam J. Math. 49, No. 1, 21–35 (2021; Zbl 1464.35350)].
For Part I, see [S. Aniţa and V. Capasso, Vietnam J. Math. 49, No. 1, 21–35 (2021; Zbl 1464.35350)].
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 92D30 | Epidemiology |
| 92C60 | Medical epidemiology |
| 35K57 | Reaction-diffusion equations |
| 35Q93 | PDEs in connection with control and optimization |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 93C95 | Application models in control theory |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65L12 | Finite difference and finite volume methods for ordinary differential equations |
Keywords:
reaction-diffusion system; regional control; optimal control; numerical simulations; epidemic system; vector borne diseases; malariaCitations:
Zbl 1464.35350References:
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