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.

Regional Control for Spatially Structured Mosquito Borne Epidemics: Part II: Computational Issues / S. Anita, V. Capasso, S. Scacchi. - In: VIETNAM JOURNAL OF MATHEMATICS. - ISSN 2305-221X. - 49:1(2021 Mar), pp. 189-206. [10.1007/s10013-021-00475-x]

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

V. Capasso
Penultimo
;
S. Scacchi
Ultimo
2021

Abstract

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.
Epidemic system; Malaria; Numerical simulations; Optimal control; Reaction-diffusion system; Regional control; Vector borne diseases
Settore MAT/08 - Analisi Numerica
Settore MAT/05 - Analisi Matematica
8-mar-2021
Article (author)
File in questo prodotto:
File Dimensione Formato  
Aniţa2021_Article_RegionalControlForSpatiallyStr.pdf

accesso aperto

Tipologia: Publisher's version/PDF
Dimensione 4.16 MB
Formato Adobe PDF
4.16 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/869785
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact