Stabilization of a reaction-diffusion system modelling malaria transmission

Sebastian Aniţa; Vincenzo Capasso

doi:10.3934/dcdsb.2012.17.1673

Article Contents

2012, Volume 17, Issue 6: 1673-1684. Doi: 10.3934/dcdsb.2012.17.1673

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Stabilization of a reaction-diffusion system modelling malaria transmission

Sebastian Aniţa^1, and
Vincenzo Capasso^2,

1.
Faculty of Mathematics, "Al.I. Cuza" University of Iaşi, Bd. Carol I nr. 11 and "Octav Mayer" Institute of Mathematics, Bd. Carol I nr. 8, Iaşi 700506
2.
Dipartimento di Matematica, Universita di Milano, Via Saldini 50, 20133 Milano

Received: December 2011

Revised: January 2012

Published: September 2012

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Abstract

A two-component reaction-diffusion system modelling a class of spatially structured epidemic systems is considered. More specifically, the system describes the spread of malaria mediated by a population of infected mosquitoes. A relevant problem, related to the possible eradication of the epidemic, is the so called zero-stabilization. We prove that it is possible to diminish exponentially the epidemic process, in the whole habitat, just by acting on the segregation rate between the population of infected mosquitoes and the susceptible human population in a nonempty and sufficiently large subset of the spatial domain.

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Mathematics Subject Classification: Primary: 35K57, 93D15; Secondary: 92D30, 93C20.

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