# American Institute of Mathematical Sciences

September  2012, 17(6): 1673-1684. doi: 10.3934/dcdsb.2012.17.1673

## Stabilization of a reaction-diffusion system modelling malaria transmission

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

Received  December 2011 Revised  January 2012 Published  May 2012

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.
Citation: Sebastian Aniţa, Vincenzo Capasso. Stabilization of a reaction-diffusion system modelling malaria transmission. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1673-1684. doi: 10.3934/dcdsb.2012.17.1673
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