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Stabilization of a reaction-diffusion system modelling malaria transmission

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


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