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Original Articles

The periodic Ross–Macdonald model with diffusion and advection

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Pages 1067-1089 | Received 24 Aug 2009, Accepted 14 Oct 2009, Published online: 15 Jun 2010
 

Abstract

In this article, we propose a periodic Ross–Macdonald type model with diffusion and advection to study the possible impact of the mobility of humans and mosquitoes on malaria transmission. We establish the existence of the leftward and rightward spreading speeds and their coincidence with the minimum wave speeds in the left and right directions, respectively. For the model in a bounded domain, we obtain a threshold result on the global attractivity of either zero or the positive periodic solution.

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Acknowledgement

This research was supported in part by the NSERC of Canada and the MITACS of Canada.

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