The periodic Ross–Macdonald model with diffusion and advection

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.

Keywords:

• Malaria transmission
• reaction–diffusion–advection model
• spreading speeds
• periodic travelling waves
• positive periodic solution
• global attractivity

AMS Subject Classifications::

• 35K57
• 37B55
• 37N25
• 92D30

Acknowledgement

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