Analysis of a reaction diffusion model for a reservoir supported spread of infectious disease

W. E. Fitzgibbon; J. J. Morgan

doi:10.3934/dcdsb.2019137

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2019, Volume 24, Issue 11: 6239-6259. Doi: 10.3934/dcdsb.2019137

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Analysis of a reaction diffusion model for a reservoir supported spread of infectious disease

W. E. Fitzgibbon and
J. J. Morgan

Department of Mathematics, University of Houston, Houston, TX 77204, USA

Received: July 2018

Early access: July 2019

Published: August 2019

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Abstract

Motivated by recent outbreaks of the Ebola Virus, we are concerned with the role that a vector reservoir plays in supporting the spatio-temporal spread of a highly lethal disease through a host population. In our context, the reservoir is a species capable of harboring and sustaining the pathogen. We develop models that describe the horizontal spread of the disease among the host population when the host population is in contact with the reservoir and when it is not in contact with the host population. These models are of reaction diffusion type, and they are analyzed, and their long term asymptotic behavior is determined.

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Mathematics Subject Classification: 34, 35K65, 92B99.

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