A Rabies Model with Distributed Incubation Period and Territorial and Diffusing Rabid Foxes

Friday, March 23, 2018 - 12:15pm
Location: 
WXLR A309

Speaker

Khalaf Alanazi
SoMSS Graduate Student
Arizona State University

Abstract

We are studying the spread of rabies in a spatially distributed fox population analytically and numerically.   Mathematical models have so far assumed that either all rabid foxes are territorial or all rabid foxes diffuse. In our mathematical models, we have two kinds of rabid foxes: territorial rabid foxes and diffusing rabid foxes. So, the model consists of partial differential equations and integral equations. Analytically, we reduce our model to a single scalar Hammerstein Volterra integral equation, then we use the Laplace transform to find the asymptotic speed of spread on unbounded domain.   We show a number of analytic results pertaining the asymptotic speed of spread.   In order to visualize the spread of fox rabies, we use suitable numerical methods on bounded domain and fixed length of the latent period to solve the resulting system of delay differential equations.   The asymptotic speeds of spread from the analytic and numerical parts are discussed and compared with those found in nature and, for special cases, in the literature.

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