Aggregation and environmental transmission in chronic wasting disease

Olga Vasilyeva; Tamer Oraby; Frithjof Lutscher

doi:10.3934/mbe.2015.12.209

Article Contents

2015, Volume 12, Issue 1: 209-231. Doi: 10.3934/mbe.2015.12.209

This issue Previous Article Virus dynamics model with intracellular delays and immune response Next Article

Aggregation and environmental transmission in chronic wasting disease

1.
Department of Mathematics, Christopher Newport University, 1 Avenue of the Arts, Newport News, VA 23606
2.
Department of Mathematics, The University of Texas-Pan American, 1201 W. University Drive, Edinburg, TX 78539
3.
Department of Mathematics, Univeristy of Ottawa, 585 King Edward, Ottawa, ON K1N 6N5

Received: February 28, 2013

Revised: September 30, 2014

Published: November 2014

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Abstract

Disease transmission depends on the interplay between the infectious agent and the behavior of the host. Some diseases, such as Chronic Wasting Disease, can be transmitted directly between hosts as well as indirectly via the environment. The social behavior of hosts affects both of these pathways, and a successful intervention requires knowledge of the relative influence of the different etiological and behavioral aspects of the disease. We develop a strategic differential equation model for Chronic Wasting Disease and include direct and indirect transmission as well as host aggregation into our model. We calculate the basic reproduction number and perform a sensitivity analysis based on Latin hypercube sampling from published parameter values. We find conditions for the existence of an endemic equilibrium, and show that, under a certain mild assumption on parameters, the model does not exhibit a backward bifurcation or bistability. Hence, the basic reproduction number constitutes the disease elimination threshold. We find that the prevalence of the disease decreases with host aggregation and increases with the lifespan of the infectious agent in the environment.

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Mathematics Subject Classification: Primary: 92D30.

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