Aggregation and environmental transmission in chronic wasting disease
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1.
Department of Mathematics, Christopher Newport University, 1 Avenue of the Arts, Newport News, VA 23606
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2.
Department of Mathematics, The University of Texas-Pan American, 1201 W. University Drive, Edinburg, TX 78539
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3.
Department of Mathematics, Univeristy of Ottawa, 585 King Edward, Ottawa, ON K1N 6N5
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Received:
01 March 2013
Accepted:
29 June 2018
Published:
01 December 2014
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MSC :
Primary: 92D30.
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Disease transmission depends on the interplay between theinfectious agent and the behavior of the host. Some diseases, suchas Chronic Wasting Disease, can be transmitted directly betweenhosts as well as indirectly via the environment. The socialbehavior of hosts affects both of these pathways, and a successfulintervention requires knowledge of the relative influence of thedifferent etiological and behavioral aspects of the disease. Wedevelop a strategic differential equation model for ChronicWasting Disease and include direct and indirect transmission aswell as host aggregation into our model. We calculate the basicreproduction number and perform a sensitivity analysis based onLatin hypercube sampling from published parameter values. We findconditions for the existence of an endemic equilibrium, and showthat, under a certain mild assumption on parameters, the modeldoes not exhibit a backward bifurcation or bistability. Hence, thebasic reproduction number constitutes the disease eliminationthreshold. We find that the prevalence of the disease decreaseswith host aggregation and increases with the lifespan of theinfectious agent in the environment.
Citation: Olga Vasilyeva, Tamer Oraby, Frithjof Lutscher. Aggregation and environmental transmission in chronic wasting disease[J]. Mathematical Biosciences and Engineering, 2015, 12(1): 209-231. doi: 10.3934/mbe.2015.12.209
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Abstract
Disease transmission depends on the interplay between theinfectious agent and the behavior of the host. Some diseases, suchas Chronic Wasting Disease, can be transmitted directly betweenhosts as well as indirectly via the environment. The socialbehavior of hosts affects both of these pathways, and a successfulintervention requires knowledge of the relative influence of thedifferent etiological and behavioral aspects of the disease. Wedevelop a strategic differential equation model for ChronicWasting Disease and include direct and indirect transmission aswell as host aggregation into our model. We calculate the basicreproduction number and perform a sensitivity analysis based onLatin hypercube sampling from published parameter values. We findconditions for the existence of an endemic equilibrium, and showthat, under a certain mild assumption on parameters, the modeldoes not exhibit a backward bifurcation or bistability. Hence, thebasic reproduction number constitutes the disease eliminationthreshold. We find that the prevalence of the disease decreaseswith host aggregation and increases with the lifespan of theinfectious agent in the environment.
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