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Open AccessArticle

Comparing Direct and Indirect Transmission in a Simple Model of Veterinary Disease

1
Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60201, USA
2
IBM Almaden Research Center, San Jose, CA 95120, USA
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1039; https://doi.org/10.3390/math7111039
Received: 24 September 2019 / Revised: 27 October 2019 / Accepted: 31 October 2019 / Published: 3 November 2019
(This article belongs to the Special Issue Mathematical Models in Epidemiology)
Foodborne diseases are a longstanding worldwide public health concern. Modeling the transmission pathways of foodborne pathogens accurately and effectively can aid in understanding the spread of pathogens and facilitate decision making for intervention. A new compartmental model is reported that integrates the effects of both direct and indirect transmission. Depending on the choice of epidemiological parameters, the model can be tuned to be purely direct, purely indirect, or used to explore the dynamics in an intermediate regime. Steady state analysis of the model and limiting cases are studied. A numerical simulation is employed to study the impact of different epidemiological parameters and dose response. Direct transmission can surpass the effect of indirect transmission for the same range of parameter values and result in an earlier epidemic. The rate at which the pathogens are removed from the environment can lead to a faster epidemic. The environmental contamination can decrease the time to reach the steady state depending on the dose response. These results can inform policy makers for control strategies to reduce foodborne pathogen transmission. View Full-Text
Keywords: ordinary differential equations; basic reproduction number; foodborne diseases; direct transmission; indirect transmission ordinary differential equations; basic reproduction number; foodborne diseases; direct transmission; indirect transmission
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Yagci Sokat, K.; Edlund, S.; Clarkson, K.; Kaufman, J. Comparing Direct and Indirect Transmission in a Simple Model of Veterinary Disease. Mathematics 2019, 7, 1039.

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