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Multiple transmission pathways and disease dynamics in a waterborne pathogen model. (English) Zbl 1198.92030

Summary: Multiple transmission pathways exist for many waterborne diseases, including cholera, Giardia, Cryptosporidium, and Campylobacter. Theoretical work exploring the effects of multiple transmission pathways on disease dynamics is incomplete. We consider a simple ODE model that extends the classical SIR framework by adding a compartment \((W)\) that tracks pathogen concentration in the water. Infected individuals shed pathogen into the water compartment, and new infections arise both through exposure to contaminated water, as well as by the classical SIR person-person transmission pathway. We compute the basic reproductive number \((\mathcal R_{0})\), epidemic growth rate, and final outbreak size for the resulting “SIWR” model, and examine how these fundamental quantities depend upon the transmission parameters for the different pathways. We prove that the endemic disease equilibrium for the SIWR model is globally stable. We identify the pathogen decay rate in the water compartment as a key parameter determining when the distinction between the different transmission routes in the SIWR model is important. When the decay rate is slow, using an SIR model rather than the SIWR model can lead to under-estimates of the basic reproductive number and over-estimates of the infectious period.

MSC:

92C50 Medical applications (general)
92C60 Medical epidemiology
37N25 Dynamical systems in biology
34D23 Global stability of solutions to ordinary differential equations
Full Text: DOI

References:

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