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Model for disease dynamics of a waterborne pathogen on a random network. (English) Zbl 1350.92052

Summary: A network epidemic SIWR model for cholera and other diseases that can be transmitted via the environment is developed and analyzed. The person-to-person contacts are modeled by a random contact network, and the contagious environment is modeled by an external node that connects to every individual. The model is adapted from the Miller network SIR model [J. C. Miller, ibid. 62, No. 3, 349–358 (2011; Zbl 1232.92067)], and in the homogeneous mixing limit becomes the Tien and Earn deterministic cholera model [J. H. Tien and D. J. D. Earn, Bull. Math. Biol. 72, No. 6, 1506–1533 (2010; Zbl 1198.92030)] without births and deaths. The dynamics of our model shows excellent agreement with stochastic simulations. The basic reproduction number \(\mathcal{R}_0\) is computed, and on a Poisson network shown to be the sum of the basic reproduction numbers of the person-to-person and person-to-water-to-person transmission pathways. However, on other networks, \(\mathcal{R}_0\) depends nonlinearly on the transmission along the two pathways. Type reproduction numbers are computed and quantify measures to control the disease. Equations giving the final epidemic size are obtained.

MSC:

92D30 Epidemiology
91D30 Social networks; opinion dynamics
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