A stochastic population model of cholera disease
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Date
2022-02
Journal Title
Journal ISSN
Volume Title
Publisher
American Institute of Mathematical Sciences
Abstract
A cholera population model with stochastic transmission and stochasticity on the environmental reservoir of the cholera bacteria is presented. It is shown that solutions are well-behaved. In comparison with the underlying deterministic model, the stochastic perturbation is shown to enhance stability of the disease-free equilibrium. The main extinction theorem is formulated in terms of an invariant which is a modification of the basic reproduction number of the underlying deterministic model. As an application, the model is calibrated as for a certain province of Nigeria. In particular, a recent outbreak (2019) in Nigeria is analysed and featured through simulations. Simulations include making forward projections in the form of confidence intervals. Also, the extinction theorem is illustrated through simulations.
Description
Keywords
Cholera, Nigeria, Exponential stability, Extinction
Citation
Witbooi, P.J., Muller, G.E., Ongansie, M.B., Ahmed, I.H.I. & Okosun, K.O. 2022, "A stochastic population model of cholera disease", Discrete and Continuous Dynamical Systems - Series S, vol. 15, no. 2, pp. 441-456.