A Stochastic Continuous-Time Markov Chain Approach for Modeling the Dynamics of Cholera Transmission: Exploring the Probability of Disease Persistence or Extinction

Leul Mekonnen Anteneh (), Mahouton Norbert Hounkonnou and Romain Glèlè Kakaï
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Leul Mekonnen Anteneh: Laboratoire de Biomathématiques et d’Estimations Forestières, University of Abomey-Calavi, Cotonou 04 BP 1525, Benin
Mahouton Norbert Hounkonnou: International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi, Cotonou 072 BP 50, Benin
Romain Glèlè Kakaï: Laboratoire de Biomathématiques et d’Estimations Forestières, University of Abomey-Calavi, Cotonou 04 BP 1525, Benin

Mathematics, 2025, vol. 13, issue 6, 1-27

Abstract: In this paper, a stochastic continuous-time Markov chain (CTMC) model is developed and analyzed to explore the dynamics of cholera. The multitype branching process is used to compute a stochastic threshold for the CTMC model. Latin hypercube sampling/partial rank correlation coefficient (LHS/PRCC) sensitivity analysis methods are implemented to derive sensitivity indices of model parameters. The results show that the natural death rate μ v of a vector is the most sensitive parameter for controlling disease outbreaks. Numerical simulations indicate that the solutions of the CTMC stochastic model are relatively close to the solutions of the deterministic model. Numerical simulations estimate the probability of both disease extinction and outbreak. The probability of cholera extinction is high when it emerges from bacterial concentrations in non-contaminated/safe water in comparison to when it emerges from all infected groups. Thus, any intervention that focuses on reducing the number of infections at the beginning of a cholera outbreak is essential for reducing its transmission.

Keywords: infectious disease; Latin hypercube sampling; multitype branching process; partial rank correlation coefficients; stochastic model; stochastic threshold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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