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Stochastic Cholera Model with Jump Perturbation
Research Article - Volume: 1, Issue: 1, 2026 (October)
Stochastic Cholera Model with Jump Perturbation Download PDF

Isah Tasi'u Basiru 1*, Umar Muhammad Dauda 1, Najib Bello Halilu 1, Abubakar Suleman Muhammad 1, Kabiru Isah 1, Muhammad Sabiu 1, Pramod Mehta 1, Karuna Laddha 1, Komal Prajapat 1, Habibu Muhammad Haris 1, Aminu Salisu Taambu 1, Adamu Garba Musa 1, Maryam Isah 1, Firdausi Umar Muhammad 1

1Department of Mathematics, Faculty of Science and Technology, Mewar University, Gangrar, Chittorgarh, Rajasthan India

*Correspondence to: Isah Tasi'u Basiru, Department of Mathematics, Faculty of Science and Technology, Mewar University, Gangrar, Chittorgarh, Rajasthan India, E-mail:

Received: August 15, 2026; Manuscript No: JMPM-26-5504; Editor Assigned: August 29, 2026; PreQc No: JMPM-26-5504 (PQ); Reviewed: August 26, 2026; Revised: September 23, 2026; Manuscript No: JMPM-26-5504 (R); Published: October 06, 2026

ABSTRACT

We revisit a deterministic χI - F model of Codeco that is linked to endemics and epidemics in order to achieve this. A stochastic differential equation SDE for the number of infectious people I(t) that are impacted by the aquatic environment is then produced by extending this model to a stochastic jump diffusion model. The existence and uniqueness of the solution to the SDE was shown. The basic reproduction number R0 and some qualitative properties (positivity and invariant region) were found for the deterministic model. Also, the stability and the biological meaning of the end points of the endemic and disease-free equilibria were investigated.The stochastic jump diffusion model was numerically simulated by the method of Euler Maruyama to obtain sample paths of I(t). The results showed that the stochastic jump diffusion trajectories fluctuate around the deterministic trajectory of the χI - F model and are continuously differentiable, but not continuously differentiable. Moreover, it is theoretically relevant and easy to understand that the proposed stochastic jump diffusion model is applicable.

Keywords: Cholera; Stochastic; Jump Diffusion; Stability Analysis; Reproduction Number R0; Endemic Equilibrium

Citation: Basiru IT, Dauda UM, Halilu NB, Abubakar SM, Isah K, Sabiu M, et al. (2026). Stochastic Cholera Model with Jump Perturbation. J. Math. Phys. Mech. Vol.1 Iss.1, October (2026), pp:143-175.
Copyright: © 2026 Isah Tasiu Basiru, Umar Muhammad Dauda, Najib Bello Halilu, Abubakar Suleman Muhammad, Kabiru Isah, Muhammad Sabiu, Pramod Mehta, Karuna Laddha, Komal Prajapat, Habibu Muhammad Haris, Aminu Salisu Taambu, Adamu Garba Musa, Maryam Isah, Firdausi Umar Muhammad. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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