Mathematical modeling of the effect of rainfall variation on cholera transmission dynamics

Simon Wekesa Simiyu; Frankline Tireito; Colleta Akinyi

doi:10.51867/asarev.maths.3.1.20

Auteurs-es

Simon Wekesa Simiyu Masinde Muliro University of Science and Technology, Kenya Auteur-e
Frankline Tireito Masinde Muliro University of Science & Technology, Kenya Auteur-e https://orcid.org/0000-0002-4106-4022
Colleta Akinyi Masinde Muliro University of Science and Technology, Kenya Auteur-e

DOI :

https://doi.org/10.51867/asarev.maths.3.1.20

Mots-clés :

Cholera, mathematical modelling, rainfall variation, transmission dynamics, SIR-B model, basic reproduction number.

Résumé

Cholera remains a major public health challenge, particularly in regions with inadequate access to safe water and sanitation. Rainfall variation has been associated with recurrent cholera outbreaks, with both heavy rainfall and drought increasing disease transmission through distinct environmental mechanisms. This study developed and analyzed a nonlinear rainfall-dependent SIR-B mathematical model to assess the effect of rainfall variation on cholera transmission dynamics. A rainfall parameter was incorporated to capture the increased transmission associated with flooding and drought. The model was shown to be well-posed through positivity and boundedness analyses, while the disease-free and endemic equilibrium points and their local stability were established. Under the rainfall conditions considered, the basic reproduction number satisfied $R_0>1$, implying an unstable disease-free equilibrium and a locally asymptotically stable endemic equilibrium. Numerical simulations performed demonstrated that heavy rainfall produced the highest infection levels and environmental pathogen concentration, moderate rainfall resulted in the lowest transmission potential, while drought exhibited an intermediate disease burden. The findings further revealed that environmental transmission contributed more substantially to the overall transmission potential than direct human-to-human transmission, confirming that rainfall variation primarily influences cholera dynamics through the environmental pathway. Generally, the proposed rainfall-dependent SIR-B model provides valuable insights into the role of rainfall variation in cholera transmission and may support the design of effective water, sanitation, hygiene, and environmental management strategies, particularly during periods of heavy rainfall and drought.

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