Mathematical Modeling of Cholera Mitigation Incorporating Handwashing

Sheila  Cherotich; Branis  Khachiti; Phelesia  Khakali; Risper Kendi

doi:10.51867/Asarev.Maths.1.1.9

Authors

Cherotich Sheila Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya Author
Khachiti Branis Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya Author
Khakali Phelesia Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya Author
Kendi Risper Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya Author

DOI:

https://doi.org/10.51867/Asarev.Maths.1.1.9

Keywords:

Cholera, Handwashing, Endemic Equilibrium

Abstract

Cholera is a bacterial infection caused by Vibrio cholerae. This bacterium produces a toxin that leads to severe diarrhea and dehydration. Cholera is often associated with areas with poor sanitation, limited access to clean water and overcrowded conditions. Cholera remains a significant global health concern, with outbreaks occurring frequently in areas with poor sanitation and hygiene practices. This study aims to investigate the role of handwashing in mitigating cholera. considering the key factors such as mode of transmission, incubation period, signs and symptoms, treatment measures, risk factors and the main causes of cholera. The study tends to assess the effectiveness of handwashing as a preventive measure against cholera transmission. The research addresses the critical gap in understanding the specific contribution of handwashing in preventing cholera, considering its complex transmission dynamics. The expected results of this study are an association between increased handwashing and a decrease in cholera occurrence. Results from this study will inform evidence-based strategies for disease prevention and contribute to the broader field of infectious disease prevention modeling. The study seeks to elucidate the dynamics of cholera transmission, considering the interplay between susceptible, infectious and recovered population. Analysis of the model shows that there exists a region where the model is mathematically and epidemiologically well posed because its solutions were positive and bounded. Computation of the basic reproduction number, was done using the next generation matrix approach. It was determined that when R₀ < 1, cholera does not spread. Stability analysis of the cholera model showed that the disease free equilibrium is both locally and globally asymptotically stable. Ideally, this means that keeping R₀ < 1 is a possible strategy for curbing the spread of the disease. Analysis of the endemic equilibrium shows its existence when R₀ > 1. Furthermore, the endemic equilibrium is also locally asymptotically stable. This shows that when R₀ > 1, the disease persists and spreads in the population. Numerical simulation was done using MATLAB software to show the effectiveness of handwashing on cholera mitigation.

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