The analysis of the mathematical stability of a Cholera disease model

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 01 بهمن 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.88685.1464

نویسندگان

issam sahib^{* 1}؛ Mohamed Baroudi¹؛ Hicham Gourram¹؛ Bouchaib Khajji²؛ Abderrahim Labzai²؛ Mohamed BELAM¹

¹Laboratory LMACS, Sultan Moulay Slimane University, MATIC Research Team: Applied Mathematics and Information and Communication Technologie, Department of Mathematics and Computer Science, Khouribga Polydisciplinary Faculty, Morocco.

²Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, Morocco.

چکیده

In this study, we developed a deterministic model for cholera transmission dynamics, incorporating vaccination campaigns, treatment of infected individuals, and water sanitation initiatives. A novel feature of our model is the inclusion of healthcare centers, which enhances the simulation of treatment dynamics, offering new insights into cholera management. The model’s central metric is the basic reproduction number $R_0$, derived from the disease-free equilibrium $(DFE)$ condition. Stability analysis shows that when $R_0 \leq 1$, the DFE is asymptotically stable, ensuring cholera eradication, while $R_0 > 1$ leads to an endemic equilibrium. Sensitivity analysis highlights that vaccination, treatment, sanitation, and public awareness campaigns are critical for reducing $R_0$. The inclusion of healthcare centers further improves the model’s effectiveness by ensuring timely treatment. Numerical simulations, validated using $MATLAB$, confirm that comprehensive public health strategies, including expanded vaccination campaigns and healthcare infrastructure, are essential for combating cholera outbreaks. This model underscores the importance of timely medical intervention in reducing infection rates and fatalities.

کلیدواژه‌ها

stability؛ sensitivity؛ optimal control؛ Disease cholera