The mathematical modeling and analysis of the cholera disease model

Abstract

We are developing a deterministic model for cholera that incorporates immunization campaigns, treatment of infected individuals, and efforts to sanitize water supplies. This model offers precise and valuable insights into specific aspects of cholera control. The basic reproduction number, R₀, derived from the disease-free equilibrium (DFE), serves as a critical metric for assessing disease control efforts. Our stability analysis reveals that the DFE is asymptotically stable both locally and globally when R₀ is less than one. Sensitivity analysis of R₀ underscores the importance of vaccination, treatment, public awareness campaigns, and sanitation in controlling cholera. We explore the local and global stability of both the disease-free and disease-endemic equilibrium by constructing Lyapunov functions and applying the Routh-Hurwitz criteria. Additionally, we perform sensitivity analyses to identify the parameters that significantly impact R₀. Finally, numerical simulations using Matlab are conducted to validate our theoretical findings.