Mathematical Modeling and Stability Analysis of Cholera Transmission Dynamics with Environmental Sanitation and Treatment Interventions

Abstract

Cholera remains a persistent public health challenge despite significant advancements in medicine and hygiene. Understanding its transmission dynamics is essential for effective control and eradication. This study develops a compartmental mathematical model to analyze the spread of Vibrio cholerae, incorporating key control measures such as treatment, natural recovery, reinfection, and environmental sanitation. The model is formulated as a system of nonlinear differential equations, representing different population compartments. A key component of the analysis is the derivation of the basic reproduction number (R₀) ,which serves as a threshold indicator for disease persistence. Stability analysis reveals that: If (R₀ <1) , the disease-free equilibrium is globally asymptotically stable, indicating eventual cholera eradication. If (R₀ >1) an endemic equilibrium exists, signifying sustained cholera transmission within the population. Sensitivity analysis identifies the most influential parameters affecting (R₀) , highlighting that increasing treatment rates and improving sanitation significantly reduce disease spread. The fourth order Runge–Kutta numerical scheme is implemented in MAPLE 21 to generate the numerical solutions, which demonstrate that, timely treatment, and environmental sanitation accelerates the reduction of R0, moving the system toward the disease-free state.