Optimal Control of Cholera Outbreaks: A Cost-Effectiveness Analysis of Vaccination, Sanitation, and Treatment Strategies

Cholera outbreaks follow complex patterns of persistence and sudden decline that make traditional modeling approaches challenging and complicate public health responses. To address this, we developed a new stochastic epidemiological model that combines three key mechanisms: ecological competition between pathogenic and non-pathogenic \textit{Vibrio cholerae} strains, the effects of waning vaccine-induced and natural immunity, and changes in the environment. We calculate the basic reproduction number \(\mathcal{R}_0\) and demonstrate the local stability of the disease-free equilibrium. Our analysis uncovers a stochastic extinction threshold \(\mathcal{R}_0^S\). This shows how environmental factors can end an outbreak, even when \(\mathcal{R}_0 > 1\). A global sensitivity analysis reveals that the symptomatic rate and pathogenic growth rate are the most significant factors for transmission. We create an optimal control framework with three intervention strategies: vaccination, environmental sanitation, and treatment. This helps determine the most cost-effective ways to manage outbreaks. Numerical simulations show that combined interventions are more effective than any single method, reducing peak infections by up to 87\% compared to no intervention. This work addresses important questions about cholera dynamics and provides public health officials with a practical tool for developing effective, context-specific intervention strategies against this ongoing global threat.