Threshold Dynamics and Integrated Control of Cholera Transmission with Sanitation and Vaccination

Abstract

Cholera transmission is sustained by interacting human and environmental pathways, making integrated control essential in settings with inadequate water, sanitation, and hygiene infrastructure. We develop and analyze a Susceptible--Infected--Recovered--Water (SIWR) model with Monod-type environmental transmission and three interventions: human sanitation, environmental sanitation, and vaccination. The control reproduction number decomposes as $\mathcal{R}_0=\mathcal{R}_0^{(h)}+\mathcal{R}_0^{(e)}$, separating direct and environmental transmission and yielding closed-form elasticity measures of pathway-specific contributions. We further quantify interactions between sanitation measures through an explicit Bliss independence synergy index. We establish local and global stability of the disease-free equilibrium and prove that the model undergoes a forward transcritical bifurcation at $\mathcal{R}_0=1$, excluding backward bifurcation. Global sensitivity analysis identifies direct transmission, the half-saturation constant, pathogen shedding, and human sanitation as major determinants of epidemic burden. Numerical simulations demonstrate that coordinated sanitation interventions can produce synergistic reductions in epidemic burden, providing a quantitative framework for evaluating integrated cholera control strategies.