Modeling the health impact of water and sanitation service deficits on waterborne disease transmission

Abstract

Abstract Cholera is a waterborne disease that continues to pose serious public health problems in many developing countries. Increasing water and sanitation coverage is a goal for local authorities in these countries, as it can eliminate one of the root causes of cholera transmission. The SIWDR (susceptible–infected–water–dumpsite–recovered) model is proposed here to evaluate the effects of the improved coverage of water and sanitation services in a community at risk of a cholera outbreak. This paper provides a mathematical study of the dynamics of the water and sanitation (WatSan) deficits and their public health impact in a community. The theoretical analysis of the SIWDR model gave a certain threshold value (known as the basic reproductive number and denoted R 0 $\mathcal{R}_{0}$ ) to stop the transmission of cholera. It was found that the disease-free equilibrium was globally asymptotically stable whenever R 0 ≤ 1 $\mathcal{R}_{0} \leq 1$ . The unique endemic equilibrium was globally asymptotically stable whenever R 0 > 1 $\mathcal{R}_{0} >1$ . Sensitivity analysis was performed to determine the relative importance of model parameters to disease transmission and prevention. The numerical simulation results, using realistic parameter values in describing cholera transmission in Haiti, showed that improving the drinking water supply, wastewater and sewage treatment, and solid waste disposal services would be effective strategies for controlling the transmission pathways of this waterborne disease.

Keywords

• Water and sanitation
• Waterborne disease
• Global stability
• Lyapunov function
• Cholera