A Model of the Transmission of Cholera in a Population with Contaminated Water

Abstract

Cholera is an infectious disease that is a major concern in countries with inadequate access to clean water and proper sanitation. According to the World Health Organization (WHO), “cholera is a disease of inequity— an ancient illness that today sickens and kills only the poorest and most vulnerable people. . .The map of cholera is essentially the same as a map of poverty.” [27] We implement a published model [9] of a SIR model that includes a bacterial reservoir. Bacterial concentration in the water, λ, or the “force of infection,” is modeled by the Monod Equation in microbiology. We investigate the sensitivity of the models to some parameters. We use parameter values for cholera in Haiti that are consistent with the ranges in meta-analysis [9] and other sources. We show the results of our numerical approximation of solutions. Our goal is to use this system of nonlinear ordinary differential equations to raise awareness among the mathematics community of the dynamics of cholera. We discuss the enhancement of undergraduate experiences by motivating learning with a real-world context in social justice implications of global health.