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 inequityan 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. 1 Overview Cholera is a well-established waterborne disease that spreads through populations of people who are already overly burdened. Controlling cholera will require investment of monetary and human resources, issues beyond the scope of this paper. Here, we seek to understand and illustrate more about the disease through a mathematical model. We begin with an overview of the disease and of the outbreak in Haiti. We review the basic

A stochastic population model of cholera disease

“…Duration 1 week implies α = 1. From [22] we obtain ω = 1.06 − 0.73 = 0.33 per day. The parameter ω can be taken as ω = 0.33 per day, following [7] (see also [12], [15]).…”

“…Mathematical modelling of epidemiological diseases is commonly used for making future projections of the prevalence of a disease in a population and to assess the effect of public health interventions. Many studies of this type have been carried out on the epidemiology of cholera disease, for example, [23,22], and most of these studies are focussed on the deterministic modelling of cholera dynamics. In this paper, we will incorporate stochasticity into the cholera model presented in [23], in order to factor in the possible effects of randomness.…”

Investigating the Impact of Segregation and Integration on Infection Dynamics: Analysis of a Cholera Model in a Two-Population System

“…While some models account for person-to-person transmission of the infection [38], this aspect remains a secondary factor in disease dynamics compared to water and environmental contamination. The majority of models in the literature concentrate on a singular population interacting with a sole reservoir, with certain studies examining clusters of populations interacting with a shared reservoir [39, 40, 41].…”