Stability analysis of a diarrheal disease model elucidated multiple transmission pathways and infants as the most vulnerable

Abstract

This study forms and analyzes a mathematical model of diarrheal disease.The model allows two pathways of disease transmission through infected people and water resources contaminated by pathogens that cause diarrhea. Babies are the most vulnerable to diarrhea, so that this modeling considers the difference in effective contact rate between susceptible babies and adults. Based on the assumptions, the model has formed a system of ordinary differential equations. A literature study is used to analyze the equilibrium and stability of it. Analysis found a disease-free equilibrium and an endemic equilibrium that are stable depends on a basic reproduction number (R0). The disease-free equilibrium is locally asymptotically stable when R0 < 1. It means diarrhea will disappear so that population is free from diarrhea for a long time. Furthermore, if R0 > 1 and several conditions are fulfilled, then the endemic equilibrium is also locally asymptotically stable. It means that for a long time, diarrhea will be an epidemic in population. Simulation of the model is given by using Matlab to verify the result of analysis.