Determination of the Equilibrium Point According to a Temporal Model of Rehydration in a Population with Cholera in Logistic Growth
K. O. Jackob *
Department of Mathematics, Masinde Muliro University of Science and Technology, P.O Box 190-50100, Kakamega, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Cholera is an infection of the small intestine of humans caused by a gram-negative bacterium called Vibrio cholerae. It is spread through eating food or drinking water contaminated with faeces from an infected person. It causes rapid dehydration and general body imbalance, and can lead to death since untreated individuals suer severely from diarrhea and vomiting. Its dynamics involves multiple interaction between the human host, the pathogen and the environment which contributes to both human to human and indirect environment to human transmission pathways. Rehydration is critical in reducing cholera death. This has been studied by other scholars but they did not consider delay in rehydration on the spread of cholera. In this paper, I formulate a mathematical model based on system of ordinary differential equation with rehydration on the spread of cholera in a logistically growing population. The existence of the steady states and the basic reproduction number is established such that disease free equilibrium point exists. Determination of endemic equilibrium shows that the model has positive points. The findings will be signicant in the sense that timely rehydration should be done during cholera outbreak and will enable individuals with symptoms to seek immediate medical attention.
Keywords: Cholera, Time delay, logistic growth model.