A Mathematical Model for the Transmission Dynamics of Cholera with Control Strategy

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Author(s) Ochoche, Jeffrey M.
Pages 797-803
Volume 2
Issue 11
Date November, 2013, 2013
Keywords Cholera, Control strategy, Epidemic, Endemic, Mathematical model, Numerical simulation.
Abstract

Cholera is generally a disease of the poor, affecting regions that lack a heightened sense of hygiene and access to safe drinking water. In this research a mathematical model for the control of cholera transmission dynamics using water treatment as a control strategy is proposed. The model is designed by dividing the system into compartments leading to corresponding differential equations. The model is built on the assumption that cholera is contracted only through the ingestion of contaminated water. Conditions are derived for the existence of the disease free and endemic equilibria. We proved that the disease free equilibrium is locally asymptotically stable under prescribed conditions on the given parameters. This means that cholera can be eradicated under such conditions in finite time. Numerical simulations are carried out using parameter values from published data to investigate the effect of transmission parameters on the dynamics of the infection. We simulated cases with no control, weak and strong control. Our results showed that water treatment is an effective method of controlling cholera however cholera cases will continue to be present in the population if the contribution of the each infected person to the aquatic environment and the contact rate with contaminated water is high.

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