A Mathematical Model for SIS Cholera Epidemic with Quarantine Effect
American Journal of Applied Mathematics
Volume 7, Issue 5, October 2019, Pages: 145-151
Received: Jul. 10, 2019; Accepted: Aug. 28, 2019; Published: Nov. 4, 2019
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Authors
Deepti Mokati, School of Studies in Mathematics, Vikram University, Ujjain, India
Viqar Hussain Badshah, School of Studies in Mathematics, Vikram University, Ujjain, India
Nirmala Gupta, Government Girls P. G. College, Vikram University, Ujjain, India
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Abstract
Cholera was prevalent in the U.S. in the 1800s, before modern water and sewage treatment systems eliminated its spread by contaminated water. Cholera is an acute intestinal infectious disease caused by the bacterium vibrio cholerae. We propose and analyse a mathematical model for cholera considering quarantine. Quarantine plays an important role to control the disease. Our goal is to control the disease through the quarantine even if infected population again becomes suscepted. Determine two equilibrium points of the model: disease-free and endemic. Also basic reproduction number Rq is obtained. Reproduction number plays as a key role for analyzing stability for disease-free and endemic equilibrium points. Stability has been discussed for both equilibrium points using Ruth-Hurwitz criterian. We concluded that the disease-free and endemic equilibria are locally asymptotically stable if Rq<1 and Rq>1 respectively. Also, Numerical simulations are carried out for the model. From the graphically representation it is more clearly seen that when the disease becomes dies out and when it persistence.
Keywords
SIS, Quarantine, Equilibrium, Stability, Ruth-Hurwitz Criteria, Reproduction Number
To cite this article
Deepti Mokati, Viqar Hussain Badshah, Nirmala Gupta, A Mathematical Model for SIS Cholera Epidemic with Quarantine Effect, American Journal of Applied Mathematics. Vol. 7, No. 5, 2019, pp. 145-151. doi: 10.11648/j.ajam.20190705.12
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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