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.
| Published in | American Journal of Applied Mathematics (Volume 7, Issue 5) |
| DOI | 10.11648/j.ajam.20190705.12 |
| Page(s) | 145-151 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
SIS, Quarantine, Equilibrium, Stability, Ruth-Hurwitz Criteria, Reproduction Number
| [1] | Agarwal M. and Verma V., Modeling and Analysis of the Spread of an Infectious Disease Cholera with Environmental Fluctuations, International Journal of Applications and Applied Mathematics, 7 (1), 406-425, 2012. |
| [2] | Chun I. and Fung H., Cholera Transmission Dynamic Models for Public Health Practitioners, Fung Emerging Themes in Epidemiology, 11 (1), 1-11, 2014. |
| [3] | Cui J., Wu Z. and Zhou X., Mathematical Analysis of a Cholera Model with Vaccination, Journal of Applied Mathematics, Hindawi Publishing Corporation, Article id. 324767, 1-16, 2014. |
| [4] | Das P. and Mukherjee D., Qualitative Analysis of a Cholera Bacteriophage Model, International Scholarly Research Network (ISRN) Biomathematics, Article id 621939, 1-13, 2012. |
| [5] | Emvudu Y. and Kokomo E., Stability Analysis of Cholera Epidemic Model of a Closed Population, Journal of Applied Mathematicsand Bioinformatics, 2 (1), 69-97, 2012. |
| [6] | Madubueze C. E., Madubueze S. C., and Ajama S., Bifurcation and Stability Analysis of the Dynamics of Cholera Model with Controls, International Journal of Mathematical, Computational, physical, Electrical and Computer Engineering, 9 (11), 633-639, 2015. |
| [7] | Nirwani N., Badshah V. H. and Khandelwal. R, SIQR Model for Transmission of Cholera, Advances in Applied Science Research, Pelagia research library, 6 (6), 181-186, 2015. |
| [8] | Pang Y., Han Y. and Li W, The Threshold of a Stochastic SIQS Epidemic Model, Advances in Difference Equations, 1, issue 320, 1-15, 2014. |
| [9] | Wang J. and Modnak C., Modeling Cholera Dynamics with Controls, Canadian Applied Mathematics Quarterly, 19 (3), 255-273, 2011. |
APA Style
Deepti Mokati, Viqar Hussain Badshah, Nirmala Gupta. (2019). A Mathematical Model for SIS Cholera Epidemic with Quarantine Effect. American Journal of Applied Mathematics, 7(5), 145-151. https://doi.org/10.11648/j.ajam.20190705.12
ACS Style
Deepti Mokati; Viqar Hussain Badshah; Nirmala Gupta. A Mathematical Model for SIS Cholera Epidemic with Quarantine Effect. Am. J. Appl. Math. 2019, 7(5), 145-151. doi: 10.11648/j.ajam.20190705.12
AMA Style
Deepti Mokati, Viqar Hussain Badshah, Nirmala Gupta. A Mathematical Model for SIS Cholera Epidemic with Quarantine Effect. Am J Appl Math. 2019;7(5):145-151. doi: 10.11648/j.ajam.20190705.12
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Download@article{10.11648/j.ajam.20190705.12,
author = {Deepti Mokati and Viqar Hussain Badshah and Nirmala Gupta},
title = {A Mathematical Model for SIS Cholera Epidemic with Quarantine Effect},
journal = {American Journal of Applied Mathematics},
volume = {7},
number = {5},
pages = {145-151},
doi = {10.11648/j.ajam.20190705.12},
url = {https://doi.org/10.11648/j.ajam.20190705.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20190705.12},
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 Rqq>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.},
year = {2019}
}
TY - JOUR T1 - A Mathematical Model for SIS Cholera Epidemic with Quarantine Effect AU - Deepti Mokati AU - Viqar Hussain Badshah AU - Nirmala Gupta Y1 - 2019/11/04 PY - 2019 N1 - https://doi.org/10.11648/j.ajam.20190705.12 DO - 10.11648/j.ajam.20190705.12 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 145 EP - 151 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20190705.12 AB - 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 Rqq>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. VL - 7 IS - 5 ER -
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