Modelling the Impact of Isolating Infected Population on the Dynamics of Diarrhea Epidemics: Applying Systems of Ordinary Differential Equations

Mideksa Tola Jiru

doi:doi:10.11648/j.sjams.20221003.11

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Modelling the Impact of Isolating Infected Population on the Dynamics of Diarrhea Epidemics: Applying Systems of Ordinary Differential Equations

Mideksa Tola Jiru

Published in Science Journal of Applied Mathematics and Statistics (Volume 10, Issue 3)

Received: 6 July 2022 Accepted: 4 August 2022 Published: 17 August 2022

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Abstract

This paper provides a mathematical study to characterize the impact of isolating infected population in the dynamics of diarrhea epidemic. System of non-linear differential equation (consists five human compartments S, I, E, I_h, R human compartment) is used to determine a certain threshold value (known as the basic reproductive number R₀ that represents the epidemic indicator obtained from the Eigen value of the next-generation matrix) to model the impact of isolating infected population in the dynamics of diarrhea epidemic. The equilibrium points of the model are calculated and the stability analysis of the numerical simulation has been shown. We investigate the local asymptotic stability of the deterministic epidemic model and similar properties in terms of the basic reproduction number. If at least one of the partial reproduction numbers is greater than unity then the disease will persist in the population. The disease free equilibrium point is locally and globally asymptotically stable when R₀ < 1 and unstable when R₀ > 1. Numerical simulation of the model is carried to assess or supplement the impact of isolation on the dynamics of diarrhea disease. Numerical simulation results show that as the rate of isolation is increases, then the recovered populations also increase. According to sensitivity analysis of the model, we presented numerical simulation results that confirm theoretical findings and the work has been illustrated through figures for different values of sensitive parameters.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 10, Issue 3)
DOI	10.11648/j.sjams.20221003.11
Page(s)	28-37
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

Keywords

Modeling, Isolation, Basic Reproductive Number, Stability, Sensitivity Analysis, Diarrhea, Numerical Simulation

References

[1]	Diekmann, J. A. P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases.
[2]	John Wiley and Sons, Chichester, 2000, Model building, Analysis and Interpretation.
[3]	WHO/UNICEF: World Diarrhea report 2008.
[4]	Hoogendoorn, S. State of the art of Vehicular Traffic Flow Modelling. Special Issue on Road Traffic Modelling and Control of the Journal of Systems and Control Engineering.
[5]	Black-Sholes option valuation for scientific computing students (January, 2004).
[6]	Dr. A. Chernov; Numerical and Analytic Methods in option pricing, Journal, (2015).
[7]	E. Shim. A note on epidemic models with infective immigrants and vaccination. Math. Bio sci. Engg, 3 (2006): 557-566.
[8]	Federal Democratic Republic of Ethiopia Ministry Of Health Ethiopia National Diarrhea Indicator Survey, Addis Ababa, 2008.
[9]	O. Diekmann, J. A. P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases.
[10]	WHO. Fact sheet number 104. Technical report, World Health Organization, Geneva, Switzerland, 2012.
[11]	Zhou Y, Ma Z. A discrete epidemic model for SARS transmission in China. Math Comput Model. 2004; 40 (13): 1491-1506.
[12]	Chaturvedi O, Jeffrey M, Lungu E, Masupe S. Epidemic model formulation and analysis for diarrheal infections caused by salmonella. Simulation Journal. 2017; 93: 543-552.
[13]	Gerald T. Keusch, Olivier Fontaine, Alok Bhargava, Cynthia BoschiPinto, Zulfiqar A. Bhutta, Eduardo Gotuzzo, Juan Rivera, Jeffrey Chow, Sonbol A. Shahid-Salles, and Ramanan Laxminarayan; on Diarrheal Diseases.
[14]	Bayor College of Medicine, Department of Molecular Virology and Micro biology, Research âA¸S Emerging Infectious Diseases. (Accessed: 19 May 2014) Available: https://www.bcm.edu/departments/molecular-virology-andmicrobiology/research.
[15]	S. O. Adewale, I. A. Olopade, S. O. Ajao and G. A. Adeniran; mathematical analysis of diarrhea in the presence of vaccine December-2015.

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APA Style

Mideksa Tola Jiru. (2022). Modelling the Impact of Isolating Infected Population on the Dynamics of Diarrhea Epidemics: Applying Systems of Ordinary Differential Equations. Science Journal of Applied Mathematics and Statistics, 10(3), 28-37. https://doi.org/10.11648/j.sjams.20221003.11

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ACS Style

Mideksa Tola Jiru. Modelling the Impact of Isolating Infected Population on the Dynamics of Diarrhea Epidemics: Applying Systems of Ordinary Differential Equations. Sci. J. Appl. Math. Stat. 2022, 10(3), 28-37. doi: 10.11648/j.sjams.20221003.11

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AMA Style

Mideksa Tola Jiru. Modelling the Impact of Isolating Infected Population on the Dynamics of Diarrhea Epidemics: Applying Systems of Ordinary Differential Equations. Sci J Appl Math Stat. 2022;10(3):28-37. doi: 10.11648/j.sjams.20221003.11

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@article{10.11648/j.sjams.20221003.11,
  author = {Mideksa Tola Jiru},
  title = {Modelling the Impact of Isolating Infected Population on the Dynamics of Diarrhea Epidemics: Applying Systems of Ordinary Differential Equations},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {10},
  number = {3},
  pages = {28-37},
  doi = {10.11648/j.sjams.20221003.11},
  url = {https://doi.org/10.11648/j.sjams.20221003.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20221003.11},
  abstract = {This paper provides a mathematical study to characterize the impact of isolating infected population in the dynamics of diarrhea epidemic. System of non-linear differential equation (consists five human compartments S, I, E, Ih, R human compartment) is used to determine a certain threshold value (known as the basic reproductive number R0 that represents the epidemic indicator obtained from the Eigen value of the next-generation matrix) to model the impact of isolating infected population in the dynamics of diarrhea epidemic. The equilibrium points of the model are calculated and the stability analysis of the numerical simulation has been shown. We investigate the local asymptotic stability of the deterministic epidemic model and similar properties in terms of the basic reproduction number. If at least one of the partial reproduction numbers is greater than unity then the disease will persist in the population. The disease free equilibrium point is locally and globally asymptotically stable when R0 0 > 1. Numerical simulation of the model is carried to assess or supplement the impact of isolation on the dynamics of diarrhea disease. Numerical simulation results show that as the rate of isolation is increases, then the recovered populations also increase. According to sensitivity analysis of the model, we presented numerical simulation results that confirm theoretical findings and the work has been illustrated through figures for different values of sensitive parameters.},
 year = {2022}
}

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TY  - JOUR
T1  - Modelling the Impact of Isolating Infected Population on the Dynamics of Diarrhea Epidemics: Applying Systems of Ordinary Differential Equations
AU  - Mideksa Tola Jiru
Y1  - 2022/08/17
PY  - 2022
N1  - https://doi.org/10.11648/j.sjams.20221003.11
DO  - 10.11648/j.sjams.20221003.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
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UR  - https://doi.org/10.11648/j.sjams.20221003.11
AB  - This paper provides a mathematical study to characterize the impact of isolating infected population in the dynamics of diarrhea epidemic. System of non-linear differential equation (consists five human compartments S, I, E, Ih, R human compartment) is used to determine a certain threshold value (known as the basic reproductive number R0 that represents the epidemic indicator obtained from the Eigen value of the next-generation matrix) to model the impact of isolating infected population in the dynamics of diarrhea epidemic. The equilibrium points of the model are calculated and the stability analysis of the numerical simulation has been shown. We investigate the local asymptotic stability of the deterministic epidemic model and similar properties in terms of the basic reproduction number. If at least one of the partial reproduction numbers is greater than unity then the disease will persist in the population. The disease free equilibrium point is locally and globally asymptotically stable when R0 0 > 1. Numerical simulation of the model is carried to assess or supplement the impact of isolation on the dynamics of diarrhea disease. Numerical simulation results show that as the rate of isolation is increases, then the recovered populations also increase. According to sensitivity analysis of the model, we presented numerical simulation results that confirm theoretical findings and the work has been illustrated through figures for different values of sensitive parameters.
VL  - 10
IS  - 3
ER  -

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Author Information

Mideksa Tola Jiru

Department of Mathematics, Hawassa College of Teacher Education, Hawassa, Ethiopia

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Plain Text BibTeX RIS

APA Style

Mideksa Tola Jiru. (2022). Modelling the Impact of Isolating Infected Population on the Dynamics of Diarrhea Epidemics: Applying Systems of Ordinary Differential Equations. Science Journal of Applied Mathematics and Statistics, 10(3), 28-37. https://doi.org/10.11648/j.sjams.20221003.11

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ACS Style

Mideksa Tola Jiru. Modelling the Impact of Isolating Infected Population on the Dynamics of Diarrhea Epidemics: Applying Systems of Ordinary Differential Equations. Sci. J. Appl. Math. Stat. 2022, 10(3), 28-37. doi: 10.11648/j.sjams.20221003.11

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AMA Style

Mideksa Tola Jiru. Modelling the Impact of Isolating Infected Population on the Dynamics of Diarrhea Epidemics: Applying Systems of Ordinary Differential Equations. Sci J Appl Math Stat. 2022;10(3):28-37. doi: 10.11648/j.sjams.20221003.11

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@article{10.11648/j.sjams.20221003.11,
  author = {Mideksa Tola Jiru},
  title = {Modelling the Impact of Isolating Infected Population on the Dynamics of Diarrhea Epidemics: Applying Systems of Ordinary Differential Equations},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {10},
  number = {3},
  pages = {28-37},
  doi = {10.11648/j.sjams.20221003.11},
  url = {https://doi.org/10.11648/j.sjams.20221003.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20221003.11},
  abstract = {This paper provides a mathematical study to characterize the impact of isolating infected population in the dynamics of diarrhea epidemic. System of non-linear differential equation (consists five human compartments S, I, E, Ih, R human compartment) is used to determine a certain threshold value (known as the basic reproductive number R0 that represents the epidemic indicator obtained from the Eigen value of the next-generation matrix) to model the impact of isolating infected population in the dynamics of diarrhea epidemic. The equilibrium points of the model are calculated and the stability analysis of the numerical simulation has been shown. We investigate the local asymptotic stability of the deterministic epidemic model and similar properties in terms of the basic reproduction number. If at least one of the partial reproduction numbers is greater than unity then the disease will persist in the population. The disease free equilibrium point is locally and globally asymptotically stable when R0 0 > 1. Numerical simulation of the model is carried to assess or supplement the impact of isolation on the dynamics of diarrhea disease. Numerical simulation results show that as the rate of isolation is increases, then the recovered populations also increase. According to sensitivity analysis of the model, we presented numerical simulation results that confirm theoretical findings and the work has been illustrated through figures for different values of sensitive parameters.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Modelling the Impact of Isolating Infected Population on the Dynamics of Diarrhea Epidemics: Applying Systems of Ordinary Differential Equations
AU  - Mideksa Tola Jiru
Y1  - 2022/08/17
PY  - 2022
N1  - https://doi.org/10.11648/j.sjams.20221003.11
DO  - 10.11648/j.sjams.20221003.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 28
EP  - 37
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20221003.11
AB  - This paper provides a mathematical study to characterize the impact of isolating infected population in the dynamics of diarrhea epidemic. System of non-linear differential equation (consists five human compartments S, I, E, Ih, R human compartment) is used to determine a certain threshold value (known as the basic reproductive number R0 that represents the epidemic indicator obtained from the Eigen value of the next-generation matrix) to model the impact of isolating infected population in the dynamics of diarrhea epidemic. The equilibrium points of the model are calculated and the stability analysis of the numerical simulation has been shown. We investigate the local asymptotic stability of the deterministic epidemic model and similar properties in terms of the basic reproduction number. If at least one of the partial reproduction numbers is greater than unity then the disease will persist in the population. The disease free equilibrium point is locally and globally asymptotically stable when R0 0 > 1. Numerical simulation of the model is carried to assess or supplement the impact of isolation on the dynamics of diarrhea disease. Numerical simulation results show that as the rate of isolation is increases, then the recovered populations also increase. According to sensitivity analysis of the model, we presented numerical simulation results that confirm theoretical findings and the work has been illustrated through figures for different values of sensitive parameters.
VL  - 10
IS  - 3
ER  -

Copy | Download