In this work, the treatment impacts of water borne disease is modeled and analyzed from a mathematical perspective via a deterministic SEIR model. The total human population is partitioned into four sub-classes namely susceptible individuals, exposed individuals, infected individuals and recovered individuals. The stability theory of non-linear differential equations and the basic reproductive number represents the epidemic indicator which is obtained from the largest eigen value of the next-generation matrix. The model explored invariant region, equilibrium condition, basic reproduction number, and stability analysis. The invariant region was proved to be positive and bounded that confirm the feasible model solution. It is also observed that the water borne disease is free equilibrium is locally asymptotically stable if the basic reproduction number is less than one. In this situation it is found that the disease is controlled whenever the treatment is allowable in the community. The disease is endemic equilibrium and globally asymptotically stable in the invariant region if the basic reproduction number is greater than one. The sensitivity analysis revealed that the rate of transmission and the rate at which exposed individuals become infectious are the most sensitive parameters. The numeric results have been illustrated through figures for different values of sensitive parameters by use of MATLAB simulation method. The findings indicate that effective treatment is adequate in eradicating and controlling water borne disease.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 10, Issue 5) |
| DOI | 10.11648/j.sjams.20221005.12 |
| Page(s) | 90-97 |
| 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 |
Water Borne, Basic Reproduction Number, Mathematical Model, Numerical Simulation
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APA Style
Mideksa Tola Jiru. (2022). Mathematical Modeling and Treatment Impacts of Water Borne Disease Spread. Science Journal of Applied Mathematics and Statistics, 10(5), 90-97. https://doi.org/10.11648/j.sjams.20221005.12
ACS Style
Mideksa Tola Jiru. Mathematical Modeling and Treatment Impacts of Water Borne Disease Spread. Sci. J. Appl. Math. Stat. 2022, 10(5), 90-97. doi: 10.11648/j.sjams.20221005.12
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Download@article{10.11648/j.sjams.20221005.12,
author = {Mideksa Tola Jiru},
title = {Mathematical Modeling and Treatment Impacts of Water Borne Disease Spread},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {10},
number = {5},
pages = {90-97},
doi = {10.11648/j.sjams.20221005.12},
url = {https://doi.org/10.11648/j.sjams.20221005.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20221005.12},
abstract = {In this work, the treatment impacts of water borne disease is modeled and analyzed from a mathematical perspective via a deterministic SEIR model. The total human population is partitioned into four sub-classes namely susceptible individuals, exposed individuals, infected individuals and recovered individuals. The stability theory of non-linear differential equations and the basic reproductive number represents the epidemic indicator which is obtained from the largest eigen value of the next-generation matrix. The model explored invariant region, equilibrium condition, basic reproduction number, and stability analysis. The invariant region was proved to be positive and bounded that confirm the feasible model solution. It is also observed that the water borne disease is free equilibrium is locally asymptotically stable if the basic reproduction number is less than one. In this situation it is found that the disease is controlled whenever the treatment is allowable in the community. The disease is endemic equilibrium and globally asymptotically stable in the invariant region if the basic reproduction number is greater than one. The sensitivity analysis revealed that the rate of transmission and the rate at which exposed individuals become infectious are the most sensitive parameters. The numeric results have been illustrated through figures for different values of sensitive parameters by use of MATLAB simulation method. The findings indicate that effective treatment is adequate in eradicating and controlling water borne disease.},
year = {2022}
}
TY - JOUR T1 - Mathematical Modeling and Treatment Impacts of Water Borne Disease Spread AU - Mideksa Tola Jiru Y1 - 2022/11/11 PY - 2022 N1 - https://doi.org/10.11648/j.sjams.20221005.12 DO - 10.11648/j.sjams.20221005.12 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 - 90 EP - 97 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20221005.12 AB - In this work, the treatment impacts of water borne disease is modeled and analyzed from a mathematical perspective via a deterministic SEIR model. The total human population is partitioned into four sub-classes namely susceptible individuals, exposed individuals, infected individuals and recovered individuals. The stability theory of non-linear differential equations and the basic reproductive number represents the epidemic indicator which is obtained from the largest eigen value of the next-generation matrix. The model explored invariant region, equilibrium condition, basic reproduction number, and stability analysis. The invariant region was proved to be positive and bounded that confirm the feasible model solution. It is also observed that the water borne disease is free equilibrium is locally asymptotically stable if the basic reproduction number is less than one. In this situation it is found that the disease is controlled whenever the treatment is allowable in the community. The disease is endemic equilibrium and globally asymptotically stable in the invariant region if the basic reproduction number is greater than one. The sensitivity analysis revealed that the rate of transmission and the rate at which exposed individuals become infectious are the most sensitive parameters. The numeric results have been illustrated through figures for different values of sensitive parameters by use of MATLAB simulation method. The findings indicate that effective treatment is adequate in eradicating and controlling water borne disease. VL - 10 IS - 5 ER -
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