Mathematical Modeling of Echinococcosis in Humans, Dogs, and Sheep
In this paper, a model for the transmission dynamics of cystic echinococcosis in the dog, sheep, and human populations is developed and analyzed. We first model and analyze the predator-prey interaction model in these populations; then, we propose a mathematical model of the transmission dynamics of...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/8482696 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849411799102783488 |
|---|---|
| author | Getachew Bitew Birhan Justin Manango W. Munganga Adamu Shitu Hassan |
| author_facet | Getachew Bitew Birhan Justin Manango W. Munganga Adamu Shitu Hassan |
| author_sort | Getachew Bitew Birhan |
| collection | DOAJ |
| description | In this paper, a model for the transmission dynamics of cystic echinococcosis in the dog, sheep, and human populations is developed and analyzed. We first model and analyze the predator-prey interaction model in these populations; then, we propose a mathematical model of the transmission dynamics of cystic echinococcosis. We calculate the basic reproduction number R0 and prove that the disease-free equilibrium is globally asymptotically stable, and hence, the disease dies out if R0<1. We further show that the endemic equilibrium is globally asymptotically stable, and hence, the disease persists if R0>1. Numerical simulations are performed to illustrate our analytic results. We give sensitivity analysis of the key parameters and give strategies that are helpful to control the transmission of cystic echinococcosis, from which the most sensitive parameter is the transmission rate of Echinococcus’ eggs from the environment to sheep (βes). Thus, the effective controlling strategies are associated with this parameter. |
| format | Article |
| id | doaj-art-62e999010c024d9999a2f345b0c54a2d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-62e999010c024d9999a2f345b0c54a2d2025-08-20T03:34:40ZengWileyJournal of Applied Mathematics1110-757X1687-00422020-01-01202010.1155/2020/84826968482696Mathematical Modeling of Echinococcosis in Humans, Dogs, and SheepGetachew Bitew Birhan0Justin Manango W. Munganga1Adamu Shitu Hassan2Department of Mathematical Sciences, College of Science, Engineering and Technology, University of South Africa, South AfricaDepartment of Mathematical Sciences, College of Science, Engineering and Technology, University of South Africa, South AfricaDepartment of Mathematical Sciences, College of Science, Engineering and Technology, University of South Africa, South AfricaIn this paper, a model for the transmission dynamics of cystic echinococcosis in the dog, sheep, and human populations is developed and analyzed. We first model and analyze the predator-prey interaction model in these populations; then, we propose a mathematical model of the transmission dynamics of cystic echinococcosis. We calculate the basic reproduction number R0 and prove that the disease-free equilibrium is globally asymptotically stable, and hence, the disease dies out if R0<1. We further show that the endemic equilibrium is globally asymptotically stable, and hence, the disease persists if R0>1. Numerical simulations are performed to illustrate our analytic results. We give sensitivity analysis of the key parameters and give strategies that are helpful to control the transmission of cystic echinococcosis, from which the most sensitive parameter is the transmission rate of Echinococcus’ eggs from the environment to sheep (βes). Thus, the effective controlling strategies are associated with this parameter.http://dx.doi.org/10.1155/2020/8482696 |
| spellingShingle | Getachew Bitew Birhan Justin Manango W. Munganga Adamu Shitu Hassan Mathematical Modeling of Echinococcosis in Humans, Dogs, and Sheep Journal of Applied Mathematics |
| title | Mathematical Modeling of Echinococcosis in Humans, Dogs, and Sheep |
| title_full | Mathematical Modeling of Echinococcosis in Humans, Dogs, and Sheep |
| title_fullStr | Mathematical Modeling of Echinococcosis in Humans, Dogs, and Sheep |
| title_full_unstemmed | Mathematical Modeling of Echinococcosis in Humans, Dogs, and Sheep |
| title_short | Mathematical Modeling of Echinococcosis in Humans, Dogs, and Sheep |
| title_sort | mathematical modeling of echinococcosis in humans dogs and sheep |
| url | http://dx.doi.org/10.1155/2020/8482696 |
| work_keys_str_mv | AT getachewbitewbirhan mathematicalmodelingofechinococcosisinhumansdogsandsheep AT justinmanangowmunganga mathematicalmodelingofechinococcosisinhumansdogsandsheep AT adamushituhassan mathematicalmodelingofechinococcosisinhumansdogsandsheep |