Modeling Cholera Epidemiology Using Stochastic Differential Equations
In this study, we extend Codeço’s classical SI-B epidemic and endemic model from a deterministic framework into a stochastic framework. Then, we formulated it as a stochastic differential equation for the number of infectious individuals It under the role of the aquatic environment. We also proved t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/7232395 |
| _version_ | 1797825719837917184 |
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| author | Wahab A. Iddrisu Inusah Iddrisu Abdul-Karim Iddrisu |
| author_facet | Wahab A. Iddrisu Inusah Iddrisu Abdul-Karim Iddrisu |
| author_sort | Wahab A. Iddrisu |
| collection | DOAJ |
| description | In this study, we extend Codeço’s classical SI-B epidemic and endemic model from a deterministic framework into a stochastic framework. Then, we formulated it as a stochastic differential equation for the number of infectious individuals It under the role of the aquatic environment. We also proved that this stochastic differential equation (SDE) exists and is unique. The reproduction number, R0, was derived for the deterministic model, and qualitative features such as the positivity and invariant region of the solution, the two equilibrium points (disease-free and endemic equilibrium), and stabilities were studied to ensure the biological meaningfulness of the model. Numerical simulations were also carried out for the stochastic differential equation (SDE) model by utilizing the Euler-Maruyama numerical method. The method was used to simulate the sample path of the SI-B stochastic differential equation for the number of infectious individuals It, and the findings showed that the sample path or trajectory of the stochastic differential equation for the number of infectious individuals It is continuous but not differentiable and that the SI-B stochastic differential equation model for the number of infectious individuals It fluctuates inside the solution of the SI-B ordinary differential equation model. Another significant feature of our proposed SDE model is its simplicity. |
| first_indexed | 2024-03-13T10:57:58Z |
| format | Article |
| id | doaj.art-fa92a1abda79435d89b6eba63bd21228 |
| institution | Directory Open Access Journal |
| issn | 1687-0042 |
| language | English |
| last_indexed | 2024-03-13T10:57:58Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj.art-fa92a1abda79435d89b6eba63bd212282023-05-17T00:00:07ZengHindawi LimitedJournal of Applied Mathematics1687-00422023-01-01202310.1155/2023/7232395Modeling Cholera Epidemiology Using Stochastic Differential EquationsWahab A. Iddrisu0Inusah Iddrisu1Abdul-Karim Iddrisu2Department of Mathematics and StatisticsDepartment of Mathematics and StatisticsDepartment of Mathematics and StatisticsIn this study, we extend Codeço’s classical SI-B epidemic and endemic model from a deterministic framework into a stochastic framework. Then, we formulated it as a stochastic differential equation for the number of infectious individuals It under the role of the aquatic environment. We also proved that this stochastic differential equation (SDE) exists and is unique. The reproduction number, R0, was derived for the deterministic model, and qualitative features such as the positivity and invariant region of the solution, the two equilibrium points (disease-free and endemic equilibrium), and stabilities were studied to ensure the biological meaningfulness of the model. Numerical simulations were also carried out for the stochastic differential equation (SDE) model by utilizing the Euler-Maruyama numerical method. The method was used to simulate the sample path of the SI-B stochastic differential equation for the number of infectious individuals It, and the findings showed that the sample path or trajectory of the stochastic differential equation for the number of infectious individuals It is continuous but not differentiable and that the SI-B stochastic differential equation model for the number of infectious individuals It fluctuates inside the solution of the SI-B ordinary differential equation model. Another significant feature of our proposed SDE model is its simplicity.http://dx.doi.org/10.1155/2023/7232395 |
| spellingShingle | Wahab A. Iddrisu Inusah Iddrisu Abdul-Karim Iddrisu Modeling Cholera Epidemiology Using Stochastic Differential Equations Journal of Applied Mathematics |
| title | Modeling Cholera Epidemiology Using Stochastic Differential Equations |
| title_full | Modeling Cholera Epidemiology Using Stochastic Differential Equations |
| title_fullStr | Modeling Cholera Epidemiology Using Stochastic Differential Equations |
| title_full_unstemmed | Modeling Cholera Epidemiology Using Stochastic Differential Equations |
| title_short | Modeling Cholera Epidemiology Using Stochastic Differential Equations |
| title_sort | modeling cholera epidemiology using stochastic differential equations |
| url | http://dx.doi.org/10.1155/2023/7232395 |
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