Mathematical Modelling of Typhoid Fever Disease with Protection Against Infection.
In this study, we provide a detailed review of major mathematical models of the spread of typhoid fever. We show that the disease burden can be controlled by managing the effective contact rate of the infected population. We prove that the disease free equilibrium is globally asymptotically stable w...
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| Format: | Thesis |
| Language: | en_US |
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Kabale University
2023
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| Online Access: | http://hdl.handle.net/20.500.12493/994 |
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| _version_ | 1803933480364539904 |
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| author | Atukwatse, Edinah |
| author_facet | Atukwatse, Edinah |
| author_sort | Atukwatse, Edinah |
| collection | KAB-DR |
| description | In this study, we provide a detailed review of major mathematical models of the spread of typhoid fever. We show that the disease burden can be controlled by managing the effective contact rate of the infected population. We prove that the disease free equilibrium is globally asymptotically stable when R < 1 and the disease asymptotically dies out without requiring any external action on the system. It is established that at the point of global stability, the Jacobian of the matrix of the dynamics of the epidemic model defining the linearized state-trajectory has all its eigenvalues in the stable region. The study reveals that if the basic reproduction number exceeds one, the disease-free equilibrium is unstable so that these state trajectories can converge asymptotically to the endemic equilibrium or exhibit an oscillatory behavior.
Keywords: Mathematical Modelling, Typhoid Fever, Disease, Protection Infection. |
| format | Thesis |
| id | oai:idr.kab.ac.ug:20.500.12493-994 |
| institution | KAB-DR |
| language | en_US |
| publishDate | 2023 |
| publisher | Kabale University |
| record_format | dspace |
| spelling | oai:idr.kab.ac.ug:20.500.12493-9942024-06-12T12:49:07Z Mathematical Modelling of Typhoid Fever Disease with Protection Against Infection. Atukwatse, Edinah Mathematical Modelling Typhoid Fever Disease Protection Infection In this study, we provide a detailed review of major mathematical models of the spread of typhoid fever. We show that the disease burden can be controlled by managing the effective contact rate of the infected population. We prove that the disease free equilibrium is globally asymptotically stable when R < 1 and the disease asymptotically dies out without requiring any external action on the system. It is established that at the point of global stability, the Jacobian of the matrix of the dynamics of the epidemic model defining the linearized state-trajectory has all its eigenvalues in the stable region. The study reveals that if the basic reproduction number exceeds one, the disease-free equilibrium is unstable so that these state trajectories can converge asymptotically to the endemic equilibrium or exhibit an oscillatory behavior. Keywords: Mathematical Modelling, Typhoid Fever, Disease, Protection Infection. 2023-02-08T09:02:26Z 2023-02-08T09:02:26Z 2021 Thesis http://hdl.handle.net/20.500.12493/994 en_US Attribution-NonCommercial-NoDerivs 3.0 United States http://creativecommons.org/licenses/by-nc-nd/3.0/us/ application/pdf Kabale University |
| spellingShingle | Mathematical Modelling Typhoid Fever Disease Protection Infection Atukwatse, Edinah Mathematical Modelling of Typhoid Fever Disease with Protection Against Infection. |
| title | Mathematical Modelling of Typhoid Fever Disease with Protection Against Infection. |
| title_full | Mathematical Modelling of Typhoid Fever Disease with Protection Against Infection. |
| title_fullStr | Mathematical Modelling of Typhoid Fever Disease with Protection Against Infection. |
| title_full_unstemmed | Mathematical Modelling of Typhoid Fever Disease with Protection Against Infection. |
| title_short | Mathematical Modelling of Typhoid Fever Disease with Protection Against Infection. |
| title_sort | mathematical modelling of typhoid fever disease with protection against infection |
| topic | Mathematical Modelling Typhoid Fever Disease Protection Infection |
| url | http://hdl.handle.net/20.500.12493/994 |
| work_keys_str_mv | AT atukwatseedinah mathematicalmodellingoftyphoidfeverdiseasewithprotectionagainstinfection |