Mathematical Modelling of Tuberculosis and Diabetes Co-Infection Using the Non-Standard Finite Difference Scheme
One of the major health challenge facing Africa and in particular, Kenya is the risk of Tuberculosis and Diabetes. To understand the dynamics of this, a nine compartmental model for tuberculosis-diabetes coinfection is formulated. The Non-standard finite difference Scheme (NSFD) of the model is form...
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| Format: | Article |
| Language: | English |
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Mathyze Publishers
2023-12-01
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| Series: | Pan-American Journal of Mathematics |
| Online Access: | https://mathyze.com/index.php/pajm/article/view/127 |
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| author | Eunice Mueni Musyoki Winfred Nduku Mutuku Nancy Matendechere Imbusi Evans Otieno Omondi |
| author_facet | Eunice Mueni Musyoki Winfred Nduku Mutuku Nancy Matendechere Imbusi Evans Otieno Omondi |
| author_sort | Eunice Mueni Musyoki |
| collection | DOAJ |
| description | One of the major health challenge facing Africa and in particular, Kenya is the risk of Tuberculosis and Diabetes. To understand the dynamics of this, a nine compartmental model for tuberculosis-diabetes coinfection is formulated. The Non-standard finite difference Scheme (NSFD) of the model is formulated from the first-order ordinary differential equations (ode) to avoid full implicit schemes that are computationally expensive. The overly small step sizes in NSFD give the user autonomy in controlling the accuracy of the results, making it suitable for disease control applications. Numerical simulations with different step sizes of the NSFD for the TB-Diabetes model are carried out to find the optimal step size, h. A comparison of the best resultant numerical simulation based on optimal h in NSDF indicates NSFD gives better results when compared with the corresponding first-order ode. The phase-plane analysis revealed that the NSFD formulated for tuberculosis and diabetes co-infection is generally asymptotically stable. Future studies should consider formulating the proposed model with varied control parameters such as medication to compare the results with those from first-order ode. |
| format | Article |
| id | doaj-art-ee328dfffdca4c84b56ee32e8d957de5 |
| institution | Kabale University |
| issn | 2832-4293 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Mathyze Publishers |
| record_format | Article |
| series | Pan-American Journal of Mathematics |
| spelling | doaj-art-ee328dfffdca4c84b56ee32e8d957de52025-08-20T03:27:01ZengMathyze PublishersPan-American Journal of Mathematics2832-42932023-12-012010.28919/cpr-pajm/2-1635Mathematical Modelling of Tuberculosis and Diabetes Co-Infection Using the Non-Standard Finite Difference SchemeEunice Mueni Musyoki0Winfred Nduku Mutuku1Nancy Matendechere Imbusi2Evans Otieno Omondi3Kenyatta UniversityKenyatta UniversityThe Technical University of KenyaStrathmore UniversityOne of the major health challenge facing Africa and in particular, Kenya is the risk of Tuberculosis and Diabetes. To understand the dynamics of this, a nine compartmental model for tuberculosis-diabetes coinfection is formulated. The Non-standard finite difference Scheme (NSFD) of the model is formulated from the first-order ordinary differential equations (ode) to avoid full implicit schemes that are computationally expensive. The overly small step sizes in NSFD give the user autonomy in controlling the accuracy of the results, making it suitable for disease control applications. Numerical simulations with different step sizes of the NSFD for the TB-Diabetes model are carried out to find the optimal step size, h. A comparison of the best resultant numerical simulation based on optimal h in NSDF indicates NSFD gives better results when compared with the corresponding first-order ode. The phase-plane analysis revealed that the NSFD formulated for tuberculosis and diabetes co-infection is generally asymptotically stable. Future studies should consider formulating the proposed model with varied control parameters such as medication to compare the results with those from first-order ode.https://mathyze.com/index.php/pajm/article/view/127 |
| spellingShingle | Eunice Mueni Musyoki Winfred Nduku Mutuku Nancy Matendechere Imbusi Evans Otieno Omondi Mathematical Modelling of Tuberculosis and Diabetes Co-Infection Using the Non-Standard Finite Difference Scheme Pan-American Journal of Mathematics |
| title | Mathematical Modelling of Tuberculosis and Diabetes Co-Infection Using the Non-Standard Finite Difference Scheme |
| title_full | Mathematical Modelling of Tuberculosis and Diabetes Co-Infection Using the Non-Standard Finite Difference Scheme |
| title_fullStr | Mathematical Modelling of Tuberculosis and Diabetes Co-Infection Using the Non-Standard Finite Difference Scheme |
| title_full_unstemmed | Mathematical Modelling of Tuberculosis and Diabetes Co-Infection Using the Non-Standard Finite Difference Scheme |
| title_short | Mathematical Modelling of Tuberculosis and Diabetes Co-Infection Using the Non-Standard Finite Difference Scheme |
| title_sort | mathematical modelling of tuberculosis and diabetes co infection using the non standard finite difference scheme |
| url | https://mathyze.com/index.php/pajm/article/view/127 |
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