Mathematical Modelling and Analysis of Dengue Transmission in Bangladesh with Saturated Incidence Rate and Constant Treatment Function
Dengue is one of the major health problems in Bangladesh and many people are died in recent years due to the severity of this disease. Therefore, in this paper, a SIRS model for the human and SI model for vector population with saturated incidence rate and constant treatment function has been presen...
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| Format: | Article |
| Language: | English |
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Indonesian Bio-Mathematical Society
2021-05-01
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| Series: | Communication in Biomathematical Sciences |
| Subjects: | |
| Online Access: | https://journals.itb.ac.id/index.php/cbms/article/view/14263 |
| _version_ | 1797245014369107968 |
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| author | Amit Kumar Chakraborty M. A. Haque M. A. Islam |
| author_facet | Amit Kumar Chakraborty M. A. Haque M. A. Islam |
| author_sort | Amit Kumar Chakraborty |
| collection | DOAJ |
| description | Dengue is one of the major health problems in Bangladesh and many people are died in recent years due to the severity of this disease. Therefore, in this paper, a SIRS model for the human and SI model for vector population with saturated incidence rate and constant treatment function has been presented to describe the transmission of dengue. The equilibrium points and the basic reproduction number have been computed. The conditions which lead the disease free equilibrium and the endemic equilibrium have been determined. The local stability for the equilibrium points has been established based on the eigenvalues of the Jacobian matrix and the global stability has been analyzed by using the Lyapunov function theory. It is found that the stability of equilibrium points can be controlled by the reproduction number. In order to calculate the infection rate, data for infected human populations have been collected from several health institutions of Bangladesh. Numerical simulations of various compartments have been generated using MATLAB to investigate the influence of the key parameters for the transmission of the disease and to support the analytical results. The effect of treatment function over the infected compartment has been illustrated. The sensitivity of the reproduction number concerning the parameters of the model has been analyzed. Finally, the most sensitive parameter that has the highest effect over reproduction number has been identified. |
| first_indexed | 2024-04-24T19:20:10Z |
| format | Article |
| id | doaj.art-db173be5163240e0a8630d9933575e26 |
| institution | Directory Open Access Journal |
| issn | 2549-2896 |
| language | English |
| last_indexed | 2024-04-24T19:20:10Z |
| publishDate | 2021-05-01 |
| publisher | Indonesian Bio-Mathematical Society |
| record_format | Article |
| series | Communication in Biomathematical Sciences |
| spelling | doaj.art-db173be5163240e0a8630d9933575e262024-03-26T01:29:14ZengIndonesian Bio-Mathematical SocietyCommunication in Biomathematical Sciences2549-28962021-05-013210111310.5614/cbms.2020.3.2.210634Mathematical Modelling and Analysis of Dengue Transmission in Bangladesh with Saturated Incidence Rate and Constant Treatment FunctionAmit Kumar Chakraborty0M. A. Haque1M. A. Islam2Department of Mathematics, Shahjalal University of Science and Technology, Sylhet-3114Department of Mathematics, Shahjalal University of Science and Technology, Sylhet-3114Department of Mathematics, Shahjalal University of Science and Technology, Sylhet-3114Dengue is one of the major health problems in Bangladesh and many people are died in recent years due to the severity of this disease. Therefore, in this paper, a SIRS model for the human and SI model for vector population with saturated incidence rate and constant treatment function has been presented to describe the transmission of dengue. The equilibrium points and the basic reproduction number have been computed. The conditions which lead the disease free equilibrium and the endemic equilibrium have been determined. The local stability for the equilibrium points has been established based on the eigenvalues of the Jacobian matrix and the global stability has been analyzed by using the Lyapunov function theory. It is found that the stability of equilibrium points can be controlled by the reproduction number. In order to calculate the infection rate, data for infected human populations have been collected from several health institutions of Bangladesh. Numerical simulations of various compartments have been generated using MATLAB to investigate the influence of the key parameters for the transmission of the disease and to support the analytical results. The effect of treatment function over the infected compartment has been illustrated. The sensitivity of the reproduction number concerning the parameters of the model has been analyzed. Finally, the most sensitive parameter that has the highest effect over reproduction number has been identified.https://journals.itb.ac.id/index.php/cbms/article/view/14263dengue diseaseendemic equilibriumglobal stabilitylyapunov functionsensitivity analysis. |
| spellingShingle | Amit Kumar Chakraborty M. A. Haque M. A. Islam Mathematical Modelling and Analysis of Dengue Transmission in Bangladesh with Saturated Incidence Rate and Constant Treatment Function Communication in Biomathematical Sciences dengue disease endemic equilibrium global stability lyapunov function sensitivity analysis. |
| title | Mathematical Modelling and Analysis of Dengue Transmission in Bangladesh with Saturated Incidence Rate and Constant Treatment Function |
| title_full | Mathematical Modelling and Analysis of Dengue Transmission in Bangladesh with Saturated Incidence Rate and Constant Treatment Function |
| title_fullStr | Mathematical Modelling and Analysis of Dengue Transmission in Bangladesh with Saturated Incidence Rate and Constant Treatment Function |
| title_full_unstemmed | Mathematical Modelling and Analysis of Dengue Transmission in Bangladesh with Saturated Incidence Rate and Constant Treatment Function |
| title_short | Mathematical Modelling and Analysis of Dengue Transmission in Bangladesh with Saturated Incidence Rate and Constant Treatment Function |
| title_sort | mathematical modelling and analysis of dengue transmission in bangladesh with saturated incidence rate and constant treatment function |
| topic | dengue disease endemic equilibrium global stability lyapunov function sensitivity analysis. |
| url | https://journals.itb.ac.id/index.php/cbms/article/view/14263 |
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