Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence
The paper considers a model for the transmission dynamics of a vector-borne disease with nonlinear incidence rate. It is proved that the global dynamics of the disease are completely determined by the basic reproduction number. In order to assess the effectiveness of disease control measures, the se...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/595487 |
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| _version_ | 1832552476360835072 |
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| author | Muhammad Ozair Abid Ali Lashari Il Hyo Jung Kazeem Oare Okosun |
| author_facet | Muhammad Ozair Abid Ali Lashari Il Hyo Jung Kazeem Oare Okosun |
| author_sort | Muhammad Ozair |
| collection | DOAJ |
| description | The paper considers a model for the transmission dynamics of a vector-borne disease with
nonlinear incidence rate. It is proved that the global dynamics of the disease are completely
determined by the basic reproduction number. In order to assess the effectiveness of disease
control measures, the sensitivity analysis of the basic reproductive number R0 and the endemic
proportions with respect to epidemiological and demographic parameters are provided. From the
results of the sensitivity analysis, the model is modified to assess the impact of three control
measures; the preventive control to minimize vector human contacts, the treatment control to the
infected human, and the insecticide control to the vector. Analytically the existence of the optimal
control is established by the use of an optimal control technique and numerically it is solved by an
iterative method. Numerical simulations and optimal analysis of the model show that restricted
and proper use of control measures might considerably decrease the number of infected humans
in a viable way. |
| format | Article |
| id | doaj-art-021dc0e7d65049a1973787767296b41d |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-021dc0e7d65049a1973787767296b41d2025-02-03T05:58:32ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/595487595487Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear IncidenceMuhammad Ozair0Abid Ali Lashari1Il Hyo Jung2Kazeem Oare Okosun3Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, H-12 Campus, Islamabad 44000, PakistanCentre for Advanced Mathematics and Physics, National University of Sciences and Technology, H-12 Campus, Islamabad 44000, PakistanDepartment of Mathematics, Pusan National University, Busan 609-735, Republic of KoreaDepartment of Mathematics, Vaal University of Technology, Andries Potgieter Boulevard, Private Bag X021, Vanderbijlpark 1900, South AfricaThe paper considers a model for the transmission dynamics of a vector-borne disease with nonlinear incidence rate. It is proved that the global dynamics of the disease are completely determined by the basic reproduction number. In order to assess the effectiveness of disease control measures, the sensitivity analysis of the basic reproductive number R0 and the endemic proportions with respect to epidemiological and demographic parameters are provided. From the results of the sensitivity analysis, the model is modified to assess the impact of three control measures; the preventive control to minimize vector human contacts, the treatment control to the infected human, and the insecticide control to the vector. Analytically the existence of the optimal control is established by the use of an optimal control technique and numerically it is solved by an iterative method. Numerical simulations and optimal analysis of the model show that restricted and proper use of control measures might considerably decrease the number of infected humans in a viable way.http://dx.doi.org/10.1155/2012/595487 |
| spellingShingle | Muhammad Ozair Abid Ali Lashari Il Hyo Jung Kazeem Oare Okosun Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence Discrete Dynamics in Nature and Society |
| title | Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence |
| title_full | Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence |
| title_fullStr | Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence |
| title_full_unstemmed | Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence |
| title_short | Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence |
| title_sort | stability analysis and optimal control of a vector borne disease with nonlinear incidence |
| url | http://dx.doi.org/10.1155/2012/595487 |
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