A Mathematical Model of Malaria Transmission with Structured Vector Population and Seasonality
In this paper, we formulate a mathematical model of nonautonomous ordinary differential equations describing the dynamics of malaria transmission with age structure for the vector population. The biting rate of mosquitoes is considered as a positive periodic function which depends on climatic factor...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2017/6754097 |
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| author | Bakary Traoré Boureima Sangaré Sado Traoré |
| author_facet | Bakary Traoré Boureima Sangaré Sado Traoré |
| author_sort | Bakary Traoré |
| collection | DOAJ |
| description | In this paper, we formulate a mathematical model of nonautonomous ordinary differential equations describing the dynamics of malaria transmission with age structure for the vector population. The biting rate of mosquitoes is considered as a positive periodic function which depends on climatic factors. The basic reproduction ratio of the model is obtained and we show that it is the threshold parameter between the extinction and the persistence of the disease. Thus, by applying the theorem of comparison and the theory of uniform persistence, we prove that if the basic reproduction ratio is less than 1, then the disease-free equilibrium is globally asymptotically stable and if it is greater than 1, then there exists at least one positive periodic solution. Finally, numerical simulations are carried out to illustrate our analytical results. |
| format | Article |
| id | doaj-art-36dcad71136c46cd8656a2d3f505931d |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-36dcad71136c46cd8656a2d3f505931d2025-08-20T02:07:41ZengWileyJournal of Applied Mathematics1110-757X1687-00422017-01-01201710.1155/2017/67540976754097A Mathematical Model of Malaria Transmission with Structured Vector Population and SeasonalityBakary Traoré0Boureima Sangaré1Sado Traoré2Department of Mathematics, Polytechnic University of Bobo Dioulasso, 01 BP 1091, Bobo-Dioulasso 01, Burkina FasoDepartment of Mathematics, Polytechnic University of Bobo Dioulasso, 01 BP 1091, Bobo-Dioulasso 01, Burkina FasoDepartment of Mathematics, Polytechnic University of Bobo Dioulasso, 01 BP 1091, Bobo-Dioulasso 01, Burkina FasoIn this paper, we formulate a mathematical model of nonautonomous ordinary differential equations describing the dynamics of malaria transmission with age structure for the vector population. The biting rate of mosquitoes is considered as a positive periodic function which depends on climatic factors. The basic reproduction ratio of the model is obtained and we show that it is the threshold parameter between the extinction and the persistence of the disease. Thus, by applying the theorem of comparison and the theory of uniform persistence, we prove that if the basic reproduction ratio is less than 1, then the disease-free equilibrium is globally asymptotically stable and if it is greater than 1, then there exists at least one positive periodic solution. Finally, numerical simulations are carried out to illustrate our analytical results.http://dx.doi.org/10.1155/2017/6754097 |
| spellingShingle | Bakary Traoré Boureima Sangaré Sado Traoré A Mathematical Model of Malaria Transmission with Structured Vector Population and Seasonality Journal of Applied Mathematics |
| title | A Mathematical Model of Malaria Transmission with Structured Vector Population and Seasonality |
| title_full | A Mathematical Model of Malaria Transmission with Structured Vector Population and Seasonality |
| title_fullStr | A Mathematical Model of Malaria Transmission with Structured Vector Population and Seasonality |
| title_full_unstemmed | A Mathematical Model of Malaria Transmission with Structured Vector Population and Seasonality |
| title_short | A Mathematical Model of Malaria Transmission with Structured Vector Population and Seasonality |
| title_sort | mathematical model of malaria transmission with structured vector population and seasonality |
| url | http://dx.doi.org/10.1155/2017/6754097 |
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