A temperature-dependent mathematical model of malaria transmission with stage-structured mosquito population dynamics
In this paper, we formulate a temperature-dependent model for malaria transmission dynamics which includes immature stages of mosquitoes. The model is constructed by using ordinary differential equations with some parameters which are periodic functions. Two thresholds dynamics associated to the mod...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2021-12-01
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| Series: | Nonautonomous Dynamical Systems |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/msds-2020-0138 |
| _version_ | 1798030145815052288 |
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| author | Traoré Bakary Barro Moussa Sangaré Boureima Traoré Sado |
| author_facet | Traoré Bakary Barro Moussa Sangaré Boureima Traoré Sado |
| author_sort | Traoré Bakary |
| collection | DOAJ |
| description | In this paper, we formulate a temperature-dependent model for malaria transmission dynamics which includes immature stages of mosquitoes. The model is constructed by using ordinary differential equations with some parameters which are periodic functions. Two thresholds dynamics associated to the model have been derived: the vector reproduction ratio ℛv and the basic reproduction ratio ℛ0. Through a rigorous analysis via theories and methods of dynamical systems, we prove that the global behavior of the model depends strongly on these two parameters. More precisely, we show that if ℛv is greater than one and ℛ0 is less than one then, the disease-free periodic equilibrium is globally attractive. If ℛv is greater than one and ℛ0 is greater than one, the disease remains persistent and the system admits at least one positive periodic solution. Finally, using the reported monthly mean temperature for Burkina Faso, numerical simulations are carried out to illustrate our mathematical results. |
| first_indexed | 2024-04-11T19:36:39Z |
| format | Article |
| id | doaj.art-c82fabbfd6f94573853f88121c18dccb |
| institution | Directory Open Access Journal |
| issn | 2353-0626 |
| language | English |
| last_indexed | 2024-04-11T19:36:39Z |
| publishDate | 2021-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonautonomous Dynamical Systems |
| spelling | doaj.art-c82fabbfd6f94573853f88121c18dccb2022-12-22T04:06:51ZengDe GruyterNonautonomous Dynamical Systems2353-06262021-12-018126729610.1515/msds-2020-0138A temperature-dependent mathematical model of malaria transmission with stage-structured mosquito population dynamicsTraoré Bakary0Barro Moussa1Sangaré Boureima2Traoré Sado3Centre Universitaire de Banfora, Laboratoire de Mathématiques Informatique et Applications, BURKINA-FASOUniversité Nazi BONI, Laboratoire de Mathématiques Informatique et Applications, BURKINA-FASOUniversité Nazi BONI, Laboratoire de Mathématiques Informatique et Applications, BURKINA-FASOUniversité Nazi BONI, Laboratoire de Mathématiques Informatique et Applications, BURKINA-FASOIn this paper, we formulate a temperature-dependent model for malaria transmission dynamics which includes immature stages of mosquitoes. The model is constructed by using ordinary differential equations with some parameters which are periodic functions. Two thresholds dynamics associated to the model have been derived: the vector reproduction ratio ℛv and the basic reproduction ratio ℛ0. Through a rigorous analysis via theories and methods of dynamical systems, we prove that the global behavior of the model depends strongly on these two parameters. More precisely, we show that if ℛv is greater than one and ℛ0 is less than one then, the disease-free periodic equilibrium is globally attractive. If ℛv is greater than one and ℛ0 is greater than one, the disease remains persistent and the system admits at least one positive periodic solution. Finally, using the reported monthly mean temperature for Burkina Faso, numerical simulations are carried out to illustrate our mathematical results.https://doi.org/10.1515/msds-2020-0138malariabasic reproduction ratiovector reproduction ratiopersistenceglobal stabilityperiodic solution34d2034d2334d4537c75 |
| spellingShingle | Traoré Bakary Barro Moussa Sangaré Boureima Traoré Sado A temperature-dependent mathematical model of malaria transmission with stage-structured mosquito population dynamics Nonautonomous Dynamical Systems malaria basic reproduction ratio vector reproduction ratio persistence global stability periodic solution 34d20 34d23 34d45 37c75 |
| title | A temperature-dependent mathematical model of malaria transmission with stage-structured mosquito population dynamics |
| title_full | A temperature-dependent mathematical model of malaria transmission with stage-structured mosquito population dynamics |
| title_fullStr | A temperature-dependent mathematical model of malaria transmission with stage-structured mosquito population dynamics |
| title_full_unstemmed | A temperature-dependent mathematical model of malaria transmission with stage-structured mosquito population dynamics |
| title_short | A temperature-dependent mathematical model of malaria transmission with stage-structured mosquito population dynamics |
| title_sort | temperature dependent mathematical model of malaria transmission with stage structured mosquito population dynamics |
| topic | malaria basic reproduction ratio vector reproduction ratio persistence global stability periodic solution 34d20 34d23 34d45 37c75 |
| url | https://doi.org/10.1515/msds-2020-0138 |
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