The impact of Wolbachia on dengue transmission dynamics in an SEI–SIS model |
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| Institution: | 1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, PR China;2. Natural Resources Institute, University of Greenwich at Medway, Central Avenue, Chatham Maritime, Chatham, Kent, ME4 4TB, UK;1. College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, PR China;2. Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China;3. Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA;4. Department of Microbiology and Molecular Genetics, Michigan State University, East Lansing, MI 48824, USA;1. Key Laboratory of Tropical Diseases Control, Ministry of Education, China;2. Sun Yat-sen University-Michigan State University Joint Center of Vector Control for Tropical Diseases, Sun Yat-sen University, Guangzhou 510080, China;3. School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China;4. Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA;5. Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China;6. College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China |
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| Abstract: | Dengue has grown dramatically in recent decades globally. In order to investigate the spread of dengue with vector control, especially, the impact of Wolbachia on dengue transmission, a mathematical model is established and analyzed to study dengue transmission between humans and mosquitoes. Firstly, model qualitative analysis including the existence and local asymptotic stability of dengue-free equilibria and endemic equilibria is done. It is found that dengue will disappear when the basic reproduction number is less than one, and dengue will prevail when the basic reproduction number is larger than one. More important finding is that the persistence of Wolbachia is determined by its fitness effect on mosquitoes, and Wolbachia can drastically reduce dengue fever transmission. All the results are verified by numerical simulation. Secondly, sensitivity analysis is done to explore the relative importance of different parameters on the system. It is obtained that parameters with strong sensitivity and controllability are the biting rate, the probability of dengue infection between mosquitoes and humans and the recovery rate of infectious humans. Finally, the control methods are discussed. |
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| Keywords: | Dengue Qualitative analysis Sensitivity analysis Control methods |
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