An impulsive model for Wolbachia infection control of mosquito-borne diseases with general birth and death rate functions |
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| Affiliation: | 1. Department of Financial Mathematics, Jiangsu University, Zhenjiang 212013, China;2. Department of Mathematics, Technical University of Iaşi, Bd. Copou 11, Iaşi 700506, Romania;3. Department of Mathematics and Mathematical Statistics, Umeå University, Umeå SE-90187, Sweden;1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, PR China;2. LAMPS, Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada;3. State Key Laboratory of Infectious Disease Prevention and Control, National Institute for Communicable Disease Control and Prevention, Chinese Center for Disease Control and Prevention, Beijing, 102206, PR China;4. Natural Resources Institute, University of Greenwich at Medway, Central Avenue, Chatham Maritime, Chatham, Kent ME4 4TB, UK;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. Center for Dynamics, Department of Mathematics, TU Dresden, D-01062 Dresden, Germany;2. Mathematical Institute, University of Koblenz-Landau, Universitätstr. 1, D-56070 Koblenz, Germany;3. Center for Applied Dynamical Systems and Computational Methods (CADSCOM), Faculty of Natural Sciences and Mathematics, Escuela Superior Politécnica del Litoral, P.O. Box 09-01-5863, Guayaquil, Ecuador |
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| Abstract: | Mosquito-borne diseases are global health problems, which mainly affect low-income populations in tropics and subtropics. In order to prevent the transmission of mosquito-borne diseases, the intracellular symbiotic bacteria named as Wolbachia is becoming a promising candidate to interrupt the virus transmission. In this paper, an impulsive mosquito population model with general birth and death rate functions is established to study the cytoplasmic incompatibility (CI) effect caused by mating of Wolbachia-infected males and uninfected females. The dynamics of the spread of Wolbachia in mosquito population are studied, and the strategies of mosquito extinction or replacing Wolbachia-uninfected mosquitoes with Wolbachia-infected mosquitoes are analyzed. Moreover, the results are applied to models with specific birth and death rate functions. It is shown that strategies may be different due to different birth and death rate functions, the type of Wolbachia strains and the initial number of Wolbachia-infected mosquitoes. Furthermore, numerical simulations are conducted to illustrate our conclusions. |
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| Keywords: | Mosquito-borne disease Wolbachia Impulsive model General birth and death rate functions |
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