Dynamics of a Dengue Transmission Model with Multiple Stages and Fluctuations

Zuwen Wang, Shaojian Cai, Guangmin Chen, Kuicheng Zheng, Fengying Wei (), Zhen Jin (), Xuerong Mao () and Jianfeng Xie ()
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Zuwen Wang: School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116, China
Shaojian Cai: Fujian Provincial Center for Disease Control and Prevention, Fuzhou 350012, China
Guangmin Chen: Fujian Provincial Center for Disease Control and Prevention, Fuzhou 350012, China
Kuicheng Zheng: Fujian Provincial Center for Disease Control and Prevention, Fuzhou 350012, China
Fengying Wei: School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116, China
Zhen Jin: Complex Models Research Center, Shanxi University, Taiyuan 030006, China
Xuerong Mao: Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK
Jianfeng Xie: Fujian Provincial Center for Disease Control and Prevention, Fuzhou 350012, China

Mathematics, 2024, vol. 12, issue 16, 1-26

Abstract: A vector–host model of dengue with multiple stages and independent fluctuations is investigated in this paper. Firstly, the existence and uniqueness of the positive solution are shown by contradiction. When the death rates of aquatic mosquitoes, adult mosquitoes, and human beings respectively control the intensities of white noises, and if R 0 s > 1 , then the persistence in the mean for both infective mosquitoes and infective human beings is derived. When R 0 s > 1 is valid, the existence of stationary distribution is derived through constructing several appropriate Lyapunov functions. If the intensities of white noises are controlled and φ < 0 is valid, then the extinction for both infective mosquitoes and infective human beings is obtained by applying the comparison theorem and ergodic theorem. Further, the main findings are verified through numerical simulations by using the positive preserving truncated Euler–Maruyama method (PPTEM). Moreover, several numerical simulations on the infection scale of dengue in Fuzhou City were conducted using surveillance data. The main results indicate that the decrease in the transfer proportion from aquatic mosquitoes to adult mosquitoes reduces the infection scale of infective human beings with dengue virus, and the death rates of aquatic mosquitoes and adult mosquitoes affect the value of the critical threshold R 0 s . Further, the controls of the death rates of mosquitoes are the effective routes by the decision-makers of the Chinese mainland against the spread of dengue.

Keywords: dengue; stochastic vector–host model; multi stage; stationary distribution; persistence and extinction; PPTEM method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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