Abstract
Dengue fever is caused by dengue virus and transmitted byAedesmosquitoes. A promising avenue to control this disease is to infect the wildAedespopulation with the bacteriumWolbachiadriven by cytoplasmic incompatibility (CI). To study the invasion ofWolbachiainto wild mosquito population, we formulate a discrete competition model and analyze the competition between released mosquitoes and wild mosquitoes. We show the global asymptotic properties of the trivial equilibrium, boundary equilibrium, and positive equilibrium and give the conditions for the successful invasion ofWolbachia. Finally, we verify our findings by numerical simulations.
Highlights
Dengue fever is a mosquito-borne infectious disease caused by dengue virus, mainly transmitted by Aedes aegypti [1]
In 2005, Xi et al established stable mosquito strains carrying Wolbachia for the first time by injecting Wolbachia into Aedes aegypti [5, 6], which is the basis of using Wolbachia to control mosquito-borne diseases. e strategies of using Wolbachia for mosquito vector control mainly include population suppression and population replacement. e former only releases infected males, and produces cytoplasmic incompatibility (CI) effect after mating with female mosquitoes in the field to suppress the number of mosquito vectors in the field [7, 8]; the latter releases both male and female mosquitoes infected with Wolbachia using vertical maternal transmission of Wolbachia and certain advantages to let Wolbachia spread in the mosquito population to stop spreading disease [9]
In order to show the dynamic stability of the model (3), we use MATLAB technical computing software for numerical simulations. e simulations for (a) and (b) in eorem 2 is mainly conducted by using different parameters
Summary
Dengue fever is a mosquito-borne infectious disease caused by dengue virus, mainly transmitted by Aedes aegypti [1]. Because Wolbachia often induces fitness cost [10], and it is reasonable to assume that 0 < d2 < d1 < 1 Considering that both xt and yt denote the numbers of Aedes aegypti, for simplicity, we ignore the difference between intraspecific competition and interspecific competition and focus on the effect of competitions on their birth rates, so we assume c11 c12 α and c21 c22 β denote the competition coefficient within (or between) species, respectively. Considering the infection Wolbachia CI mechanism of mosquito population and vertical maternal transmission of Wolbachia [23], the birth rate of yt is replaced by b2yt/(xt + yt); the discrete model of competition between two species is as follows: b1xt α xt +.
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