Abstract
Endosymbiotic Wolbachia bacteria are widely applied for the control of dengue fever by manipulating the reproductive mechanism of mosquitoes, including maternal inheritance and cytoplasmic incompatibility (CI). CI means that the offsprings from the matings between Wolbachia infected males and uninfected females can not be hatched. At present, CI effect is assumed as a constant in most of dynamic systems for the spread of Wolbachia. However, their spread may arouse the evolution of mosquitoes to resist CI. Thus, a multiscale model combining a birth-pulse model with a gene-induced discrete model for the frequencies of alleles is proposed to describe the spread of Wolbachia in mosquito population with resistance allele of CI. The main results indicate that the strategy of population eradication can not be realized, while the strategy of population replacement may be realized with the success of sensitive or resistance allele. If appropriate Wolbachia strains can not be selected, then there is a high probability of the failure of population replacement. Moreover, Wolbachia-induced parameters may arouse the catastrophic shifts among stable states of the model. In addition, the demographic parameters and Wolbachia-induced parameters may affect the level and the speed of population replacement and the density of uninfected mosquitoes.
Highlights
Dengue fever as one type of vector-borne diseases, is caused by dengue virus mainly transmitted by mosquitoes[1,2]
In this paper, based on Mendelian inheritance, we propose a multiscale model to study the effects of resistance allele of cytoplasmic incompatibility (CI) mechanism on dynamic behaviors of mosquito populations so that the strategies of population replacement with high level and speed can be succeeded
We first study the frequencies of three genotypes, the fitnesses of three genotypes, the genotype frequencies of new born offsprings and the frequencies of two alleles step by step
Summary
The frequencies of alleles R and S in Wolbachia infected (uninfected) mosquitoes at generation n are denoted as pI,n and qI,n (pU,n and qU,n), respectively, we have pI + qI = I/(I + U) and pU + qU = U/(I + U). The fitnesses of three genotypes are different at generation n owing to CI effect in the progress of genetic evolution, which causes the frequencies of alleles in infected and uninfected mosquitoes change constantly. Note that Wolbachia infected females never undergo CI mechanism, and all the female mosquitoes mating with uninfected males can not be affected by CI. These matings without CI mechanism are renamed as group one.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
