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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.

Multiscale modelling the effects of CI genetic evolution in mosquito population on the control of dengue fever