Dynamics of an impulsive reaction-diffusion mosquitoes model with multiple control measures

Abstract

<abstract><p>It is well-known that mosquito control is one of the effective methods to reduce and prevent the transmission of mosquito-borne diseases. In this paper, we formulate a reaction-diffusion impulsive hybrid model incorporating <italic>Wolbachia</italic>, impulsively spraying of insecticides, spatial heterogeneity, and seasonality to investigate the control of mosquito population. The sufficient conditions for mosquito extinction or successful <italic>Wolbachia</italic> persistence in a population of natural mosquitoes are derived. More importantly, we give the estimations of the spraying times of insecticides during a period for achieving the mosquito extinction and population replacement in a special case. A global attractivity of the positive periodic solution is analyzed under appropriate conditions. Numerical simulations disclose that spatial heterogeneity and seasonality have significant impacts on the design of mosquitoes control strategies. It is suggested to combine biological control and chemical pulse control under certain situations to reduce the natural mosquitoes. Further, our results reveal that the establishment of a higher level of population replacement depends on the strain type of the <italic>Wolbachia</italic> and the high initial occupancy of the <italic>Wolbachia</italic>-infected mosquitoes.</p></abstract>