Wolbachia spreading dynamics in Nilaparvata lugens with two strains

Abstract

The Nilaparvata lugens is primary vector of rice diseases such as rice ragged stunt. A recent study reported the Wolbachia wStri can cause the cytoplasmic incompatibility of N.lugens, and inhibit the infection and transmission of rice ragged stunt virus in the laboratory. In this work, based on multi-strains infection mechanisms including incomplete cytoplasmic incompatibility and imperfect maternal transmission, we use differential equations to describe the spreading dynamics of Wolbachia wStri and wLug in N.lugens population. The system can exhibit one or two stable equilibria. The stability of equilibrium infected with wStri shows that wStri can invade wild populations when the cytoplasmic incompatibility intensity of wStri and the maternal inheritance leakage rate of wLug are higher than some certain thresholds. The stability conditions of the equilibria are related to the mutual fitness of the populations. If one population is more adaptable than the other, it will be in the ascendancy. An initial value region is found, from which the trajectory of system tends to the equilibrium infected with wStri. Studies on subsystem without wStri demonstrate there is a symbiotic relation between Wolbachia wLug and N.lugens population, and Wolbachia wLug can promote the reproduction of N.lugens. In addition, our numerical results are consistent with relevant literatures experimental results. Our results can guide the release of N.lugens infected with wStri in rice fields to control the growth of wild N.lugens population.