The effect of migration on transmission of <i>Wolbachia</i> in <i>Nilaparvata lugens</i>

Abstract

<abstract><p>Brown planthopper <italic>Nilaparvata lugens</italic>, which can transmit rice ragged stunt virus, is a serious and damaging pest to rice plants. Rice plants can protect themselves from the associated diseases of <italic>N.lugens</italic> by either suppressing or replacing <italic>N.lugens</italic> by releasing <italic>N.lugens</italic> infected by a special strain of <italic>Wolbachia</italic> <italic>wStri</italic>. The long-distance migration habit of <italic>N.lugens</italic> is one of the important precursors leading up to the large-scale occurrence of <italic>N.lugens</italic>. To study the effect of migration on the transmission of <italic>Wolbachia</italic> in <italic>N.lugens</italic>, a <italic>Wolbachia</italic> spreading dynamics model with migration of <italic>N.lugens</italic> between two patches is put forward. The existence and local stability conditions of equilibrium points of the system and its subsystems are obtained. Moreover, the effects of migration on the dynamic properties and the control of <italic>N.lugens</italic> are analyzed; the results show that the system can exhibit a bistable phenomenon, and the migration can change the stability of equilibrium infected with <italic>wStri</italic> from stable to unstable. The quantitative control methods for the migration of the insect <italic>N.lugens</italic> are proposed, which provide a theoretical guidance for future field experiments. Lastly, we use the Markov chain Monte Carlo (MCMC) method to estimate the parameters of the wild <italic>N.lugens</italic> migration model based on limited observational data; the numerical simulation results show that migration can increase the quantity of <italic>N.lugens</italic>, which is consistent with the relevant experimental results.</p></abstract>