Nonlinear dynamics and stochastic optimal control of a Huanglongbing epidemic model with resistance

Citrus Huanglongbing(HLB)epidemic diseases is a destructive threat to the citrus industryworldwide. In this paper, a stochastic epidemic model is proposed for the transmission ofHuanglongbing in scenarios between Asian citrus psyllid and the citrus trees host. The influence ofinsecticide resistance is considered and the dynamical properties of the new model are mathematicallyanalyzed. It is proved that the model is well-posed by obtaining the existence of a single global positivesolution. Further, whenR(2 )> 1, weak persistence in the mean is obtained by developing a suitableLyapunov function and sufficient criteriaR(1 )< 1 is derived for the extinction of the disease. Moreover,the analysis of stochastic optimality is used, and a proper strategy is studied to provide a theoreticalbasis for the prevention and control of HLB. Numerical simulations and examples are carried out toverify the main theoretical results