Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments

Abstract

We analyze the impact of seasonal activity of psyllid on the dynamics of Huanglongbing (HLB) infection. A new model about HLB transmission with Logistic growth in psyllid insect vectors and periodic coefficients has been investigated. It is shown that the global dynamics are determined by the basic reproduction number $R_0$ which is defined through the spectral radius of a linear integral operator. If $R_0$ < 1, then the disease-free periodic solution is globally asymptotically stable and if $R_0$ > 1, then the disease persists. Numerical values of parameters of the model are evaluated taken from the literatures. Furthermore, numerical simulations support our analytical conclusions and the sensitive analysis on the basic reproduction number to the changes of average and amplitude values of the recruitment function of citrus are shown. Finally, some useful comments on controlling the transmission of HLB are given.