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 numberR0which is defined through the spectral radius of a linear integral operator. IfR0< 1, then the disease-free periodic solution is globally asymptotically stable and ifR0> 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.
Highlights
Plant disease is an important constraint to crop production
We introduce some notations and lemmas which will be used for our further argument
Let Cω be function from the ordered Banach space of all ω-periodic R → R2, which is equipped with maximum norm ‖ ⋅ ‖∞ and the positive cone Cω+ = {φ ∈ Cω : φ(t) ≥ 0, for all t ∈ R}
Summary
Plant disease is an important constraint to crop production. Due to plant diseases, more than 10% of global food production is lost and 800 million people do not have adequate food in the world [1,2,3]. Mathematical models play an important role in understanding the epidemiology of vector-transmitted plant diseases. In [8], the authors proposed a deterministic compartmental mathematic model to analyze HLB spread between citrus plants. They assumed that all coefficients of the model are constant (autonomous systems). We propose a model with periodic transmission rates to investigate the seasonal HLB epidemics [10, 11]. In this model, we consider Logistic growth term for dynamics of susceptible psyllid vector.
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