Bifurcation and optimal control analysis of delayed models for huanglongbing

Abstract

In this paper, a delayed differential model of citrus Huanglongbing infection is analyzed, in which the latencies of the citrus tree and Asian citrus psyllid are considered as two time delay factors. We compute the equilibrium points and the basic reproductive numbers with and without time delays, i.e. [Formula: see text] and [Formula: see text], and then show that [Formula: see text] completely determines the local stability of the disease-free equilibrium. Moreover, the conditions for the existence of transcritical bifurcation are derived from Sotomayor’s Theorem. The stability of the endemic equilibrium and the existence of Hopf bifurcation are investigated in four cases: (1) [Formula: see text], (2) [Formula: see text], (3) [Formula: see text] and (4) [Formula: see text]. Optimal control theory is then applied to the model to study two time-dependent treatment efforts and minimize the infection in citrus and psyllids, while keeping the implementation cost at a minimum. Numerical simulations of the overall systems are implemented in MatLab for demonstration of the theoretical results.

Role of vector resistance and grafting infection in Huanglongbing control models

“…Lately, Guo et al. ( Guo et al., 2022 ) extended the work to delay differential equation models. Optimal control theory is applied to investigate the effects of roguing and insecticide use with a goal of minimizing the infected plants and ACPs.…”