Modeling huanglongbing transmission within a citrus tree

Abstract

The citrus disease huanglongbing (HLB), associated with an uncultured bacterial pathogen, is threatening the citrus industry worldwide. A mathematical model of the transmission of HLB between its psyllid vector and citrus host has been developed to characterize the dynamics of the vector and disease development, focusing on the spread of the pathogen from flush to flush (a newly developing cluster of very young leaves on the expanding terminal end of a shoot) within a tree. This approach differs from that of prior models for vector-transmitted plant diseases where the entire plant is the unit of analysis. Dynamics of vector and host populations are simulated realistically as the flush population approaches complete infection. Model analysis indicates that vector activity is essential for initial infection but is not necessary for continued infection because infection can occur from flush to flush through internal movement in the tree. Flush production, within-tree spread, and latent period are the most important parameters influencing HLB development. The model shows that the effect of spraying of psyllids depends on time of initial spraying, frequency, and efficacy of the insecticides. Similarly, effects of removal of symptomatic flush depend on the frequency of removal and the time of initiation of this practice since the start of the epidemic. Within-tree resistance to spread, possibly affected by inherent or induced resistance, is a major factor affecting epidemic development, supporting the notion that alternate routes of transmission besides that by the vector can be important for epidemic development.

Fig. 1.

Model flow diagram showing the transmission of Ca. Liberibacter asiaticus between the psyllids and the host flush. The flush compartments are uninfected and healthy , infected and asymptomatic but not yet infectious (latent) , infectious and asymptomatic , and infectious and symptomatic . The vector compartments are uninfected nymphs , infected nymphs , uninfected adult psyllids , infected adults that acquired CLas during the adult stage , and infected adults that acquired CLas during the nymphal stage .

Fig. 2.

(A–D) Proportions of healthy and latent flush (A), proportions of asymptomatic and symptomatic flush (B), populations of uninfected and infected nymphs per flush (C), and populations of uninfected and infected adult psyllids per flush (D). The latent flush is infected but not yet infectious. The asymptomatic and symptomatic flush are both infected and infectious. Infected adult psyllids are infectious and consist of categories A1 = and A2 = . Input rate of healthy flush follows a periodic function with two peaks in 1 y. The parameter for internal movement of the pathogen in the tree, .

Fig. 3.

(A–D) Populations of uninfected and infected nymphs per flush (A), populations of uninfected and infected adult psyllids per flush (B), proportions of healthy and latent flush (C), and proportions of asymptomatic and symptomatic flush (D). The latent flush is infected but not yet infectious. The asymptomatic and symptomatic flush are both infected and infectious. Infected adult psyllids are infectious and consist of categories A1 = and A2 = . Input rate of healthy flush follows a periodic function with two peaks in 1 y. Internal movement parameter of the pathogen in the tree, .

Fig. 4.

(A–D) Proportion of healthy flush (A) and of asymptomatic flush (B) when psyllids are sprayed twice every year with an insecticide that is 0.75 effective, 360 d, 450 d, and 540 d after initial infection and proportions of symptomatic flush when symptomatic flush are removed every 3 mo (C) and every 6 mo (D) starting 360 d, 540 d, and 720 d after inoculation.