Pierce's Disease of Grapevines: A Review of Control Strategies and an Outline of an Epidemiological Model

Abstract

Xylella fastidiosa is a notorious plant pathogenic bacterium that represents a threat to crops worldwide. Its subspecies, Xylella fastidiosa subsp. fastidiosa is the causal agent of Pierce's disease of grapevines. Pierce's disease has presented a serious challenge for the grapevine industry in the United States and turned into an epidemic in Southern California due to the invasion of the insect vector Homalodisca vitripennis. In an attempt to minimize the effects of Xylella fastidiosa subsp. fastidiosa in vineyards, various studies have been developing and testing strategies to prevent the occurrence of Pierce's disease, i.e., prophylactic strategies. Research has also been undertaken to investigate therapeutic strategies to cure vines infected by Xylella fastidiosa subsp. fastidiosa. This report explicitly reviews all the strategies published to date and specifies their current status. Furthermore, an epidemiological model of Xylella fastidiosa subsp. fastidiosa is proposed and key parameters for the spread of Pierce's disease deciphered in a sensitivity analysis of all model parameters. Based on these results, it is concluded that future studies should prioritize therapeutic strategies, while investments should only be made in prophylactic strategies that have demonstrated promising results in vineyards.

Keywords: Homalodisca vitripennis; Pierce's disease; Xylella fastidiosa; control strategies; epidemiological model; grapevine; prophylactic; therapeutic.

Figure 1

Summary of all types of prophylactic and therapeutic strategies against PD presented in this paper. Prophylactic strategies address healthy vines in an attempt to prevent PD (A), while therapeutic strategies address Xff-infected vines in order to cure them of PD (B).

Figure 2

Schematic of the Xff epidemiological model showing the transition of the vine and GWSS populations to different stages due to Xff presence. State variables referring to the stages of GWSS are healthy S_v and infected I_v. State variables referring to the stages of vines are healthy S_h, latent L_h and symptomatic I_h. Displayed on each transition between the state variables are the rates at which they happen in the model (see Equations 1–5). The model parameters can be found in Table 4.

Figure 3

Equilibrium prevalence of PD in the GWSS population (A) and in the vine population (B), as a function of GWSS density, i.e., the relation between the equilibrium total number of GWSS, N^*and the maximum number of vines N_h0. The equilibrium values are presented using the expression of the state variables in the fractional system. These are infected GWSS over the total number of GWSS i_v, healthy vines over the maximum number of vines s_h, latent vines over the maximum number of vines l_h and infected vines over the maximum number of vines i_h. Denoted as N_h/N_h0 is the number of vines in the population at a given time over the maximum number of vines. To obtain the equilibria at different GWSS densities, a numerical simulation was run with each value, starting from an initial low level of infection (i_v = 0.1 and s_h = 1) until the system had converged to a steady state. Other parameter values remain as in Table 5. The plot shows that PD becomes endemic at a GWSS density of ~0.01 GWSS per vine.

Figure 4

A numerical simulation of the model, with parameter values given in Table 5, in order to confirm the existence of a stable endemic equilibrium. The initial conditions for the state variables (Table 3) were: S_h = 10,000; L_h = 0; I_v = 0; S_v = 18,000; I_v = 2,000. The plot shows that a stable endemic equilibrium is indeed established within ~2 years for both the GWSS and vine populations (A,B, respectively).

Figure 5

The basic reproduction number R₀ indicates whether a disease can establish itself in a healthy population through an initial infection. Namely when R₀ < 1, the disease-free equilibrium of the whole system, $i_v,N_v,s_h,l_h,i_h=(0,N_v^{*},s_h^{*},0,0),$ is stable and a small number of infected individuals will not cause endemic PD. GWSS density is defined as $N^{*}/N_{h0}$, which is the relation between the equilibrium total number of GWSS, N^*, and the maximum number of vines N_h0. The plot shows how the combined increase in GWSS density and probing rate positively affects R₀. The rest of the model parameters are fixed to the values given in Table 5.