**2.1 Framework of the model and estimation of the parameters**

In this simulation, we targeted the region of the Mekong Delta, Vietnam, in order to establish the basic parameters. Some parameters were provided by previous reports and some by our own observations in the target area. The model is summarized in Fig. 1.

From Kobori et al. (2010).

Fig. 1. (a) Change in tree status over time. (b) Summary of citrus greening disease-spread simulation by our model.

Development of an Individual-Based Simulation Model

between trees.

Ratio of *D. citri* remaining on trees on which they developed

tree. From Kobori et al. (2011a).

intervals (for the marking method, see Nakata, 2008).

plants, they too hardly moved again.

for the Spread of Citrus Greening Disease by the Vector Insect *Diaphorina citri* 91

prevent adult movement between trees. These results suggest that adult *D. citri* do not select trees with new buds from a distance but recognize them by means of random movement

Solid lines: trees with buds; broken lines: trees without buds; N: initial number of adult *D. citri* on the

Fig. 2. Relationship between the number of days and the number of migrating adult *D. citri*.

Through artificial release experiments, we estimated mean dispersal distance, frequency of movement and dispersal direction (Kobori et al., 2011b). We artificially released, in separate experiments, 10,000 and 1,000 adult *D. citri*, marked in pink, at the center of the experimental field, in which 33 X 33 potted host plants were set out in a grid at 2.5 m

In the 10,000-adult experiment, the mean dispersal distance from the release point was 5-6 m, and in the 1,000-adult experiment it was 6-12 m. In each case, the proportion of *D. citri* found on different days over the experimental periods declined with increasing distance from the release point, and did not change substantially over time (Fig. 4). These results suggested that once the adult *D. citri* arrived on the host plants they hardly moved again. Moreover, the center of distribution would be expected to move with the wind direction, if each *D. citri* continued its random movement, because the same wind direction was observed throughout most of each experimental period; however, the center of distribution in fact stayed close to the release point throughout the experimental periods (Fig. 5). Individuals that moved more than 7.5 m from the release point were found on the lee side. These results suggested that once *D. citri*, here carried by the wind, had arrived on the host

High density, N=106 Low density, N=65 Low density, N=67 High density, N=109

High density, N=104 High density, N=108 Low density, N=65

Low density, N=61

(Days)

We assumed that the citrus trees were arranged in a two-dimensional regular lattice, with the position of a given tree as '(x, y)', where x and y are integers, and –*L* ≤ x ≤ *L* and –*M* ≤ y ≤ *M* determines the spatial dimensions of the lattice. The distance between trees was assumed to be 2.5 m, in accordance with the common planting regime in the region. We assumed a discrete time progression defined by one month (*t*).

Tree status was defined as one of the following: (1) healthy period (*H*), when the tree is healthy and has the potential to be infected with HLB by the feeding of virulent *D. citri*; (2) latent period (*LP*), when the tree has been infected with HLB by *D. citri* but still does not have infective ability; (3) infectious period (*IP*), when the *D. citri* growing on the tree have the potential to transmit HLB with a probability of *V*; and (4) dead period (*D*), when the tree is dead or there is no tree at the given point in the lattice. The value *V* was estimated at 0.9 from our aforementioned previous study (Ohto & Kobori, unpublished data). Transition through these tree statuses is irreversible: *H*→*LP*→*IP*→*D*. There have been few previous reports that estimated the latent and infectious periods of HLB. The growth stage, cultivar and environmental differences of the host plant may affect these, but we do not know the details. Hence, in this model, we estimated the default values, based on our own field observation and a survey questionnaire conducted in Vietnam, as the following: the *LP* tree essentially changes status to *IP* in 3*t*, and the *IP* to *D* in 45*t* (Fig. 1 (a)).

The vector insects are assumed to move around according to a given dispersal kernel. We discuss the determination of this kernel in Section 2.2. If the insect is virulent, it transmits HLB with a probability of *Tr* to tree *H*. In this report, we set *Tr* at 0.3, in accordance with our aforementioned previous study (Ohto & Kobori, unpublished data). A vector insect individual produces an average of *Rp* next-generation individuals according to Gaussian distribution. In this report we assumed an *Rp*-value of 10, in accordance with our life-table study in Japan (Kobori, un-published data) and similar observations in Vietnam. We also established a threshold number, of 100 individuals of the next generation on a given tree, from our observations in Vietnam.

To exclude edge and corner effects associated with a rectangular two-dimensional space, the model space was assumed to be a torus. In addition, we distributed enough *D* trees around the simulation to prevent adults from arriving at the edge.

## **2.2 Determination of the dispersal kernel**

To determine the dispersal kernel of the *D. citri*, we carried out choice and no-choice tests in a glass house, and artificial release experiments in the experimental field in Japan.

In the glass house, we estimated factors affecting the dispersal activity of *D. citri*, first by means of a no-choice test. Movement from a 'growth' tree (that is, one on which the *D. citri* has grown from egg to adult) to another tree was observed, in time, for each situation (Kobori et al., 2011a). We examined high – low insect density situations, and new-bud – nonew-bud situations, for the growth tree. The dispersal movement of the adult *D. citri* was greater for trees with new buds than for trees without new buds (Fig. 2). The effects of *D. citri* density were not detected in this experiment. Additionally, we investigated host-plant selection by *D. citri* through choice tests (Fig. 3). Choice testing between trees with and without buds revealed that released adults preferred trees with buds during the testing period. This preference disappeared when both trees were treated with a sticky spray to

We assumed that the citrus trees were arranged in a two-dimensional regular lattice, with the position of a given tree as '(x, y)', where x and y are integers, and –*L* ≤ x ≤ *L* and –*M* ≤ y ≤ *M* determines the spatial dimensions of the lattice. The distance between trees was assumed to be 2.5 m, in accordance with the common planting regime in the region. We assumed a

Tree status was defined as one of the following: (1) healthy period (*H*), when the tree is healthy and has the potential to be infected with HLB by the feeding of virulent *D. citri*; (2) latent period (*LP*), when the tree has been infected with HLB by *D. citri* but still does not have infective ability; (3) infectious period (*IP*), when the *D. citri* growing on the tree have the potential to transmit HLB with a probability of *V*; and (4) dead period (*D*), when the tree is dead or there is no tree at the given point in the lattice. The value *V* was estimated at 0.9 from our aforementioned previous study (Ohto & Kobori, unpublished data). Transition through these tree statuses is irreversible: *H*→*LP*→*IP*→*D*. There have been few previous reports that estimated the latent and infectious periods of HLB. The growth stage, cultivar and environmental differences of the host plant may affect these, but we do not know the details. Hence, in this model, we estimated the default values, based on our own field observation and a survey questionnaire conducted in Vietnam, as the following: the *LP* tree

The vector insects are assumed to move around according to a given dispersal kernel. We discuss the determination of this kernel in Section 2.2. If the insect is virulent, it transmits HLB with a probability of *Tr* to tree *H*. In this report, we set *Tr* at 0.3, in accordance with our aforementioned previous study (Ohto & Kobori, unpublished data). A vector insect individual produces an average of *Rp* next-generation individuals according to Gaussian distribution. In this report we assumed an *Rp*-value of 10, in accordance with our life-table study in Japan (Kobori, un-published data) and similar observations in Vietnam. We also established a threshold number, of 100 individuals of the next generation on a given tree,

To exclude edge and corner effects associated with a rectangular two-dimensional space, the model space was assumed to be a torus. In addition, we distributed enough *D* trees around

To determine the dispersal kernel of the *D. citri*, we carried out choice and no-choice tests in

In the glass house, we estimated factors affecting the dispersal activity of *D. citri*, first by means of a no-choice test. Movement from a 'growth' tree (that is, one on which the *D. citri* has grown from egg to adult) to another tree was observed, in time, for each situation (Kobori et al., 2011a). We examined high – low insect density situations, and new-bud – nonew-bud situations, for the growth tree. The dispersal movement of the adult *D. citri* was greater for trees with new buds than for trees without new buds (Fig. 2). The effects of *D. citri* density were not detected in this experiment. Additionally, we investigated host-plant selection by *D. citri* through choice tests (Fig. 3). Choice testing between trees with and without buds revealed that released adults preferred trees with buds during the testing period. This preference disappeared when both trees were treated with a sticky spray to

a glass house, and artificial release experiments in the experimental field in Japan.

discrete time progression defined by one month (*t*).

from our observations in Vietnam.

**2.2 Determination of the dispersal kernel** 

essentially changes status to *IP* in 3*t*, and the *IP* to *D* in 45*t* (Fig. 1 (a)).

the simulation to prevent adults from arriving at the edge.

prevent adult movement between trees. These results suggest that adult *D. citri* do not select trees with new buds from a distance but recognize them by means of random movement between trees.

Solid lines: trees with buds; broken lines: trees without buds; N: initial number of adult *D. citri* on the tree. From Kobori et al. (2011a).

Fig. 2. Relationship between the number of days and the number of migrating adult *D. citri*.

Through artificial release experiments, we estimated mean dispersal distance, frequency of movement and dispersal direction (Kobori et al., 2011b). We artificially released, in separate experiments, 10,000 and 1,000 adult *D. citri*, marked in pink, at the center of the experimental field, in which 33 X 33 potted host plants were set out in a grid at 2.5 m intervals (for the marking method, see Nakata, 2008).

In the 10,000-adult experiment, the mean dispersal distance from the release point was 5-6 m, and in the 1,000-adult experiment it was 6-12 m. In each case, the proportion of *D. citri* found on different days over the experimental periods declined with increasing distance from the release point, and did not change substantially over time (Fig. 4). These results suggested that once the adult *D. citri* arrived on the host plants they hardly moved again. Moreover, the center of distribution would be expected to move with the wind direction, if each *D. citri* continued its random movement, because the same wind direction was observed throughout most of each experimental period; however, the center of distribution in fact stayed close to the release point throughout the experimental periods (Fig. 5). Individuals that moved more than 7.5 m from the release point were found on the lee side. These results suggested that once *D. citri*, here carried by the wind, had arrived on the host plants, they too hardly moved again.

Development of an Individual-Based Simulation Model

0

0

20

40

Density of adult insects ,

*D*

60

80

(b)

20

40

Density of adult insects ,

*D*

60

80

(a)

for the Spread of Citrus Greening Disease by the Vector Insect *Diaphorina citri* 93

γ was estimated at 0.8 from previous experiments (Fig. 4). As a result of a given movement, the insect lands on the nearest-neighbour host tree. If the insect lands on a *D* tree, the individual moves again without feeding or reproducing, in accordance with the kernel.

0 10 20 30 40

0 10 20 30 40 Distance from the release point (m)

These values were calculated in a one-dimensional cross-section from south to north in the field. Density of adult insects = (number of individuals / total number of the individuals in field) × 100. ▲: 3days, ■: 7 days, ×: 14 days, ●: (a) 20 days, (b) 21 days after release. From Kobori et al. (2011b). Fig. 4. The density of *D. citri* (*D*) found at different time periods, plotted against distance

When the individual lands on an *H*, *LP* or *IP* tree, it does not move again. In the process of moving, individuals have a certain probability (*Dm*) of dying. After reproduction, individuals have a certain probability (*Dl*) of dying; individuals remaining alive (probability

from the release point; (a) 10,000 adults released, (b) 1,000 adults released.

Distance from the release point (m)

Tree with buds: 8 to 10 buds present on the tree; tree without buds: no buds on the tree; other: individuals found on the side wall of the glasshouse or missing inside the glasshouse. From Kobori et al. (2011a).

Fig. 3. Results of a choice test with adult *D. citri* (mean ± S.E.).

In light of the above results, we determined the dispersal kernel. We did not include the effects of vector insect density in the frequency of movement in the kernel. On the other hand, it is highly possible that the existence of new buds affects movement behavior. However, in the Mekong Delta, Vietnam, our targeted area, there are new buds on the host trees almost the entire year. Thus, we did not include bud effects in our model. The direction of movement was isotropic, and the distance of a given movement, r, follows a probability distribution w(r). For the dispersal kernel, we approximated mobility by means of the formula:

$$\mathbf{w}\left(\mathbf{r}\right) = \mathbf{y}^{\mathbf{e}\cdot\mathbf{y}\cdot\mathbf{r}}\tag{1}$$

Tree with buds Tree with buds No-movement Other

N.S.

(a) Tree with buds vs. Tree with buds

p<0.01

(b) Tree with buds vs. Tree without buds

N.S.

Tree with buds Tree without buds Other

No-movement

No-movement

Migration choice

In light of the above results, we determined the dispersal kernel. We did not include the effects of vector insect density in the frequency of movement in the kernel. On the other hand, it is highly possible that the existence of new buds affects movement behavior. However, in the Mekong Delta, Vietnam, our targeted area, there are new buds on the host trees almost the entire year. Thus, we did not include bud effects in our model. The direction of movement was isotropic, and the distance of a given movement, r, follows a probability distribution w(r). For the dispersal kernel, we approximated mobility by means of the

(c) Tree with buds vs. Tree without buds (sticky spray treated)

Other

w (r) = γ e–γ r (1)

Tree without buds (sticky)

Tree with buds: 8 to 10 buds present on the tree; tree without buds: no buds on the tree; other: individuals found on the side wall of the glasshouse or missing inside the glasshouse. From Kobori et

No. of *D. citri*

al. (2011a).

formula:

Tree with buds (sticky)

Fig. 3. Results of a choice test with adult *D. citri* (mean ± S.E.).

γ was estimated at 0.8 from previous experiments (Fig. 4). As a result of a given movement, the insect lands on the nearest-neighbour host tree. If the insect lands on a *D* tree, the individual moves again without feeding or reproducing, in accordance with the kernel.

These values were calculated in a one-dimensional cross-section from south to north in the field. Density of adult insects = (number of individuals / total number of the individuals in field) × 100. ▲: 3days, ■: 7 days, ×: 14 days, ●: (a) 20 days, (b) 21 days after release. From Kobori et al. (2011b).

Fig. 4. The density of *D. citri* (*D*) found at different time periods, plotted against distance from the release point; (a) 10,000 adults released, (b) 1,000 adults released.

When the individual lands on an *H*, *LP* or *IP* tree, it does not move again. In the process of moving, individuals have a certain probability (*Dm*) of dying. After reproduction, individuals have a certain probability (*Dl*) of dying; individuals remaining alive (probability

Development of an Individual-Based Simulation Model


10 20


*t*=12


10 20


(a)

(b)

No. of newly infected trees

simulated field (1,681 trees).

of trees newly infected in the field over time.

than half of the *H* trees had changed status to *LP, IP* or *D*.

for the Spread of Citrus Greening Disease by the Vector Insect *Diaphorina citri* 95

Within 12*t*, more than 10 newly infected trees had appeared in the given field (Fig. 6 (a)). The spread speed increased with time (Fig. 6 (b)). By the end of the calculation period, more



10 20



10 20


10 20



10 20


*t*=72

*t*=24 *t*=36 *t*=48


10 20



10 20


*t*=56 *t*=68 *t*=84

*t*

20 40 60 80

Blue dot indicates Latent Period (*LP*); red: Infectious Period (*IP*), black: Dead (*D*). Healthy (*H*) trees are not shown. Solid line: number of trees newly infected; dotted line: number of initial *H* trees in the

Fig. 6. (a) Snapshots of tree-status distribution for *t*=12, 24, 36, 48, 56, 68, 72, 84. (b) Number

of 1-*Dl*) are integrated into the next generation. There is insufficient previous research to provide estimates for these parameters, and we could not estimate their value by certain observation or experiment. Thus, we roughly estimated these parameters at *Dm*: 0.7 and *Dl*: 0.9 by speculative inference from life-table analysis and our own limited observation in this report (e.g. Mead, 1977; Tsai et al., 2002).

Empty and solid circles indicate 10,000 adults and 1,000 adults released, respectively. The two arrows (solid: 10,000 adults; dashed: 1,000 adults) indicate the composite wind vectors over the experimental periods, as calculated from the daily dominant wind directions. The average velocities were 2.42 m/s in the case of 10,000 adults released, and 3.98 m/s in the case of 1,000 adults released. From Kobori et al. (2011b).

Fig. 5. Center of distribution, over the experimental period, of insects released at the zero coordinate.
