Team:NYMU-Taipei/Project-Model


第一頁

Epidemic

B. dorsalis is a major cause of annual agricultural losses due to oviposition in fruits. We hereby introduce our prototype trap and M. anisopliae, our genetically engineered fungi, to address this issue.
Our model aims to demonstrate that combining our prototype with the fungi can reduce the population of B. dorsalis. We selected and revised the SEIR model, which fits the ideal assumption in epidemiology, to make it more practical for our purpose.

Symbol

Description

Susceptible

B. dorsalis is slightly or moderately resistant to M. anisopliae

Exposed

B. dorsalis is exposed to a low amount of M. anisopliae in our trap; disease will be spread further during mating.

Infected

M. anisopliae enters B. dorsalis’ hemolymph and initiates cell division.

Death

B. dorsalis dies from the infection of M. anisopliae.

Based on our assumptions, we developed a set of differential equations that characterizes the nature of the epidemic in our model:


Parameter


Type

Name

Meaning (Value)

Reference

Constant

Mating　rate

0.8635

 

daily_capture

40

 

daily_move_in

0

 

K

adult death rate (0.05)

[1]

k0

larval death rate (0.23)

[2]

Variable

ms

susceptible male

 

Fs

susceptible female

me

exposed male

Fe

exposed female

mi

infected male

Fi

infected female

D

Death

Result


The graph above shows the initial increase in population due to the attraction of B. dorsalis from the surrounding environment. However, the population subsequently drops when the M. anisopliae infection begin to spread. The results indicate that the use of prototype combined with the fungi yields a 70% decrease in the B. dorsalis population. Thus, we deduce that our product can be deployed in orchards and farms a few weeks prior to harvest to minimize crop damage.


Reference

1. Life History and Demographic Parameters of Three Laboratory-reared Tephritids (Diptera: Tephritidae) R. Vargas - D. Miyashita - T. Nishida - Annals of the Entomological Society of America - 1984

2. Effect of Temperature on the Development and Survival of Immature Stages of the Carambola Fruit Fly,Bactrocera carambolae, and the Asian Papaya Fruit Fly,Bactrocera papayae, Reared On Guava Diet Solomon Danjuma - Narit Thaochan - Surakrai Permkam - Chutamas Satasook - Journal of Insect Science - 2014


另一頁

Purpose

        Our model aims to figure out the efficacy of the IOS system by comparing the population of B. dorsalis with and without this system. Written in NetLogo(1), , a software designed for modeling complex situations, the model combines both stochastic and deterministic methods. The stochastic part of the model was used to estimate the Metarhizium Anisopliae infection by our traps, whereas the deterministic part was used to simulate natural population growth of the flies. The efficiency of our IOS system predicted by this model is further used to analyze the cost-effectiveness of our prototype.

Rules

Assumption

This model follows the assumptions listed below:

  1. The fly influx and efflux are always the same in the orchard.
  2. The mortality caused by naturally existing anisopliae is considered as natural death while the death caused by M.anisopliae inside the traps and its infection afterward is regarded as IOS-caused deaths
  3. The fly population has already reached the stable stage before the start of the simulation.

Natural Condition

The fly population obeys the discrete time logistic function:

  represents the population of fruit flies at time t.

  1. Population of next generation is proportional to that of this generation by the coefficient r.
  2. Population reaches a stable stage regulated by the number of capacity K.
  3. Death caused by naturally existing anisopliae is considered as a part of K.

With IOS system

The addition of our IOS system leads to greater death rate caused by M. anisopliae in our traps and . The additional term is modified from SIR epidemic model:

  1. Male flies within the attraction radius of the methyl eugenol from trap will be attracted to the trap by a certain probability.
  2. After being trapped, male flies will be infected by anisopliae and released later.
  3. Infected males are prone to spread anisopliae conidia to females while mating.
  4. Females are likely to re-mate and thus are likely to spread anisopliae conidia further.
  5. The overall lethality of the infection is described by the formula where  represents the rate of infection spread, and and  represents the population of susceptible and infected flies at  units of time before.

Parameters

Model was a simulation of a one-hectare (100100m) orchard. Four traps and three counters (not shown) were deployed symmetrically in the orchard and their effective distance completely cover all the orchard.

Parameter

Value

Meaning

male-fly-color

blue

 

female-fly-color

yellow

 

counter-color

black

 

r-value

0.17

Growth rate of fly. Calculated value from doubling time(2).

Infection-rate

0.42

M. anisopliae infection spread rate. Calculated value from mating frequency(3).

average-flies-per-day

Depending on simulation conditions

The average population of fly per day.

max-fly-stride

8

The distance a fly flies per day. Assumed value.

M.A.switch

On/off

Our IOS system is implemented when its value is “on”, and the original state is presented when its value is “off”.

fly-initial-amount

360

The initial population of oriental fruit fly in a hectare of orchard. Estimation based on this report(4).

Infective-distance

50

The distance that methyl eugenol in a trap is attractive to a fly.

attraction-rate

0.7

The probability that a male fly within the infective-distance will be attracted toward the closest trap.

base

360

The upper limit of the population in the model orchard environment. Since we presume the population already reached stable state before modeling, its value is exactly the same as fly-initial-amount.

Results

Population of both original state and IOS implementing conditions has been modeled and is shown below.

Scenario 1: the original state of fruit fly population



Scenario 2: fruit fly population after IOS implementation


The original population of fly per day is 355 and this number decreased to 231 after implementation of our IOS system. The population decreased by 35% when our IOS system is implemented, suggesting the high efficiency of our system.

Code

Reference

1. Wilensky, U. (1999). NetLogo.http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

2. Vargas, R. I., Walsh, W. A., Kanehisa, D., Jang, E. B., & Armstrong, J. W. (1997). Demography of Four Hawaiian Fruit Flies (Diptera: Tephritidae) Reared at Five Constant Temperatures.Annals of the Entomological Society of America, 90(2), 162-168. doi:10.1093/aesa/90.2.162

3. Ji, Q. E., Chen, J. H., Mcinnis, D. O., & Guo, Q. L. (2011). The effect of methyl eugenol exposure on subsequent mating performance of sterile males ofBactrocera dorsalis. Journal of Applied Entomology, 137, 238-243. doi:10.1111/j.1439-0418.2011.01686.x

4. 鄭明發.”東方果實蠅防治策略”.台灣柑橘產業發展研究會專刊.