## Simulation 4 Simulating the use of pesticide to control an insect population

We have already a model to simulate the development of an insect pest population (see Simulation 3). Now let's see how we can simulate what happens if a farmer sprays pesticides to control the pest. We will have to decide when to spray, and we have to decide the effect of the spray. Let's look at two different scenarios. In the first scenario the farmer uses "calendar spraying". This means that he will spray at fixed intervals, regardless of the population size. In the second scenario the farmer will only spray if the pest population has reached a certain level or threshold. In both simulations the objective of the farmer is to keep the pest population below a certain level, which is lower than K

For the "calendar spray" the model will work with the following parameters:

For the population growth (see equation [7]) we need:

N_{0 }= Population size
at the start of the simulation.

N_{t }= Population size at time t (after t
days)

b = Birth factor

m = Mortality factor

r = b-m = Reproduction factor

K = Carrying capacity of the environment

For pesticide application:

f = First spray date (days after start
of the simulation)

i = Spray interval (every i days the spray will be repeated)

p = Percentage killed by the pesticide application

The model is very straightforward. After calculating the population development up to day (f) it will reduce the population size by (p) percent. The population growth continues with that new size for (i) days, when the next spray is applied, and so on. The equation to calculate the effect of pesticide spray is:

[8] Nt = Nt × (100-p)/100

In simulation 4 you can try this with some different parameters. You can change the default settings, then run the simulation.

### Simulation 4

This simulation shows maximum 300 days.

The simulation ends when the population size is above 10,000,000
or below 1.

If you try different parameters you will find that it is possible to keep the population below a certain level, which is what a farmer would want to do if he repeatedly sprays his crop. That level depends on the interval and the efficiency of the pesticide application. You will also find out that if you spray very frequently or with a very efficient pesticide, you would be able to completely wipe out the population. This of course is not a realistic situation because in a real farmer's field new pest insects would migrate into the field and population growth would start again. That's why later on we will have to include migration into the model.

Let's look at another spraying strategy.

Go to Simulation 5: Pesticide applications at a threshold level.

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