This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.

We incorporate logistic growth into the moose dynamics, and we replace the death flow of the moose with a kill rate modeled from the kill rate data found on the Isle Royale website.

A decent match to the data is made with
Wolf Death Rate = 0.15
Wolf Birth Rate Factor = 0.0203
Moose Death Rate Factor = 1.08
Moose Birth Rate = 0.4
Carrying Capacity = 2000
Initial Moose: 563
Initial Wolves: 20

I used RK-4 with step-size 0.1, from 1959 for 60 years.

The moose birth flow is MBR*M*(1-M/K)
Moose death flow is MDRF*Sqrt(M*W)
Wolf birth flow is WBRF*Sqrt(M*W)
Wolf death flow is WDR*W

About the Model

This model is designed to simulate the youth population in Bourke, specifically focusing on the number of criminals and incarcerated dependent on a few key variables.

Within the model, a young person living in Bourke can be classified as being in any of five states:

Young Community Member: The portion of the youth population that is not committing crime and will not commit crime in the future. Essentially the well behaved youths. A percentage of these youths will become alienated and at risk.

Alienated and At Risk Youths: The youths of Bourke that are on the path of becoming criminals, this could be caused by disruptive home lives, alcohol and drug problems, and peer pressure, among other things.

Criminal: The youths of Bourke who are committing crimes. Of these criminals a percentage will be caught and convicted and become imprisoned, while the remainder will either go back to being at risk and commit more crimes, or change their behaviour and go back to being a behaving community member.

Imprisoned: The youths of Bourke who are currently serving time in a juvenile detention centre. Half of the imprisoned are released every period at a delay of 6 months.

Released: Those youths that have been released from a detention centre. All released youths either rehabilitate and go back to being a community member or are likely to re-offend and become an alienated and at risk youth.

The variables used in the model are:

Police- This determines the police expenditure in Bourke, which relates to the number of police officers, the investment in surveillance methods and investment in criminal investigations. The level of expenditure effects how many youths are becoming criminals and how many are being caught. An increase in police expenditure causes an increase in imprisoned youths and a decrease in criminals.

Community Engagement Programs- The level of investment in community engagement programs that are targeted to keep youths in Bourke from becoming criminals. The programs include sporting facilities and clubs, educational seminars, mentoring programs and driving lessons. Increasing the expenditure in community engagement programs causes more young community members and less criminals and at risk youths.

Community Service Programs- The level of investment in community service programs that are provided for youths released from juvenile detention to help them rehabilitate and reintegrate back into the community. An increase in community service expenditure leads to more released prisoners going back into the community, rather than continuing to be at risk. Since community service programs are giving back to the community, the model also shows that an increase in expenditure causes a decrease in the amount of at risk youths.

All three of these variables are adjustable. The number of variables has been kept at three in order to ensure the simulation runs smoothly at all times without complicated outputs, limitations have also been set on how the variables can be adjusted as the simulation does not act the same out of these boundaries.

Key Assumptions:

The model does not account for the youths’ memory or learning.

There is no differentiation in the type of criminals and the sentences they serve. Realistically, not all crimes would justify juvenile detention and some crimes would actually have a longer than six-month sentence.

The constants within in the calculations of the model have been chosen arbitrarily and should be adjusted based on actual Bourke population data if this model were to be a realistic representation of Bourke’s population.

The model assumes that there are no other factors affecting youth crime and imprisonment in Bourke.

There are 1500 youths in Bourke. At the beginning of the simulation:

Young Community Member = 700

Alienated and At Risk Youth = 300

Criminal = 300

Imprisoned = 200

Noteworthy observations:

Raising Police expenditure has a very minimal effect on the number of at risk youths. This can be clearly seen by raising Police expenditure to the maximum of twenty and leaving the other two variables at a minimum. The number of Alienated and at Risk Youths is significantly higher than the other states.

Leaving Police expenditure at the minimum of one and increasing community development programs and community service programs to their maximum values shows that, in this model, crime can be decreased to nearly zero through community initiatives alone.

Leaving all the variables at the minimum position results in a relatively large amount of crime, a very low amount of imprisoned youth, and a very large proportion of the population alienated and at risk.

An ideal and more realistic simulation can be found by using the settings: Police = 12, Community Engagement Programs = 14, Community Service Programs = 10. This results in a large proportion of the population being young community members and relatively low amounts of criminals and imprisoned.

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This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.

Experiment with adjusting the initial number of moose and wolves on the island.

Documentation

Modified from Sterman (2006) article and Gene Bellinger's Assumptions IM-351 by Dr Rosemarie Sadsad UNSW See also Complex Decision Technologies IM and IM-63975