From Stephen Toulmin's Book The Uses of Argument Cambridge University Press 2003. See wikipedia Also Francis Miller Claim Hexagon 2025 web article
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.
- http://www.nku.edu/~longa/classes/2020spring/mat375/mathematica/SIRModel-MAA.nb
- https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-the-differential-equation-model
Details:
<!--[if !supportLists]-->- <!--[endif]-->This model shows the effect of ‘reinvestment program ‘or the expenditure on policing and community development affects the cycles of petty-crime and youth detention, and domestic violence and jail.
More details:
<!--[if !supportLists]-->- <!--[endif]--> Bourke is a town of 3000 people in the North West of New South Wales, about 750Km from Sydney. See the map: https://goo.gl/maps/VgNqgMNzJ7H2. It’s nowhere and there’s not much to do there if you’re young. So, a lot of kids get into mischief, and a lot of adult’s drink. Sometimes they’re violent.
<!--[if !supportLists]-->- <!--[endif]-->http://www.justreinvest.org.au/justice-reinvestment-in-bourke/
Assumption:
<!--[if !supportLists]-->· <!--[endif]-->Bourke Funding consist of Law enforcement funding and Community Development funding only
<!--[if !supportLists]-->o <!--[endif]-->Bourke budget only has $400,000
<!--[if !supportLists]-->· <!--[endif]-->Juvenile detention stay last for 6 months
<!--[if !supportLists]-->· <!--[endif]-->There is only 2 options as a Youth, commit petty crime or engage in Youth development programs
<!--[if !supportLists]-->· <!--[endif]-->1 unit of Police, Juvenile and Educational program HR and Equipment is = 0.25
<!--[if !supportLists]-->o <!--[endif]-->1 unit increase results in an 0.25 effectiveness increase
<!--[if !supportLists]-->· <!--[endif]-->Sport clubs, educational programs and social programs are comprised into Youth Development Program as 1 stock.
<!--[if !supportLists]-->· <!--[endif]-->Juvenile support relies on encouraging youth who are in detention centers to join youth development programs, if not they will reoffend.
Stocks:
<!--[if !supportLists]-->o <!--[endif]-->Home
<!--[if !supportLists]-->o <!--[endif]-->Youth Development program
<!--[if !supportLists]-->o <!--[endif]-->Discharged
<!--[if !supportLists]-->o <!--[endif]-->Juvenile detention center
<!--[if !supportLists]-->o <!--[endif]-->Petty Crime
Variable:
<!--[if !supportLists]-->· <!--[endif]-->Reinvestment Allocation – ranges from 0 – 1 , law enforcement investment allocation is 1 – reinvestment allocation. Slide the slider through 0 to 1 to change the reinvestment allocation by 10% l
<!--[if !supportLists]-->· <!--[endif]-->Bourke funding budget is fixed to make it seem more realistic (imagine employing a whole army of teachers or police, it wouldn’t make sense)
<!--[if !supportLists]-->· <!--[endif]-->Youth Population varies , from 1000 to 10,000 for realism along with its time period (4 years). Slider the the slider to increase or decrease the population by 1,000s
Juvenile support effectiveness rate, Youth development program effectiveness rate, conviction rate, Police HR/ equipment, Juvenile Support HR/ equipment, Youth Development program HR/ equipment
Interrelationship and reinforcing loops
<!--[if !supportLists]-->· <!--[endif]-->The youth population starts as as Neutral (Home) then leans towards alienation and connectedness
<!--[if !supportLists]-->· <!--[endif]-->Alienation Reinforcing Loop - Alienation has Conviction rate as a factor as conviction rate increase Alienation increase. This is because as youths get arrested, meaning they’ll have to stay in Detention centers, their friends are more likely to follow on due to them getting ‘bored’.
<!--[if !supportLists]-->· <!--[endif]-->Connectedness Reinforcing Loop - The opposite exist with Connectedness, as educational program effectiveness increase so as Connectedness. This follows onto the same assumption that youth will always follow peer pressure. The more friends they have in the program, the more likely they will join aswell.
Analysis:
<!--[if !supportLists]-->1. <!--[endif]-->Which loop is the youth in?
<!--[if !supportLists]-->· <!--[endif]-->Once the allocation slider is used with its minimum or maximum value, the loop at which majority of the youth population is ‘stuck in’ becomes obvious. E.g. Once allocation = 1, the entire youth is stuck between educational program and their home, showing the effectiveness of community development funding. On the other hand, once allocation = 0, the entire youth loops around from doing Petty Crimes, spending their time in Juvenile detention centers, then getting discharged to only commit petty crimes again.
<!--[if !supportLists]-->2. <!--[endif]-->Alienation vs. Connectedness
<!--[if !supportLists]-->· <!--[endif]-->Set the allocation slider on 0.8, The massive difference between the youth of population feeling connected with their community and youth being alienated can be seen. The increase in Reinvestment, the increase in connectedness. Try the extremes as well, 100% reinvestment funding results in 0 Alienation rate.
<!--[if !supportLists]-->3. <!--[endif]--> What is the Youth Engaged in ? Educational Programs or Petty Crime ?
<!--[if !supportLists]-->· <!--[endif]-->Leaving the slider on 0.8, it can be seen that the there are more youth engaged into educational programs than petty crime. This shows that reinvestment and petty crime has a negative relationship .
<!--[if !supportLists]-->4. <!--[endif]-->More police = safer ?
<!--[if !supportLists]-->- <!--[endif]-->Set the slider on 0.1 , it can be seen that Conviction which has police as a factor is positively correlated to Crime. This means that an increase in conviction rate is equivalent to more youth being alienated and committing crime. Therefore, more police less safer.
Have fun!
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.
I start with these parameters:
Wolf Death Rate = 0.15
Wolf Birth Rate = 0.0187963
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 logistic, MBR*M*(1-M/K)
Moose death flow is Kill Rate (in Moose/Year)
Wolf birth flow is WBR*Kill Rate (in Wolves/Year)
Wolf death flow is WDR*W
