Portions
Government statistics from the Australian Bureau of Statistics (ABS) show that Bourke Shire Regional Council has approximately 3000 residents, made up of 65-63% adults and 35-37% youths.
Crime Rate
Police variable is in the denominator to create a hyperbolic trend. The aim was to achieve a lower crime rate if police expenditure was increased, thus also a higher crime rate if police expenditure was decreased. The figure in the numerator can be changed with the ‘maximum crime rate’ variable which represents the asymptotic crime rate percentage. Where police = 100 the selected crime rate is maximised.
Avoiding Gaol
Originally the formula incorporated the police as a variable, where the total amount of convicted crimes was subtracted from the total amount of crimes committed. However, the constant flow of crimes from repeat offender/a created an unrealistic fluctuation in the simulation. I settled for a constant avoidance rate of 25%. This assumes that an adult or youth committing a crime for the first time is just as likely to avoid conviction as a repeat offender.
Conviction
It is difficult to predict in a mathematical model how many adults or youths are convicted of crimes they commit. I determined a reasonable guess of maximum 75% conviction rate when Police = 100. In this formula, decreasing police spending equates into decreased conviction rate, which is considered a realistic representation.
Released
It is assumed that the average sentence for a youth is approximately 6 months detention. For an adult, it will be assumed that the average sentence is 12 months gaol. The discrepancy is due to a few basic considerations that include 1. Adults are more often involved in serious crime which carries a longer sentence 2. youths are convicted with shorter sentences for the same crime, in the hopes that they will have a higher probability of full rehabilitation.
Engagement
Rate of adult/youth engagement was estimated to be a linear relation. The maximum rate of engagement, assuming expenditure = 100, is set to 80%. This rate of engagement is a reasonable guess with consideration that there will also exist adults who refused to engage in the community and end up in crime, and adults or youth that refuse to engage in the community or crime.
Boredom
Engagement Expenditure variable is in the denominator to create a hyperbolic trend. The aim was to achieve a lower boredom rate with a higher engagement expenditure, and thus a higher boredom rate with a lower engagement expenditure. The figure in the numerator of 25 represents the asymptotic boredom rate percentage, where if engagement expenditure = 100 the adult/youth boredom rate is maximised at 25%.
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
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
power model - 12*0.1251361120909615*([Moose]/[Wolves])^.44491970277839954*[Wolves]
Kill rate sqrt = 12*(0.0933207+.0873463*([Moose]/[Wolves])^.5)*[Wolves]
Holling Type III - ((0.986198*([Moose]/[Wolves])^2)/ (601.468 +([Moose]/[Wolves])^2))*[Wolves]*12
linear - 12*[Wolves]*(.400271+.00560299([Moose]/[Wolves]))
This model depicts the complex relationships between crime, number of police, investment in community development programs and the youth population of the small country town, Bourke.
In this system dynamics model, the user can observe how modifying the spending on community development programs and changing the number of police in the town affects the crime rate and the engagement of youth.
These variables can be altered using the sliders which are provided underneath the notes. The model runs for a period of 5 years. This was deemed the optimal time during which any generational changes could be observed.
The model is explained with more detail below, along with any assumptions and their appropriate reasoning.
Variables
Investment in Community Development Programs
It is assumed that the minimum that can be invested is $1000 and the maximum is $100 000.
Number of Police
It is assumed that the minimum number of police officers that can be present in Bourke is 10 and the maximum is 100.
Stocks and Flows
Bourke Population
The population of Bourke is set as 3000 as stated in the Justice Reinvestment document.
Boredom and lack of opportunity leads to
This flow is given the equation: (50000/[Investment in Community Development Programs])* 2. The greater the investment in community development programs, the lesser the number of youths who are bored.
Disengaged and Alienated Youth
Since there are not many activities for young adults (as stated in the Justice Reinvestment document), it is assumed that they are all currently disengaged and alienated. The disengaged and alienated youth population of Bourke is thus set as 1000 before the model is run.
Petty Crime
Since the youth crime rate for Bourke is quite high, it was assumed that 800 out of the 1000 youth would engage in petty crime. This is before any additions to the police force or increase in community development programs investment.
Commit
This flow is dependent on both the number of disengaged youth and the number of police. The more police that are present in Bourke, the more disengaged the youth become. This ensures that the level of petty crime committed is directly related to the number of police officers.
Convicted
This flow is given a constant rate of 7*[Number of Police] + (0.1*[Petty Crime]). This means that the greater the number of police officers present, the greater the number of convictions. It also means that at the highest number of police officers available (100), the highest the number of convictions is 700 + 10% of youths who commit a crime. Since the model assumes that there are 800 youths committing crime at the beginning of the models’ commencement, it realistically represents the police’s inability to catch ALL criminals.
Not Convicted
This flow has the equation ([Petty Crime]/[Number of Police])*2. Since the number of police is in the denominator, the lower the number, the higher the number of delinquents who are not convicted. This attempts to keep the model realistic. At the maximum level of 100 police officers, there will still remain some delinquents who escape conviction and this remains true to life.
Lesson Learnt
Since youth crime is so rife in Bourke, it is assumed that only 20% of offenders in the juvenile detention centre learn their lesson and never commit crime again. This was done to simplify the modelling.
Still Disenchanted
It is assumed that 80% of offenders do not learn their lesson after their time in the juvenile detention centre.
Feel Estranged
This flow is given the equation: [Number of Police]*5 + 50/([Investment in Community Development Programs]/1000).
Thus, the higher the number of police, the greater the number of youths who feel estranged. The greater the investment in community development programs, the lesser the number of youths who feel estranged.
Participate and engage in
This flow is dependent on the level of investment in community development programs. The greater the investment, the greater the participation. This is realistic as the more money is spent on such programs, the more interested that youths will be in participating.
Develop Inter-community relationships
It is estimated that the majority of youths who participate in community development programs will develop inter-community relationships. This model assumes that such programs will be largely successful in encouraging social harmony amongst the youths.
Relapse
However, youths
participating in the community development programs may relapse and head back
into the path of crime. However, this is assumed to only be a small minority (1/8
of those who participate).
Interesting Observations
1) Number of Police: 10 (minimum)
Investment in Community Development Programs: $1000 (minimum)
It is important to note that even the minimal amount of investment in community development programs is enough to cause the crime rate to decrease, to the point where, after 3 years, there are more youths who are Reformed and Engaged than those involved in Petty Crime. However, the number of youths who are Reformed decreases after some time, indicating greater investment is needed. Somewhat surprisingly, the number of youths who are involved in the community development programs is at its highest, further suggesting the need for increased investment.
2) Number of Police: 100 (maximum)
Investment in Community Development Programs: $1000 (minimum)
Predictably, Petty Crime has drastically decreased, and in a much shorter time than when there were only 10 police officers. The number of youths who are Reformed and Engaged and those who are involved in the Community Development Programs has also increased, but they are not as high as in the previous observation, most likely due to increased alienation caused by the high police presence.
3) Number of Police: 10 (minimum)
Investment in Community Development Programs: $100 000(maximum)
Quite surprisingly, Petty Crime has decreased drastically, despite the low number of police officers present in Bourke. This shows that the large sums of money being invested in the Community Development Programs has created a social change within the town’s youth population with high numbers of youths participating in these programs and thus becoming Reformed and Engaged. Another interesting aspect is that while the number of youths participating in the programs reduces to zero at the end of the fifth year, the number of youths who are Reformed and Engaged is at an all time high.
4) Number of Police: 100 (maximum)
Investment in Community Development Programs: $100 000 (maximum)
While Petty Crime has decreased significantly, the number of youths who are Reformed and Engaged and those who participate in Community Development Programs is not as high as Scenario 3. Extremely large numbers of youths are also spending time in the Juvenile Detention Centre during the first 2 years of the 5-year model. While repeat offences are low, this may be more due to fear of police brutality and the prospects of harsher sentences than any conscious effort on the youth population’s part to be more harmonious members of society.
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
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
- 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
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
**Scroll down for adjustable sliders**
Key Assumptions & Things to Note:
-Model interactions and consequences only focused on the effects of youth not adults.
-Total youth population assumed to be 1,500 out of the total 3,000 people in Bourke
-Model moves in monthly increments
-Model duration is 5 years (60 Months) as this seems like a realistic time frame for such a project plan to span over
-Engagement return modification allows between 0 and 6 months return to allow insight into the positive effects a shorter engagement time can have on the community
-Police Investment allows adjustment of police force units between 15 and 50
-Community Investment allows an investment of between 0 and 100 to provide a full spectrum of the town with or without investment
Model Prerequisite Understandings:
The model commences with 400 people engaging in criminal activity, and a further 300 people already in juvenile detention to provide a more realistic start point.
Model Analysis:
The most important message this model shows is that there is no one sided solution for everything. Without community investment, regardless of how many police you have the town is still going to be full of bored people committing crimes - just more will be caught and convicted.
On the flip side a town with no police and only community investment may have a low rate of people in juvenile detention and a high number of people in sports teams - but criminal activity may still be higher than optimal due to a low chance of getting caught.
You can see these results for yourselves simply by adjusting the variable sliders on the bottom right of the page to suit your investment interests. Relevant boundaries have been set to give only useful and meaningful information. Furthermore an engagement return tool has been added to show the effects of a slow or fast engagement pickup time ranging from 0 to 6 months. You will note that things change a lot quicker with a shorter engagement return time.
An interesting thing to note is how evenly 3 of the 4 key data fields in the first simulation display (with the outlier being sports team enrolment) when police investment is set to maximum and community investment is set to the minimum - we see essentially an even split between the 3 possibilities: In town, In Juvenile Detention or engaging in Criminal Activity. a 2:1 split of "bad" to "good" things happening. This shows with certainty that just adding policing with no positive reward or outlet for good behaviour results in a flattened cycle of boredom, criminal activity and conviction.
In this model it also seems that Bourke does require a fairly even but high matching of Police and Community Investment. For example setting the policing at 20 and the community engagement higher at say 50 results in indeed a high intake and output of town to sports team memberships however crime rates do still maintain a steady high dictating a more even match between policing and community investment like 40 and 60 to the former and latter to "eradicate" crime. (Of course this will never be 0 in the real world but it is a positive indicator here)
