We start with an SEIR social virality model and adapt it to model social media adoption of Playcast Hosts.  *Note that this model does not attempt to model WOM emergent virality.  

We start with an SEIR social virality model and adapt it to model social media adoption of Playcast Hosts.  *Note that this model does not attempt to model WOM emergent virality.  

Based on the Market and Price simulation model in System Zoo 3, Z504. I made some more intrusive changes that make the model more realistic, or more 'economic', in another version 'simplified and improved'. 
Based on the Market and Price simulation model in System Zoo 3, Z504. I made some more intrusive changes that make the model more realistic, or more 'economic', in another version 'simplified and improved'. 
Multilevel context mechanisms and outcomes for hospital infection control
Multilevel context mechanisms and outcomes for hospital infection control
  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 program

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.

 Spring, 2020:       With the onset of the Covid-19 coronavirus crisis, we focus on SIRD models, which might realistically model the course of the disease.     We start with an SIR model, such as that featured in the MAA model featured in   https://www.maa.org/press/periodicals/loci/joma/the-sir-mod
Spring, 2020:

With the onset of the Covid-19 coronavirus crisis, we focus on SIRD models, which might realistically model the course of the disease.

We start with an SIR model, such as that featured in the MAA model featured in

Without mortality, with time measured in days, with infection rate 1/2, recovery rate 1/3, and initial infectious population I_0=1.27x10-6, we recover their figure

With a death rate of .005 (one two-hundredth of the infected per day), an infectivity rate of 0.5, and a recovery rate of .145 or so (takes about a week to recover), we get some pretty significant losses -- about 3.2% of the total population.

Resources:
​ The Model      The model displayed depicts the interaction that the youth of Bourke has with the justice system and focuses on how factors like policing and community development affect the crime rate within this area. Bourke is a rural town that has a significant crime rate among youth. Local com
The Model

The model displayed depicts the interaction that the youth of Bourke has with the justice system and focuses on how factors like policing and community development affect the crime rate within this area. Bourke is a rural town that has a significant crime rate among youth. Local community members call for action to be taken in regards to this, meaning that steps must be taken to reduce the crime rate. This simple model explores how the amount of police and the investment of community development can have an effect on the town in regards to its issue of crime among youth.


Assumptions
  • Bourke's youth population is 1200, with 700 in town, 200 committing crimes and 300 already in jail
  • The amount of police, the expenditure on community development, and the domestic violence rate are the factors which have the potential to influence youth to commit crimes. The domestic violence rate is also influenced by the expenditure on community development.
  • Sporting clubs, interpersonal relationships between youth and police, and teaching trade skills all make up community expenditure
  • Activities relating to expenditure on community development run throughout the year, indicating that there is no delay where youth are not involved in these activities.
  • Every 6 months, only 60% of jailed youth are released. This may be for various factors such as committing crime in jail or being issued with lengthier sentences due to the severity of the crime(s) committed
  • 10% of youth who agree that domestic violence is an issue at home will commit crime
  • There is a delay of 1 month before youth go to jail for crime(s) committed. This model assumes that youth who have committed crime either return home (by decision or by not being caught) or go to jail. It also assumes that other punishments such as community service refer to returning back home.
  • The simulation takes place over a duration of 5 years (60 months)
  • Adults have little effect on the youth. Only where domestic violence is concerned do they play a factor within this model

How the Model Works

The model begins with the assumptions previously stated. Youth have the potential to commit a crime. 3 main variables influence this decision, including the amount of police, expenditure on community development, and domestic violence rate (which is influenced by the previous variable). These 3 variables are able to be adjusted using the relevant sliders with 0.5 indicating a low investment and 0.9 indicating a high investment. Police also have an influence on this decision. This variable is also able to be adjusted by a slider. Last of all, the domestic violence rate also contributes to this decision and this variable is negatively influenced by community development.

Once a youth has committed a crime they are either convicted and sent to jail or return back to town. The conviction rate is also influenced by the amount of police in town, as youth are more likely to get caught and thus jailed. Once again, the Police variable is able to be adjusted via the slider. This process takes a month.

From here, youth typically spend 6 months in jail. After this time period 60% are released while the remaining 40% remain in jail either due to lengthier sentences for more severe crimes or due to incidents within jail. The process then repeats.


Parameter Settings and Results
  • Initially there is a state of fluctuation within this model. It may be a good idea to ignore it and pay attention to how variables change over time from their initial state
  • Increasing the amount of police will raise the amount of people jailed and decrease crime
  • Increasing the community development variables from a minimal investment (i.e. set at 0.5) to a high investment (i.e. set at 0.9) will reduce both the crime rate and the conviction rate. It is worth noting that the community development variable also influences the domestic violence rate variable which also has an effect on the results
  • If only 2 of the 3 community development variables have a high investment then there is not much effect on the crime rate or jail rate. All 3 variables should be given the same level of investment to give us a desired outcome
  • The model does allow for a maximum of 40 police (as we do not want to spend more money on police than we already have in the past), as well as the maximum investment for community development. When choosing settings it may be necessary to ponder if it is financially realistic to maintain both a large number of police as well as investing heavily into community development
This simulation allows you to compare different approaches to influence flow, the Flow Times and the throughput of a work process.   By adjusting the sliders below you can    observe the work process  without  any work in process limitations ( WIP Limits ),   with process step specific WIP Limits* (
This simulation allows you to compare different approaches to influence flow, the Flow Times and the throughput of a work process.

By adjusting the sliders below you can 
  • observe the work process without any work in process limitations (WIP Limits), 
  • with process step specific WIP Limits* (work state WIP limits), 
  • or you may want to see the impact of the Tameflow approach with Kanban Token and Replenishment Token 
  • or see the impact of the Drum-Buffer-Rope** method. 
* Well know in (agile) Kanban
** Known in the physical world of factory production

The "Tameflow approach" using Kanban Token and Replenishment Token as well as the Drum-Buffer-Rope method take oth the Constraint (the weakest link of the work process) into consideration when pulling in new work items into the delivery "system". 

You can also simulate the effects of PUSH instead of PULL. 

Feel free to play around and recognize the different effects of work scheduling methods. 

If you have questions or feedback get in touch via twitter @swilluda

The work flow itself
Look at the simulation as if you would look on a kanban board

The simulation mimics a "typical" software delivery process. 

From left to right you find the following ten process steps. 
  1. Input Queue (Backlog)
  2. Selected for work (waiting for analysis or work break down)
  3. Analyse, break down and understand
  4. Waiting for development
  5. In development
  6. Waiting for review
  7. In review
  8. Waiting for deployment
  9. In deployment
  10. Done
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 websi
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.

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

           This version of the   CAPABILITY DEMONSTRATION   model has been further calibrated (additional calibration phases will occur as better standardized data becomes available).  Note that the net causal interactions have been effectively captured in a very scoped and/or simplified format.  Re
This version of the CAPABILITY DEMONSTRATION model has been further calibrated (additional calibration phases will occur as better standardized data becomes available).  Note that the net causal interactions have been effectively captured in a very scoped and/or simplified format.  Relative magnitudes and durations of impact remain in need of further data & adjustment (calibration). In the interests of maintaining steady progress and respecting budget & time constraints, significant simplifying assumptions have been made: assumptions that mitigate both completeness & accuracy of the outputs.  This model meets the criteria for a Capability demonstration model, but should not be taken as complete or realistic in terms of specific magnitudes of effect or sufficient build out of causal dynamics.  Rather, the model demonstrates the interplay of a minimum set of causal forces on a net student progress construct -- as informed and extrapolated from the non-causal research literature.
Provided further interest and funding, this  basic capability model may further de-abstracted and built out to: higher provenance levels -- coupled with increased factorization, rigorous causal inclusion and improved parameterization.
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 websi
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.

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

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 websi
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.

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