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Assignment 3 – Complex Systems

 Ryan Salvaggio - 43668070

 

The Model

This model conceptualizes the effects on a real-estate market-model utilizing agent based modelling. This model utilizes basic economic principles of supply and demand.

The model bases itself on two Agents - one being ‘Customers’ of the real estate market model, whilst the other being the Real estate itself, coined 'Houses'.

Consumers (Demand)

The Agent population, ‘Consumers’ specifies the total amount of people whom can potentially become buyers within the market. This is limited to 30 for conceptual purposes. The Agent ‘Consumer’ exists in two states, either being an ‘Active Customer’ (Active) or an ‘Inactive Customer’ (Inactive).  The transition from Inactive to Active occurs upon the basis that the ‘Budget’ of the Consumer meets the desired price of the marketplace, this is specified through the variable ‘Budget’ defining the probability that this transition will occur – this is adjustable by the user indicating a highly resistive or by accepting the market. ‘Budget’s probability in a real life scenario would be based upon numerous factors however conceptually utilizing the slider can present many of these various situations.

Upon transitioning into an active state an ‘Active consumer’ will attempt to find the closest ‘For sale household’, this is represented and carried out through the ‘Enter’ action.  Upon finding a household the consumer and house will both return to their respected inactive state thus repeating the process.

Demand – ‘Count of active customers – demand’ is then calculated by a count of Consumers transitioned and currently in the Active state. A high demand would be indicative through a high ‘Budget’ responsiveness whilst a low demand would be indicative of a low ‘Budget’ responsiveness. The increase in Price and hence supply of household thus reduces demand and vise versa.  

House (Supply)

The Agent population, ‘Houses’ specifies the total amount of households that can potentially become for sale within the market. This is limited to 112 for conceptual purposes. The Agent ‘House’ exists in two states, either being ‘For Sale’ (Active) or ‘Not for Sale’ (Inactive).  The transition from Inactive to Active occurs upon the basis that the ‘Motivation to Sell’ of the House is satisfied, this satisfaction is specified by a set probability that this transition will occur – this is adjustable by the user indicating a highly responsive or restricted house market. ‘Motivation to sell’ probability in a real life scenario would be based upon numerous factors however conceptually utilizing the slider can present many of these various situations.

Upon transitioning into an active state a ‘For Sale’ house will wait for an ‘Active Customer’ ‘this is represented and carried out through the ‘Search’ action. Upon completion of the action both states become inactive and the process continues.

Supply – ‘Count of houses for sale –supply’ is then calculated by a count of Houses ‘For Sale’ that are currently in the active state. Ultimately a high Motivation to sell would sharply increase supply, whilst a low motivation would have the adverse effects.  

Movement Speed

Movement speed – describes the base movement rate of Consumers. This variable describes the transition into the ‘Inactive’ state of a consumer, ultimately when a household is found and purchased. Movement speed affects both demand and supply in the sense that the transitioning of stages is quickened and more responsive. (Indicated by a more rigid demand and supply curve).

Market Price

In economics Price is a linear function (straight line) of the proportion of houses for sale (positive slope), and also a linear function of the proportion of buyers (negative slope).Therefore , the variable ‘Market Price’ is calculated by 10 * the portion of ‘House’ in the active state (which is the supply) over the portion of ‘Consumers’ in the active state (which is the demand) Ultimately this presents the economic principles  that as Supply is directly related to Price and demand is inversely related to Price.

Note

Each simulation (with the same settings) will present a different and unique simulation. I have set a Random Boolean to the active component that randomizes the amount of Customers or houses that begin in their active state. The probability is only 0.008 but is useful in describing the effects on the market from various position’s and seeing unique models.  

References

https://www.youtube.com/watch?v=ynuoZQbqeUg - Your First ABM/Part II

https://insightmaker.com/insight/35714/Foraging-Model

Assignment 3 - Ryan Salvaggio 43668070
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The simulation integrates or sums (INTEG) the Nj population, with a change of Delta N in each generation, starting with an initial value of 5.
The equation for DeltaN is a version of 
Nj+1 = Nj  + mu (1- Nj / Nmax ) Nj
the maximum population is set to be one million, and the growth rate constant mu = 3.
 
Nj: is the “number of items” in our current generation.

Delta Nj: is the “change in number of items” as we go from the present generation into the next generation. This is just the number of items born minus the number of items who have died.

mu: is the growth or birth rate parameter, similar to that in the exponential growth and decay model. However, as we extend our model it will no longer be the actual growth rate, but rather just a constant that tends to control the actual growth rate without being directly proportional to it.

F(Nj) = mu(1‐Nj/Nmax): is our model for the effective “growth rate”, a rate that decreases as the number of items approaches the maximum allowed by external factors such as food supply, disease or predation. (You can think of mu as the growth or birth rate in the absence of population pressure from other items.) We write this rate as F(Nj), which is a mathematical way of saying F is affected by the number of items, i.e., “F is a function of Nj”. It combines both growth and all the various environmental constraints on growth into a single function. This is a good approach to modeling; start with something that works (exponential growth) and then modify it incrementally, while still incorporating the working model.

Nj+1 = Nj + Delta Nj : This is a mathematical way to say, “The new number of items equals the old number of items plus the change in number of items”.

Nj/Nmax: is what fraction a population has reached of the maximum "carrying capacity" allowed by the external environment. We use this fraction to change the overall growth rate of the population. In the real world, as well as in our model, it is possible for a population to be greater than the maximum population (which is usually an average of many years), at least for a short period of time. This means that we can expect fluctuations in which Nj/Nmax is greater than 1.

This equation is a form of what is known as the logistic map or equation. It is a map because it "maps'' the population in one year into the population of the next year. It is "logistic'' in the military sense of supplying a population with its needs. It a nonlinear equation because it contains a term proportional to Nj^2 and not just Nj. The logistic map equation is also an example of discrete mathematics. It is discrete because the time variable j assumes just integer values, and consequently the variables Nj+1 and Nj do not change continuously into each other, as would a function N(t). In addition to the variables Nj and j, the equation also contains the two parameters mu, the growth rate, and Nmax, the maximum population. You can think of these as "constants'' whose values are determined from external sources and remain fixed as one year of items gets mapped into the next year. However, as part of viewing the computer as a laboratory in which to experiment, and as part of the scientific process, you should vary the parameters in order to explore how the model reacts to changes in them.
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Social determinants of health are economic and social conditions that influence the health of people and communities. These conditions are shaped by the amount of money, power, and resources that people have, all of which are influenced by policy choices. Social determinants of health affect factors that are related to health outcomes. Factors related to health outcomes include:
  • How a person develops during the first few years of life (early childhood development)
  • How much education a persons obtains
  • Being able to get and keep a job
  • What kind of work a person does
  • Having food or being able to get food (food security)
  • Having access to health services and the quality of those services
  • Housing status
  • How much money a person earns
  • Discrimination and social support
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This page provides a structural analysis of POTUS Candidate Lindsey Graham's economic policy based on the information at: http://www.lindseygraham.com/issue/restore-fiscal-discipline/     http://www.lindseygraham.com/issue/ease-tax-and-regulatory-burdens/      http://www.lindseygraham.com/issue/achieve-energy-independence/     http://www.lindseygraham.com/issue/reform-entitlements/       The method used is Integrative Propositional Analysis (IPA) available: ​ http://scipolicy.org/uploads/3/4/6/9/3469675/wallis_white_paper_-_the_ipa_answer_2014.12.11.pdf
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This model is developed to simulate how Burnie can deal with a new outbreak of COVID-19 considering health and economic outcomes. The time limit of the simulation is 100 days when a stable circumstance is reached. 

Stocks
There are four stocks involved in this model. Susceptible represents the number of people that potentially could be infected. Infected refers to the number of people infected at the moment. Recovered means the number of people that has been cured, but it could turn into susceptible given a specific period of time since the immunity does not seem everlasting. Death case refers to the total number of death since the beginning of outbreak. The sum of these four stocks add up to the initial population of the town.

Variables
There are four variables in grey colour that indicate rates or factors of infection, recovery, death or economic outcomes. They usually cannot be accurately identified until it happen, therefore they can be modified by the user to adjust for a better simulation outcome.

Immunity loss rate seems to be less relevant in this case because it is usually unsure and varies for individuals, therefore it is fixed in this model.

The most interesting variable in green represents the government policy, which in this situation should be shifting the financial resources to medical resources to control infection rate, reduce death rate and increase recovery rate. It is limited from 0 to 0.8 since a government cannot shift all of the resources. Bigger scale means more resources are shifted. The change of government policy will be well reflected in the economic outcome, users are encouraged to adjust it to see the change.

The economic outcome is the variable that roughly reflects the daily income of the whole town, which cannot be accurate but it does indicate the trend.

Assumptions:
The recovery of the infected won't happen until 30 days later since it is usually a long process. And the start of death will be delayed for 14 days considering the characteristic of the virus.
Economic outcome will be affected by the number of infected since the infected cannot normally perform financial activities.
Immunity effect is fixed at 30 days after recovery.

Interesting Insights:
 In this model it is not hard to find that extreme government policy does not result in the best economic outcome, but the values in-between around 0.5 seems to reach the best financial outcome while the health issues are not compromised. That is why usually the government need to balance health and economic according to the circumstance. 
 

New outbreak of COVID-19 in Burnie