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Introduction:

This simulation model demonstrates the outbreak of Covid-19 in Burnie, Tasmania and how the corresponding government’s responses affect the spreading of Covid-19. Meanwhile, this model also shows how the economy in Burnie is influenced by the impacts of both Covid-19 and government policies.

Variables:

This simulation contains some relevant variables as follow:

Variables in Covid-19 outbreaks: (1) Infection rate, (2) Recovery rate, (3) Death rate, (4) Immunity loss rate

Variables in Government policies: (1) Vaccination rate, (2) Lockdown, (3) Travel ban, (4)Quarantine

Variables in Economy: (1) E-commerce business, (2) Unemployment rate, (3) Economic growth rate.

Assumption:

Government responses would be triggered when reported Covid-19 cases are at least 10.

The government policies reduce the spreading of Covid-19, but they would also limit economic development at the same time due to the negative impact of the policies on the economy is greater than the positive impact.

The increase in reported Covid-19 cases would negatively affect economic growth.

Interesting Insights:

The first finding is that the death number would keep increasing even though the infection rate has decreased, but with stronger government policies (such as implementing a coefficient over 25%), no more death numbers will occur caused by Covid-19.

The second finding is that as government policies limit business activities, with the increasing number of reported Covid-19 cases, economic growth will suffer a severe blow even if e-commerce grows, it can’t make up for this economic loss.

BMA 708 assignment 3 - simulation model of Covid-19 Outbreak in Burnie, Tasmania

Xuanze Liang

Goodwin Model:

This is a basic version of the Goodwin Model based on Kaoru Yamagushi (2013), Money and Macroeconomic Dynamics, Chapter 4.5 (link)

Equilibrium conditions:

Labor Supply = 100

Devation from the equilibrium conditions generates growth cycles.

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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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Introduction:

This model demonstrates the COVID-19 outbreak in Burnie, Tasmania. It shows how the government policy tries to reduce the spread of COVID-19 whilst also impacting the local economy.

Assumptions:

This model has four variables that influence the number of COVID-19 cases: infection rate, immunity loss rate, recovery rate and death rate.

In order to reduce the pandemic spread, in this model, assume the government released six policies when Burnie COVID-19 cases are equal or over 10 cases. Policies are vaccination promotion, travel restriction to Burnie, quarantine, social distance, lockdown and testing rate.

Government policies would reduce the pandemic. However, it decreases economic growth at the same time. In this model, only list three variable that influence local economic activities.

Travel restrictions and quarantine will reduce Burnie tourism and decrease the local economy. On the other hand, quarantine, social distance, lockdown allow people to stay at home, increasing E-commerce business.

As a result, policies that cause fewer COVID-19 cases also cause more considerable negative damage to the economy.

Interesting insights:

One of the interesting findings is that the government policy would reduce the COVID-19 spread significantly if I adjust the total government policies are over 20% (vaccine promotion, travel restriction, quarantine, social distance, lockdown), 3560 people will die, then no more people get COVID-19.

However, if I change the total government policy to less than 5%, the whole Burnie people will die according to the model. Therefore, we need to follow the polices, which saves our lives.

BMA708 assignment3 - Model of COVID-19 outbreak in Burnie

Zhiyuan Wang

This is a reconstruction of the SIMM model presented in Chapter 2 of Feedback Economics (Contemporary Systems Thinking)

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Nick Lakon

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Geoff McDonnell

Explanation of the Model

This is a Model of COVID-19 outbreak in Burnie, Tasmania which shows the government actions in response to the pandemic COVID-19 and its affects on the Economy. The government health policy changes depending on the reported cases, which is a dependent upon the testing rate.

Assumptions

Lockdown and travel ban were the main factor in government policy. It negatively impacts on the Economic growth as individuals are not going out which is directly affects the business around the world, in this insight 'Burnie'. This reduces the economic growth and the factors positively effecting economic growth such as Tourism.

Government policies has a negative impact on Exposer of individuals. Moreover, it also has a negative impact on chances of infection when exposed as well as other general infection rate.

Interesting Insight

There is a significant impact of test rating on COVID-19 outbreak. Higher rates increases the government involvement, which decreases cases as well as the total death.

In contrast, lower testing rates increase the death rate and cases.

Tourism which plays a avital role in Tasmanian Economy greatly affects the Economic Growth. The decline of Tourism in parts of Tasmania such as Burnie, would directly decrease the economy of Tasmania.

BMA 708, Assessment Tast 3: Complex System, Burnie COVID-19 outbreak, Diprina Shakya-519673

Diprina Shakya

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