Description
Model of Covid-19 outbreak in Burnie, Tasmania
This model was designed from the SIR model(susceptible, infected, recovered) to determine the effect of the covid-19 outbreak on economic outcomes via government policy.
Assumptions
The government policy is triggered when the number of infected is more than ten.
The government policies will take a negative effect on Covid-19 outbreaks and the financial system.
Parameters
We set some fixed and adjusted variables.
Covid-19 outbreak's parameter
Fixed parameters: Infection rate, Background disease, recovery rate.
Adjusted parameter: Immunity loss rate can be changed from vaccination rate.
Government policy's parameters
Adjusted parameters: Testing rate(from 0.15 to 0.95), vaccination rate(from 0.3 to 1), travel ban(from 0 to 0.9), social distancing(from 0.1 to 0.8), Quarantine(from 0.1 to 0.9)
Economic's parameters
Fixed parameter: Tourism
Adjusted parameter: Economic growth rate(from 0.3 to 0.5)
Interesting insight
An increased vaccination rate and testing rate will decrease the number of infected cases and have a little more negative effect on the economic system. However, the financial system still needs a long time to recover in both cases.
Assumptions
1. The current Burnie population in 19550. Therefore, the susceptible population is equal to the current Burnie population.
2. Since Burnie is just a regional city, the virus infection rate is 25% as 5000 people in Burnie went into quarantine during the outbreak last year.
3. 50% of people who are infected will recover.
4. 20% of people who are infected will die because Burnie population average is old.
5. Government intervention and policy will reduce the Infection
6. COVID-19 is only countable as a case if the infected people have been tested, and the percentage of testing depends on how many infected people have been tested.
7. Following a recovery, there is a chance that people could lose their immunity, and also the immunity loss rate measures this.
8. Government intervention will reduce the infection rate by 15%.
9. Lockdown will cause tourism industry to shut down and affect the overall economic activity.
10. Lockdown is one of the most effective way to prevent infection.
11. Strict health protocol also contributes to reduce the infection.
12. Vaccination will not make people fully immune to the virus. However, vaccinated people will reduce the immunity loss percentage.
13. Economic growth rate percentage is based on year 2020.
Findings
1. COVID-19 could be significantly reduced in number and the spread of the vaccine could make a significant impact on the epidemic.
2. Economic activity will drop during the first phase of government intervention, However, it will steadily increase overtime
3. Less people going to be susceptible as government imposed covid 19 rules.
This model indicate indicates the modeling COVID-19 outbreaks and responses from government policies with the effect on the local economy. Model was occurred at Burnie, Tasmania. The model mainly contains three parts: COVID-19 pandemic outbreak, four differences government policies and what the impact on economy from those policies.
Assumptions:
(1) Various variables influence the model, which can result in varied outcomes. The following values are based on an estimate and may differ from actual values. Government initiatives are focused at reducing Covid-19 infections and, as a result, affecting (both positive and negative) economic growth.
(2) 42% of infected people will recovery. 10% of people who are infected will die and the rate relatively higher due to the much old people living in Burnie, Tasmania.
78% of cases get tested.
(3) Government policy will only be implemented when there are ten or more recorded cases. Four government policies have had influences on infection.
(4) The rising number of instances will have a negative impact on Burnie's economic growth.
Insights:
1. As a result of the government's covid 19 rules, fewer people will be vulnerable. Less people going to be susceptible.
2. After the government policy intervention, there is a effectively reduce of infected people.
3. Overall, there is no big differences of economic performance from the graph, might due to the positive and negative effect of economy. And after two weeks, the economy maintained a level of development without much decline.
The Logistic Map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. The map was popularized in a seminal 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation first created by Pierre François Verhulst.
Mathematically, the logistic map is writtenwhere:
is a number between zero and one, and represents the ratio of existing population to the maximum possible population at year n, and hence x0 represents the initial ratio of population to max. population (at year 0)r is a positive number, and represents a combined rate for reproduction and starvation.For approximate Continuous Behavior set 'R Base' to a small number like 0.125To generate a bifurcation diagram, set 'r base' to 2 and 'r ramp' to 1
To demonstrate sensitivity to initial conditions, try two runs with 'r base' set to 3 and 'Initial X' of 0.5 and 0.501, then look at first ~20 time steps
