Insight diagram
An SIR model for Covid-19

This is a simple example of an SIR model for my Mathematics for Liberal Arts classes at Northern Kentucky University, Spring of 2022.

Let's think about things on the scale of a week. What happens over a week?

With an Ro of 2 (2 people infected for each infected individual, over the course of a week); recovery rate of 1 (every infected person loses their infectiousness after a week), and resusceptible rate of .05 (meaning .05, or a twentieth of the recovered lose their immunity each week), the disease peaks -- does the wave, then waves again before the year is out, then ultimately becomes
"endemic" (that is, it's never going away, which is clear after two years -- that is, a time of 104 weeks). This is like our seasonal flu (only the disease in this simulation doesn't illustrate seasonality -- that requires a more complicated model).

With an Ro of .9, recovery rate of 1, and resusceptible rate of .05, the disease is eliminated.

Masking, social distancing (including quarantining following contact), and quarantines all serve to reduce infectivity. And if we can drive infectivity down far enough, the disease can be eliminated. Other things that help is slowing down the resusceptibility, by vaccinating. Vaccines (in general) impart an immune response that reduces -- or even eliminates -- your susceptibility. We are still learning the extent to which these vaccines impart long-term immunity.

Other tools at our disposal include Covid-19 treatments, which increase the recovery rate, and vaccinations, which reduce the resusceptible rate. These can also serve to help us eradicate a disease, so that it doesn't become endemic (and so plague us forever).

Andy Long
Mathematics and Statistics

Some resources:
  1. Wear a good mask: https://www.cdc.gov/coronavirus/2019-ncov/your-health/effective-masks.html
  2. Gotta catch those sneezes: https://www.dailymail.co.uk/sciencetech/article-8221773/Video-shows-26-foot-trajectory-coronavirus-infected-sneeze.html

Insight diagram
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.
Insight diagram

The complex model reflects the COVID-19 outbreak in Burnie, Tasmania. The model explains how the COVID-19 outbreak will influence the government policies and economic impacts. The infected population will be based on how many susceptible, infected, and recovered individuals in Burnie. It influences the probability of infected population meeting with susceptible individuals.

The fatality rate will be influenced by the elderly population and pre-existing medical conditions. Even though individuals can recover from COVID-19 disease, some of them will have immunity loss and become part of the susceptible individuals, or they will be diagnosed with long term illnesses (mental and physical). Thus, these variables influence the number of confirmed cases in Burnie and the implementation of government policies.

The government policies depend on the confirmed COVID-19 cases. The government policies include business restrictions, lock down, vaccination and testing rate. These variables have negative impacts on the infection of COVID-19 disease. However, these policies have some negative effects on commercial industry and positive effects on e-commerce and medical industry. These businesses growth rate can influence the economic growth of Burnie with the economic

Most of the variables are adjustable with the slider provided below. They can be adjusted from 0 to 1, which illustrates the percentages associated with the specific variables. They can also be adjusted to three decimal points, i.e., from 0.1 to 0.001.


Assumptions

- The maximum population of Burnie is 20000.
- The maximum number of infected individuals is 100.
- Government policies are triggered when the COVID-19 cases reach 10 or above.
- The government policies include business restrictions, lock down, vaccination and testing rates only. Other policies are not being considered under this model.
- The vaccination policy implemented by the government is compulsory.
- The testing rate is set by the government. The slider should not be changed unless the testing rate is adjusted by the government.
- The fatality rate is influenced by the elderly population and pre-existing medical conditions only. Other factors are not being considered under this model.
- People who recovered from COVID-19 disease will definitely suffer form immunity loss or any other long term illnesses.
- Long term illnesses include mental illnesses and physical illnesses only. Other illnesses are not being considered under this model.
- Economic activities are provided with an assumption value of 1000.
- The higher the number of COVID-19 cases, the more negative impact they have on the economy of Burnie. 


Interesting Insights

A higher recovery rate can decrease the number of COVID-19 cases as well as the probability of infected population meeting with susceptible persons, but it takes longer for the economy to recover compared to a lower recovery rate. A higher recovery rate can generate a larger number of people diagnosed with long term illnesses.

Testing rate triggers multiple variables, such as government policies, positive cases, susceptible and infected individuals. A lower testing rate can decrease the COVID-19 confirmed cases, but it can increase the number of susceptible people. And a higher testing rate can trigger the implementation of government policies, thus decreasing the infection rate. As the testing rate has a strong correlation with the government policies, it can also influence the economy of Burnie.