A Susceptible-Infected-Recovered (SIR) disease model with waning immunity

Here we have a basic SEIR model and we will investigate what changes would be appropriate for modelling the 2019 Coronavirus 

Overview:

The COVID-19 Outbreak in Burnie Tasmania shows the process of COVID-19 outbreak, the impacts of government policy on both the COVID-19 outbreak and the GDP growth in Burnie.

Assumptions:

We set some variables at fix rates, including the immunity loss rate, recovery rate, death rate, infection rate and case impact rate, as they usually depend on the individual health conditions and social activities.

It should be noticed that we set the rate of recovery, which is 0.7, is higher than that of immunity loss rate, which is 0.5, so, the number of susceptible could be reduced over time.

Adjustments: (please compare the numbers at week 52)

Step 1: Set all the variables at minimum values and simulate

results: Number of Infected – 135; Recovered – 218; Cases – 597; Death – 18,175; GDP – 10,879.

Step 2: Increase the variables of Health Policy, Quarantine, and Travel Restriction to 0.03, others keep the same as step 1, and simulate

results: Number of Infected – 166 (up); Recovered – 249 (up); Cases – 554 (down); Death – 18,077 (down); GDP – 824 (down).

So, the increase of health policy, quarantine and travel restriction will help increase recovery, decrease confirmed cases, decrease death, but also decrease GDP.

Step 3: Increase the variables of Testing Rate to 0.4, others keep the same as step 2, and simulate

results: Number of Infected – 152 (down); Recovered – 243 (down); Cases – 1022 (up); Death – 17,625 (down); GDP – 824 (same).

So, the increase of testing rate will help to increase the confirmed cases.

Step 4: Change GDP Growth Rate to 0.14, Tourism Growth Rate to 0.02, others keep the same as step 3, and simulate

results: Number of Infected – 152 (same); Recovered – 243 (same); Cases – 1022 (same); Death – 17,625 (same); GDP – 6,632 (up).

So, the increase of GDP growth rate and tourism growth rate will helps to improve the GDP in Burnie.

Introduction;

This model shows COVID-19 outbreak in Burnie have some impact for local economy situation and government policy. The main government policy is lockdown during the spreading period which can help reduce the infected rate, and also increase the test scale to help susceptible confirm their situation.

Variables;

Infection rate, Death rate, Recovery rate, test rate, susceptible, immunity rate, economy growth rate

These variables are influenced by different situation.

When cases over 10, government will implement lockdown policy.

Conclusion;

When cases increase too much , they will influence the economic situation.

Interesting insights:

If the recover rate is higher, more people will recover from the disease. It seems to be a positive sign. However, it would lead to a higher number of recovered people and more susceptible. As a result, there would be more cases, and would have a negative impact on the economic growth.