|Infected at Peak Day||2351|
|Phase 1 Basic Reproduction Number||4.000|
|Phase 2 Basic Reproduction Number||2.000|
SIR model consists of three compartments:
The SIR model will need two inputs that represent the two transition rates:
Basic reproduction number or basic reproduction ratio is defined as the ratio of the contact rate to the recover rate. This number reflects the number of contacts by an infected individual with others before the infected has recovered. If this number is greater than 1, the infection will spread in a population. The higher the number is, the harder to control the epidemic. For example, SARS has a basic reproduction number in the range of 2-5.
new corona virus, COVID-19, is highly contagious and caused world wide pandemic. The basic reproduction number for COVID-19 is estimated in the range of 2.13 to 3.11. The average number of days of the infection is about 14. Using that number we can input a recover rate at 0.07. Using 2.62 as the basic reproduction number, then we can input the contact rate as 0.182. Then you can input different values of the total population into the model to view the peak and number of infectious by day. By trying different population values, you can get an rough estimation of the total population infected.
Using the two phases SIR model, we can set the first 45 days as the uncontrolled period. Adding the 10 days of incubation period we can input 55 days for phase 1. In this pahse, there is no actions taken to control the infection. Therefore, the contact rate is much higher. After phase 1, the Chinese government took strong actions to control the spreading of the virus and that reduced the contact rate significantly. In this model, we input 0.28 for phase 1, 0.14 for phase 2 as the contact rate to reflect that fact. The model tells us that 75000 total infection is a reasonable projection of the total population and peak at day 49, at the peak day, the net infected number is 2351.