SIR Modelling and Prediction of COVID-19 infection in India (Part 1)
Kshitij Shrestha
The objective of this post is to share with you the modeling
of COVID-19 infection using real data of India till today. I am using R-software to do all the modeling. The source code has not been displayed here, as most of
you will have difficulty understanding that code. If you are really interested, contact me, I can
share with you that one.
The modeling is done using SIR (susceptible , infected , recovered ) model. For more information about such model please
read the following links: Link to Wikipedia, Link to MAA information page. There are much more information in the website.
I am going to use real data of COVID-19 infection from India. I will do the modelling and would like to evaluate the impact of lock-down on the flattening of the
curve. The first confirmed case in India started in January 30,
2020. The confirmed case remained less than 5 in number, till march 03, 2020. On a single day 23 confirmed cases were found on march 04, 2020. Afterwards, the number of infection increased exponentially.
The government announced lock-down on march 25 and is still continuing it till
date.
I have decided to do modeling in 4 stages.
Stage 1: exponential growth stage before starting lock-down (from
march 04 to march 25)
Stage 2: first two weeks after lock down
Stage 3: third and fourth weeks after lock down
Stage 4: fifth and sixth weeks after lock-down
For each stage, the data has been used to do SIR modeling to
estimate beta, gamma and R0 parameter.
The beta parameter is indication of rate of infection and gamma
parameter is indication of rate of recovery and R0 is reproduction number.
Please read relevant literature for more details about them.
After modeling in each stage, I have used model parameter to
estimate around 200 days future prediction. That shows the scenarios likely to be if the situation would have been constant ( model parameters remaining
constant).
Lets start with first stage:
1. Stage1:
Before Lock-down started
# March 04 to March 25 (before starting the lock-down)
# before that date, situation was stable with less than 5
confirmed cases
# on march 04, 23 confirmed cases were found and the growth
afterwards was exponential
Prediction with such situation without lock-down is shown below. It shows that more than 70 % population could have been infected at the peak
point, which is likely to reach in August/September. The second graph is presented in
logarithmic scale for better viewing. The predicted scenarios without lock-down is really scary.
2) Stage2: first two weeks after lock-down
# March 26 to April 08
start_date <- "2020-03-26"
end_date <- "2020-04-08"
The lock-down was started on march 25, 2020.
The growth of confirmed cases continues to be exponential. The observation below is very similar to the one we observed during stage 1. Majority of this infection probably occurred before lock-down. It was confirmed only in this week due to the incubation period of the virus infection.
The data does not indicate any impact of lock-down yet. The prediction still looks scary.
The modelling and prediction for stage 3 and stage 4 will be provided in the next post. We have not seen any impact of lock-down till stage 2.
Do you expect to see impact in stage 3 and 4. Give your comments. Please provide feedback for improvements. Follow me to read stage 3 and 4.
Coming soon...........