Author: Shreepada Shivananda, Data scientist

According to WHO CoVID-19 is already a global pandemic, Germany announces that close to 60-70% people can be exposed to the virus. With more than 600 thousand cases the epicentre of CoVID-19 moved from Chain to Europe and then to USA in a span of mere 3 weeks getting into the new heights every week. The alarming impacts what we have seen so far are just tip of the ice berg but the second wave of impact are coming from all directions including like job loss, declined per capita, global slowdown, renewed fight for global dominance (China and USA) and more.

This article talks about spread of CoVID-19, how can the epidemic model be used to estimate the global cases and life cycle of corona virus. Also, the article talks about why an epidemic model better suits than a traditional time series model for these estimation. The data source used for the analysis is from Johns Hopkins University Center for Systems Science and Engineering (JHU CSSE).

Where do we stand now?

It took 67 days for CovID-19 to infect 100 thousand people globally but for subsequent 100 thousand just took 11 days, 4 days and the latest one took less than 2 days. This means the Infection rate is exponential, reason being susceptible population is large with current infection rate at about 13% (for last one week). Because of which coronavirus is increasing drastically and managing to find new host every day. Below charts represents the increase of active cases globally.

Above chart gives clear indication that Infected cases has dynamic pattern and epidemiological models like SIR or SIER can help estimating such growth.

What is SIR model?

An SIR model is an epidemiological model that computes the number of people infected with a contagious illness in a closed population over time. The name of this class of models derives from the fact that they involve coupled equations relating the number of susceptible people S(t), number of people infected I(t), and number of people who have recovered R(t)

The dynamics of an epidemic, for example the flu, are often much faster than the dynamics of birth and death, therefore, birth and death are often omitted in simple compartmental models. The SIR system without so-called vital dynamics (birth and death) described above can be expressed by the following set of ordinary differential equations:

where  S is the stock of susceptible population, I is the stock of infected, R is the stock of recovered population(It’s also called removed population because part of the population end up with death), and N is the sum of these three.

How to model SIR?

As SIR needs 3 important indicators to build the model we can define the indicators as:

1. Stock of susceptible population(S)
In case of the CoVID-19 this can be as big as the global population of 7.7 billion. But with the self-awareness of individuals and effort of governments the susceptible will be lower. Hence considering the awareness of people I would consider the modest number of 100 million

2. Infection rate (It)
Infected rate is the rate at which the coronavirus is spreading. Currently it’s at an average rate of 7% in last 30 days and 12.5% in last one week. This means the rate is going to increase but on the other hand governments is trying to contain the spread by imposing the quarantine. Gradually by these efforts will yield results but I am considering infected rate(I) of 12.5% for next 1 week as any new case which would be reported from today are already infected and quarantine cannot help.

3. Recovery rate (Rt)

       Recovery rate is the ratio of number of patients are getting recovered and Number of active cases. Currently its same for a week and month, which is at 2%

Let’s see how the trend looks when we build the model with above indicators. Chart is for infected cases in next week and it will increase exponentially.

Supporting data for next one week:

The trend continues for 30 days globally, more and more measure would dampen the spread of infection but this would be the completely responsibility of the government and people to contain it. The chart below suggests with current set of measures below will be the trend which would take the total infection reported close to 6 million.

What is the lifespan of Corona?

Considering above indicators of SIR model we have estimated the spread as below:

1. We would see the impact for an year in various parts of the world (In a best case scenario)
2. The increase in new cases would continue globally for next 45 days at least, with all the measures
3. The estimated number of people who would get infected will be a max of 60 million people at a given point of time

The lifespan of CoVID-19 has to be estimated considering various factors like Government policies, Response of people, breakthrough in medicine, self-developed immunity, healthcare facility, seasonality, and more. Please note the model do not considers the impact of all these factors which will have a greater effect on the Infection rate in future.

Conclusion:

The reported cases are already sent shockwaves from last one week and the measures are still not containing the spread. Model like SIR will help to understand our position in near future, also grab the attention of decision makers to act fast. When compared with time series models, SIR is effective because of transparency in the assumption and gives the clear picture of complete life span of the epidemic.

Disclaimer:

This article does not talk about authenticity of the data because of various reasons like minor infections are not getting reported, lack of testing kits, governments trying to shield reality, etc.

Author: Shreepada Shivananda, Data scientist