These days, we are accustomed to social distancing from the past month and a similar situation is likely to extend. Almost every industry is affected during this lockdown period and suffering losses. Despite such losses, we continue to do so in hope that social distancing will fetch us enormous results when it comes to curtailing the spread of the coronavirus, which is all wanted at the cost of humongous losses to our economy. Here we will see AI Predictive Analysis of Social Distancing.
The real question is “Is social distancing worth our efforts?”, let’s find out.
In the previous article on how AI or predictive analysis help in fighting against the coronavirus does, I mentioned the impact. In this article, I’ll show an analysis out of fictitious numbers to generate the plots and visualizations to demonstrate the efficacy of “social distancing” weapon on the coronavirus. Based on Compartmental model of epidemiology which classifies people into four categories in terms of their state with respect to the disease.
- Susceptible – They have high chances to be prone to the disease
- Infectious – They are infected by the disease
- Carrier – They don’t show symptoms, but do carry the disease with them
- Recovered – They successfully managed to recover from the disease
One strange thing about the coronavirus, I would say that “X-factor” is that there is no guarantee that the person who got recovered by the coronavirus won’t be re-affected by it in future.
This happens to be a serious issue while evaluating the effect of the lockdown. Since it doesn’t matter whenever the lockdown is lifted, people are going to be re-affected.
Extension for SIR model:
To the classic SIR model, an extension is made adding “Exposed” people as well. Out of many exposed people, a few get infected.
Where S stands for Susceptible, E for exposed, I for infected and R for recovered people.
The evaluation of the effect of the pandemic is an amalgamation of all these factors with three parameters: α, β, and γ where
α is the inverse of the incubation period (1/t_incubation)
β is the average contact rate in the population
γ is the inverse of the mean infectious period (1/t_infectious)
t_incubation is the time taken for incubation and t_infectious is the time taken for exposed to convert into the infectious stage.
Equation 1 gives the change in people susceptible to the disease and is calculated by the number of infected people and their contact with the infected.
Equation 2 is the count of the people who has been exposed to the disease. It grows based on the contact rate and decreases based on the incubation period. Some of them eventually turn to infected people.
Equation 3 stands for infected people based on the exposed population and the incubation period. It decreases based on the infectious period. The higher γ is, the more quickly people die/recover and move on to the final stage in Equation 4.
Equation 4 stands for the recovered people who were initially infected.
Equation 5 is a constraint that ignores new births or population migration effects in the model; It essentially assumes a fixed population from beginning to end.
The R0 factor
Apart from all of these, there is a parameter for every epidemic or pandemic which shows the spread effectiveness of the disease. It’s the R0 factor. The more the R0 factor, the more is the spread effectiveness of the disease.
They can be related to our parameters through the relationship given in Equation 6.
Introduction of “SOCIAL DISTANCING” factor to modelling
Social distancing includes avoiding physical contact within 3 feet radius of us, large gatherings, and other efforts to mitigate the spread of infectious disease.
According to the updated model, the term this is going to impact is our contact rate, β.
Let’s introduce a new value, ρ (rho), to capture our social distancing effect. This is going to be a constant term between 0–1, where 0 indicates everyone is locked down and quarantined while 1 is equivalent to general lifted the lockdown.
Now, since it affects β, equations 1 and 2 will be,
Based on these, we are going to model it and visualize the effect of “Social distancing” on pandemic as follows.
Python modelling of the new model
This is the visualization we can get based on these values after plotting our model.
The first for blue plots are non-social distancing factors whereas last two red graphs are included (rho) factor as a factor of social distancing and we can see that there is a significant effect of social distancing on curtailing the pandemic spread. We can see the curve flattening effect as more social distancing takes place throughout the population as it reduces the contact rate.
We can see that from a peak of 10% of the population is infected if there is no social distance is reduced to about 7.5% and later the infected is reduced to a low of 3%.
Impact on how strictly social distancing is implemented
I have updated the values of ‘rho’ in the equations and re-run the simulation thereby we get the real impact of social distancing.
The strict the implementation of Social distancing, the better is the control of the spread.
How many days should the lockdown continue? (Economy vs safety)
Everyone, by now understood the impact of social distancing. But, ultimately, it’s all about how many days we can implement social distancing on effective control of spread.
There is a terminology – “Herd Immunity”.
It can be defined as with a longer the lockdown, the susceptible (S) people gradually reduce slowly over time, so that even when the lockdown is relaxed, there will be a very less susceptible people left over for the virus to infect.
But the lockdown can’t go beyond a specific level. After 150 days, the susceptible fraction level does not go down significantly. The curve is almost the same after it. Therefore, to build herd immunity, the lockdown will be effective only up to a certain period.
Conclusion – AI Predictive Analysis of Social Distancing
I can say that, after the first lockdown, there are chances that the coronavirus can again spread rapidly, but good thing is that if the first lockdown is effective and for a longer duration, we can avoid the spreading initially by building the herd immunity thereby avoiding second and third lockdowns in due course of time.
“Social distancing if taken for a certain time is definitely a boon, if goes beyond extent is a bane on the economy”.
AI Predictive Analysis of Social Distancing