Simulation Model of the Effectiveness of Countermeasures to the Coronavirus Infection Spread


By – Maitreya Natu
(Product Owner | ignio™AI.WorkloadManagement | Digitate)
www.digitate.com

By – Mayank Shrivastava
(Data Scientist | Digitate)
www.digitate.com

When first whispers of a new virus in China were heard, no one thought that in a matter of a couple of months it will bring the whole world to a screeching halt. The world has descended into chaos caused by deaths and economic destruction. There are more than 3.75 million confirmed cases of infection and 275,000 deaths. For many countries, this curve still has an increasing trend.

What has made this viral spread more frightening is the fact that a cure or vaccine is still not in sight. There are reports of successful experiments from across the globe but scientist are still working tirelessly on a full-fledged industrial level cure. Due to this, every country is trying to contain the spread of the infection through some alternate routes. They have adopted methods ranging from complete lockdown of whole country to waiting for herd immunity to kick in. As the cases of infections are still on the rising path, we are not sure which methods works best, or if they even work.

We at Digitate help our customers with predicting and preventing problems and outages in their business with the help of our in-house simulation and what-if engines. In this article, we have leveraged the power of these engines of ignioTM to simulate some of these countermeasures. We will also compare them to see how they perform relative to one another.

Experiment design

We simulate the spread of a similar air-borne, highly contagious viral infections. In the simulation, we characterize the infection spread by the following four factors:

  • Fatality rate: percentage of deaths over population infected.
  • Immunity rate: percentage of population not infected even when in contact of a host.
  • Healing rate: percentage of infected population healing either by itself or with external help (medications) after certain time duration.
  • Relapse rate: percentage of population becoming host again after being free from the disease.

We first establish a baseline to assess how the infection would spread over a period of 14 weeks, if no counter-measures are taken. Next we simulate the effect of different counter-measures to assess how much reduction can be achieved by these counter-measures.

Baseline

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Figure 1: Infections and deaths when no counter-measures put in place

We first run a simulation by planting a patient zero on day zero with our factors set at:

  • fatality rate = 2%
  • immunity rate = 50%
  • healing rate = 10%
  • relapse rate = 20%

We do not apply any counter-measures and assess the effect of the spread. Figure 1 shows how the number of infections and number of deaths are likely to increase over a span of 14 weeks.

Key messages which come out of this baseline simulation are:

  • The number of infections and deaths increase at an almost exponential rate with time.
  • Even with a fatality rate less than 2%, deaths are in thousands.

With a baseline in place, now we simulate the counter measures adopted by various countries and track their effectiveness.

Effect of Complete Lockdown


Figure 2: Effect of complete lock-down on infections and deaths

This is the strictest measure opted by some countries. Here countries have gone on complete shutdown. Almost all population is under home quarantine barring essential services.

To observe the effect of this counter measure, we assume that 99% of the population will stay at home. Also all the population staying at home will not get infected. Our infection parameters remain the same as in baseline case.

Just by looking at the plots, this is clear that this measure is very effective in curbing the spread. Comparison between baseline and this methods shows that number of infections at the end of final week reduced drastically, from 285k to a mere 6000. This is a reduction of almost 98%. Similarly, total number of deaths came down from 6000 to just 136.

Effect of Herd Immunity


Figure 3: Effect of herd immunity on infections and deaths

This measure is being considered by a few countries. This relies on the naturally occurring phenomenon of herd immunity, according to which the majority of a given population gains immunity to an infectious disease either by recovering from it or through vaccination.

To observe the effect of this counter measure, we assume that once 10% of population gets infected, herd immunity will kick in. After herd immunity starts, the immunity of a recovered person increases at a linear rate with time, till it reaches 95%. Our initial infection parameters remain the same as in baseline case.

Comparison between baseline and this method shows that number of infections at the end of the final week reduced from 280k to 80k. Similarly, total number of deaths came down from 6000 to 1600.

Effect of Partial Lockdown


Figure 4: Effect of partial lock-down on infections and deaths

This is the most common counter measure currently being adopted. Governments have ordered or asked their citizens to remain in self quarantine. A large percentage of population is staying indoors and only venturing outside if absolutely necessary.

To observe the effects of this counter measure, we assume that 80% of the population will stay at home. The remaining 20% will show movement. Also all the population staying at home will not get infected. Our infection parameters remain the same as in baseline case.

Adoption of this counter measure is helpful in containing spread of infection to some extent. Comparison between baseline and these methods shows that number of infection at the end of final week reduced by almost 25%, from 285k to 220k. Similarly, total number of deaths came down from 6000 to 4500.

Further Analyzing the Partial Lockdown Scenario

Complete lock-down is the most aggressive approach while herd immunity is the most conservative approach. Being two extremes, both are very difficult to implement in practice. Partial lockdown though not as effective as the other two approaches seems to be a practically viable option. However, various factors impact the effectiveness of a partial lockdown.

Effect of How Early the Partial Lock-Down Is Started


Figure 5: Effect of earliness of partial lock-down on infections and deaths

Here we compare the effect of various start days of partial lockdown. Intuitively, earlier the lockdown starts, better the spread can be contained. This also follows from the chart below. Delay in implementing the lockdown with each passing week increases the number of infections and deaths by an order of magnitude.

Effect of What Percentage of Population is Under Lock-Down


Figure 6: Effect of percentage of lock-down population on infections and deaths

Another variable at play is the percentage of population that is under lockdown. Even if a small number of population is not following the lockdown, it results in a large increase in spread and deaths.

So folks, if your government asks you to stay inside, please stay inside and stay say safe!

Flattening of Infection Curve after Vaccine is Available

We have seen the effect of all the counter-measures and their effectiveness in the above sections. Even the best counter-measure like complete lockdown is not the solution but a measure to contain the spread of infection to a certain extent. This pandemic will end only when a medication or vaccine is discovered.

We are in no position to predict when a vaccine will be available, but we tried simulating the effect of discovery of a vaccine. Here we assumed that a vaccine will be commercially available at the end of 7th week and will be successfully administered to 15% of the infected population every day. To keep things simple, we assumed that once the vaccine is administered to a person, they become completely immune to infection.


Figure 7: Effect of percentage of lock-down population on infections and deaths

From the above chart it is clear that, no matter what countermeasures were implemented in a country, it will take 7 to 8 weeks to bring the pandemic to an end after the vaccine is available.

An interesting observation was that even after zero cases of infection were reported from Week 14 to Week 19, there were suddenly 3 or 4 odd cases observed in Weeks 19, 20, and 21. This gives us the hint that the infection can lie dormant and pop up again. So, we will have to be careful and keep taking precautions even after we have the vaccine.

Conclusion

We are in unprecedented times and our understanding is evolving every day on the factors that are driving and containing the infection of COVID-19. The intent of this study is to demonstrate the rapid spread of an infectious disease such as COVID-19 and to generate scenarios to test the effect of different control measures. We believe that such simulations can be an effective way to convince the society for the need of the mammoth effort that is required by everybody to contain the spread of this infection.

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