Mathematical modelling by ICMR to predict the spread of WuhanVirus in India

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Mathematical modelling by ICMR to predict the spread of WuhanVirus in India

24 Mar 2020
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Nilesh Rane (वैमानिकी)

Twitter Id: @nileshjrane



Finally we see some mathematical modelling from ICMR. The gist of the study is

- Screening all symptomatic incoming travelers would only delay the introduction of the virus in India by only 3-21 days. Because large number of asymptomatic travelers will escape this screening.

- Strict quarantine of symptomatic and high risk travelers would reduce overall nos of cases by 62% and the peak number by a massive 89% (flattening the curve).

- Of course the results are subject to a lot of uncertainties, however I think it effectively underlines the importance of strict quarantine of travelers.

GOI's strategy so far is clearly influences by this or similar mathematical modelling. Unfortunately many Citizens actively sabotaged this strategy by breaking quarantine rules.

- This also underlines the importance of strict lock-down, given there are a lot of leaks from initial quarantine. We can still slow-down the transmission rate significantly if we maintain 2 weeks of strict lock-down and aggressive quarantine of discovered cases to "isolate and contain" the virus. 

Lets dive deeper in the paper. But remember, I am not an expert in this field and I have done only a cursory reading of the paper. So take it FWIW.
The work focuses on identifying rational intervention strategies rather than predicting the spread of COVID19 infection and number cases. Given the limited understanding about COVID-19 in early days and a large number of uncertainties involved at modelling and input parameters, the results are important for their qualitative value not the exact numbers. This should be kept in mind while reading the numbers. 

If one can gloss over the mathematical part and some of the intricate details, the paper is actually fairly simple to understand. The first focus is on containment of the Virus thru Airpot screening. To evaluate impact of screening on the delay to reach 1000 cases. 

The plot shows number of symptomatic and asymptomatic cases effectively screened and quarantined vs delay in days to reach 1000 cases. The blue portion shows that capturing/quarantining increasing proportion of only symptomatic travelers has little impact over on the time to 1000 cases (remains at ~45 days for 0-100% of symptomatic patient screening). The real difference is seen in how efficiently we screen and quarantine the asymptomatic patients. Notice the red curve. The nos of days to 1000 cases especially start increasing with 70% or more of the asymptomatic cases. What this means is the more travellers we quarantine the better it is to delay the onset of community transmission in India.
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Accordingly, GOI started a strict screening for all travelers coming from High-risk countries starting with China. Symptomatic and those who were deemed high-risk travelers were quarantined in Govt controlled facilities and rest all were asked to remain in home-quarantine. If this protocol was followed by everyone to the last letter, we would have been able to capture 100% symptomatic and very high % of the asymptomatic patients (they would have developed symptoms during the 14-day quarantine period, but since they remained in quarantine, unintentional transmission would have been really low). Since the end of Jan, till date we have screened >15L travelers.

Unfortunately we saw quite few leaks through the quarantine. Despite this, we managed to delay the Community transmission for more than 2 months now. This is not luck, the great Indian Summer, or high immunity of Indians. Its the strict screening that has shielded us frm large outbreak of WUHAN VIRUS.

And note that past data suggests that avg 3565 travelers come to India per day from China. That's not a small number. The proactive and very early restrictions on travel from China reduced this number significantly and the screening ensured only 3 cases passed through and they never managed to start even Local Transmission of the Virus. As the Virus spread across Europe, Iran and US, travelers coming from their actually brought all later cases to India, rather from China. The number of travelers coming to India from all all these regions are too large to handle. We had the inevitable leaks which lead to Level 2 transmission & possibly Level 3 by now.

So whatever any "eggspurt" may say, the real reason we were so far shielded seems to be the proactive screening at the Airports. 

Note that the curve shown above is based on assumptions, one of which is - in incoming travelers asymptomatic population is assumed to be 2x the symptomatic. In real life from the revelations in recent times, this factor is likely much larger. The red curve would have even more 

prominent impact in that case.

The second area of focus is Mitigation thru within-country interventions. To assess the impact of intervention, the study modeled spread of the disease in 4 cities

- DEL, BOM, BLR & Kolkata.

Two scenarios considered  - Optimistic & Pessimistic

Image

R0 is basically tells us how fast a disease transmits - larger the number faster is the growth. Infectiousness factor tells how likely asymptomatic case is to transmit the disease compared to a symptomatic case.

In a hypothetical case of Transmission starting in Delhi and spreading in other 3 cities based on their inter-connectivity, he spread of COVID-19 is calculated, with and without Intervention strategy.

The assumed intervention here is - 50% symptomatic cases quarantined within avg 3 days of developing the symptoms. 

Two important observations -
1. In optimistic case, the intervention strategy reduces the cumulative incidence by 62% and the peak prevalence by 89% i.e. it "flattens the curve" drastically.

2. In Pessimistic situation, the numbers are only 2% and 8%. IOW, if the disease is if spreading very rapidly with significant asymptomatic transmission, quarantine of only the symptomatic patients has practically no impact on the epidemic. But in case of much slower spread with no asymptomatic transmission, the quarantine of symptomatic patients has a massive impact on the epidemic dynamics.

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Of course, from current revelations, COVID-19 situation seems to be between these two scenarios with lower R0 but significant asymptomatic transmission. So which strategies are likely work in this case..? 

Remember the aim is to "break the chain of transmission"

Keeping in mind the asymptomatic transmission, its important to quarantine both, symptomatic & asymptomatic cases. That's should be the intervention we should be aiming for.

Strategies to achieve the intervention - 

A. Indiscriminate testing of entire population to identify asymptomatic cases along with the symptomatic and quarantine all the cases.Problem is given long incubation time of avg 14 days or likely even more in some cases, one round of testing won't be sufficient. Multiple round on large population means huge number of tests which may not be possible due to time limitation. This is practically possible in small population like how it was tried in Italian town of Vo with 3000 residents.
 

In one Italian town, we showed mass testing could eradicate the coronavirus | Andrea Crisanti and Antonio CassoneBy identifying and isolating clusters of infected people, we wiped out Covid-19 in Vò, say Andrea Crisanti, a professor of microbiology, and Antonio Cassone, a former official at the Italian institut…https://www.theguardian.com/commentisfree/2020/mar/20/eradicated-coronavirus-mass-testing-covid-19-italy-vo

The strategy would be to test all residents, filter all positive cases and quarantine. Test again after a few days, filter out new cases. Keep doing this until you stop finding new cases.But there will always be danger of outbreak from another external source once things go bak to normal if this is not tried for entire world or we have a vaccine developed.

B. Full-scale lock-down for 2-3 weeks, to ensure bare minimum person-to-person contact at community level. Keep catching the symptomatic patients and limited testing to catch asymptomatic patients who have travel history or contact with known positive case. Quarantine all as the yare caught. The lock-down would ensure all asymptomatic patients either recuperate automatically or become symptomatic. There will be local transmission limited to close contacts like Family. Isolate these clusters until they are fully cured.

There will be leaks in this too. But due to breaking of large scale asymptomatic as well symptomatic transmission chain the number of cases will remain at manageable level where they can be isolated easily. Its easy to see how this will lead to significantly reduced peak nos of cases and flattening of the curve to a more manageable level.

Though this approach is more practical from medical perspective, unless we figure out a way to maintain the economic activity, this will lead to prolonged reduced economic activity ie recession.But in India's case currently, where, in all probability we have a minuscule % of our total population infected as of now. Otherwise it would have been seen as a spike in ICU admission by now.

Given this situation, the lock-down with targeted strategy seems like the best option for India as of now. It potentially gives us another chance to "Isolate and contain" the Virus, given we have a long-enough effective lock-down larger than the incubation time of the virus and we manage to isolate all asymptotic cases, In the end the paper presents following plots showing duration of epidemic wrt R0 rate with and without intervention (quarantine of 50% symptomatic patients) for optimistic and pessimistic cases.

cImage

For a realistic case as discussed above with R0 of ~2.5 & significant asymptomati transmission (i.e. Pessimistic case with R0 ~ 2.5) the impact of the particular intervention strategy is not very effective. But clearly if we can isolate 100% symptomatic and a large portion of asymptomatic cases we are bound to get a larger impact here. 

Clearly ICMR has been conducting concrete scientific studies to come up with best ways to tackle the #WuhanVirus Pandemic. These studies are guiding govt strategies and are also proving effective. ICMR mentioned they have further models which are relevant in case of Community 

Transmission. Those models will be helpful in estimating total number of cases, no of hospitalizations and no of severe cases. These numbers will be essential for GOI in planning for the Medical infrastructure. ICMR has indicated that they will release results of their 

mathematical models in future as an when they become relevant. The paper includes following interesting numbers related to this matter. These numbers are in the same ballpark as the numbers seen for some other countries.

ImageImage

Going forward, we will definitely need a multi-prong approach and we should leave no stone unturned. Currently the most essential thing is lock-down to break the chain of transmission. Next our aim should be to produce large number of PPEs, test kits and ICU requirements. 

We should put some trust in our Govt and Medical agencies. Those are the same professionals who have saved India earlier too. They have the capabilities and the intent to save India from Wuhan Virus. They have done a marvelous job so far. We need to unconditionally support them.


Originally Published as Twitter thread. Thead.

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