COVID-19
After Coronavirus broke out, we have started conducting research into its dynamics, in an effort to (save the world) / (help the community fight corona) / (understand the disease even if we can't do anything about it) / (cash in on it) in increasing order of cynicism.
Some notes :
1. The core team consists of MOHIT SHARMA of Weill Cornell Medicine and myself. MOHIT and I are accompanied by different other authors in different Articles.
2. Articles are arranged in chronological order.
3. Articles indexed by date, thus DD-MM. All novel ones are uploaded to the MedRxiv server. Beyond 27-09, many are at various stages of process in journals and/or conferences. For those which have completed the often arduous and tortuous journey to publication, we give the date in bold green.
4. Due to the rapidly evolving situation, our initial few contributions have become obsolescent and have been entirely superseded by the later contributions. Obsolescent contributions are marked in grey. We also use grey for original versions of non-obsolescent contributions, which have subsequently been improved in later Articles in this list, for example due to reviewer suggestions.
25-03 [OBSOLETE - SEE 22-07] Here we have constructed a model for community transmission of the virus. Our model is the first which accounts for the delays on account of the latency period of the virus and the waiting times for tests. The paper dates from 25-03-2020. We find that as a result of these delays, (a) the disease peaks in society a few days before the peak in test results is reached, (b) the optimal interval for imposing a limited duration lockdown is one which straddles the peak in the absence of the lockdown and (c) the effects of lockdown may not be apparent from a naive interpretation of the time history of cases.
Corona
15-04 [OBSOLETE - SEE 22-07] In the second paper, we have tried to predict and describe what is perhaps the quickest path to the end of COVID-19. We call it self-burnout. In this phase, a region can use 6-feet separation minima, sanitization, contact tracing and preventive testing to slowly starve the virus of new targets. The paper dates from 15-04-2020. We find that if things go smoothly, the pandemic may be over by the end of summer.
Self-burnout
xx-05 This paper focusses on data fits of various regions, using the model from 15-04 above.
Fitting
03-06-A [UPDATED VERSION = 22-07] 'A' because it dates from 03-06-2020 as against a later from this day, next year. About a month after Article 15-04, it became clear that our hope of lockdowns and attendant measures putting an end to the scourge worldwide was fond. Various cities in India, USA, Canada and Russia exploded despite remaining under hard lockdown. So what was going wrong ? We claim that it's the asymptomatic carriers who are driving this spread against a lockdown. In this paperwe explain this mathematically, and propose the retarded logistic equation as a universal dynamic model for the spread of corona. We also discuss some broader implications of our results. I have marked this as obsolete only becuase the next item in this list presents the derivation in a more elegant and easily generalizable manner. The retarded logistic equation however is NOT obsolete in a technical way.
Retarded logistic
22-07 Here is a different presentation of the current content from Nos. 10-30. It is more mathematical than the original Articles and contains a new derivation of the retarded logistic equation. We believe that this derivation is easier to understand than the one presented in Nos. 10-30. The content is current upto 03-06-2020 although the Article itself was written a couple of weeks later.
Revised version
This has been published in two pieces in the Proceedings of the KIML workshop at the conference KDD2020. The links to the published versions are here and here.
30-06 [UPDATED VERSION = 27-09] For the retarded logistic equation we assume like most studies that COVID-19 immunity is permanent. Suppose this were not true, then what would happen ? This study mentions some of the possibilities. The paper dates from 30-06-2020. The content has now become subsumed into the next Article in this list, so you might wish to skip straight to that one.
Temporary immunity (preliminary)
27-09 As several phylogenetically confirmed reinfection cases started cropping up, we turned in greater earnest to the question considered in Article 40 above - that what happens if COVID-19 immunity is temporary ? Here we consider two cases - one where the loss of immunity after a certain period is total, and the second where sterilizing immunity wanes off but severity-reducing immunity persists for a long time. We have also included a scoping review of immunity literature, which we shall keep updating every few weeks. The original version dates from 27-09-2020.
Temporary immunity
Updated 10-11. This has been published at International Journal of Infectious Diseases. The link to the published version is here.
28-10 We now explore the modeling aspects in greater detail. The model which we conceived in Articles 30 onwards actually admits a lot of generalizations to cover non-trivial phenomena such as contact tracing and periodic testing in a realistic manner. This makes it relevant for any infectious disease, not just corona. This Article gives a look into the various possibilities. It dates from 28-10-2020.
General model
This has been published at Mathematical Modeling of Natural Phenomena, a journal brought out by EDP Sciences. The link to the published version is here.
09-12 After back-to-back papers on 27-09 and 28-10, a third on 29-11 would have made a perfect Dilli triplet. However, we missed the day by ten days. As a vaccine veers into view, here is the answer to all your vaccine questions - how long will it take to kill COVID with vaccination, can you have fun after getting vaccinated etc etc. It dates from 09-12-2020.
Vaccination dynamics
19-01 [UPDATED VERSION = 12-02] The new year has brought a new development - the start of vaccination drives all over the world. A question which many of us have is, if I get the vaccine, can I attend a concert or a party with others who have got it as well ? Can I travel without wearing a hell-mask for 24 continuous hours or more ? Or can such behaviour on my part fuel a wave of cases ? The answer we find is : if the vaccine efficacy is 80 percent or more then vaccinated people can be immediately and preferentially cleared to return to normal life. If it's 60 percent however then social restrictions must continue for everyone. The paper dates from 19-01-2021.
Selective relaxation
12-02 Article 19-01 above brought us very useful comments from a journal Reviewer. This person suggested that instead of a one-component model, we should use an age-structured model to accommodate the facts that children cannot be vaccinated and that older people are especially vulnerable. We have implemented this feature in this paper. In the process, it had to be overhauled so it has become substantially different from No. 80 and we give it a new number and a new MedRxiv submission. This incorporates only the "no travel" situation from the previous Article - we shall implement the travel in a spearate article after this gets verified. The paper dates from 12-02-2021.
Selective relaxation with age-structuring
Unfortunately, after the revisions were made, the paper got rejected. The grounds given were flimsy at best. The journal in question was Journal of Travel Medicine. The only reason we can figure out for the rejection is that, at that time, the prevalent view was that social restrictions would have to remain in force for vaccinees as well. Our position was a minority opinion, which the journal was probably reluctant to accept. The situation in USA now shows that the minority opinion had been correct in this case.
03-06-B [UPDATED VERSION = 05-10] By March-April 2021 we all thought that corona was on the way out. Then, India exploded like a nuke. Nobody had a clue as to why it happened and in the absence of logical explanations, illogical ones took hold. Some weeks after India, Taiwan also became swamped with the disease. Similar phenomena had occurred in European countries as well, although several months earlier. Evidently, there was something in the transmission dynamics which everyone - including ourselves - was missing. After weeks of work, we came to the conclusion that the missing factor is interaction heterogeneity. We have now proposed a model which takes this into account. We call this cluster seeding and transmission (CST) model. It can explain how huge waves of epidemic can come out of nowhere, or more prosaically, out of a background solution of constant and low daily case rate. The paper dates from 03-06-2021.
Cluster transmission model
08-06 The above gives a general overview of what can cause sudden waves. Specificially in India however, what exactly happened ? How much of the wave was out of our control ? What can we do to prevent a third wave ? The paper dates from 08-06-2021 and is uploaded to SocArxiv instead of MedRxiv due to entirely qualitative. It is the first concrete application of CST model to a perplexing corona curve.
Second wave in India
05-10 A revised version of 03-06-B above which features many improvements of presentation as well as incorporating some content from 08-06. The final revision dates from 05-10-2021.
Cluster transmission model - revised
This has published in Chaos : An Interdisciplinary Journal of Nonlinear Science. The link to the published version is here.
16-09 [UPDATED VERSION = 29-11] When we add contact tracing to the basic cluster seeding and transmission model, it can exhibit a wide range of surprising phenomena. These phenomena make it possible to explain real-world observations regarding the disease trajectories. We also find a potential advance warning indicator of an imminent wave. The paper dates from 16-09-2021.
CST model with contact tracing
29-11 We missed Dilli's primary runway last year. But this [redacted] virus has been with us so long that we made up for it this year. Here is a possible explanation of why the worldwide COVID-19 curves are behaving so erratically, and a potential means of anticipating an impending wave a few days in advance. This is a refined presentation of the CST model with contact tracing from 16-09 above. This time, we have presented the main contribution as a short paper, followed by the model details and then the supplementary information. We also have clarified numerous points of the prsesntation in response to reader feedbacks. It dates from 29-11-2021.
Counter-intuitive COVID-19 curves unravelled