Public Health Implications of a delay differential equation model for COVID 19 Mohit M Sharma B Shayak Population and Health Sciences Sibley School of Mechanical and Weill Cornell Medicine Aerospace Engineering New York City, USA Cornell University Ithaca, New York State, USA mos4004@med.cornell.edu sb2344@cornell.edu ABSTRACT 175,000 by August 15th, 2020 [3]. Some features however, both nationally and globally, have proved counterintuitive. For This paper describes the strategies derived from a novel delay example, a 76-day lockdown resulted in the outbreak’s differential equation model[1], signifying a practical extension containment in Wuhan. A similar measure has produced similar of our recent work. COVID -19 is an extremely ferocious and an results in New Zealand. However, lockdown appeared only unpredictable pandemic which poses unique challenges for marginally effective in New York State, USA where the case and public health authorities, on account of which “case races” death counts decreased only after reaching horrifying peak levels among various countries and states do not serve any purpose and [4]. It was contended that the stay at home order in New York present delusive appearances while ignoring significant came too late. This apparent delay was not present in California, determinants. We aim to propose comprehensive planning USA. The case counts there went up all the same, and the rate is guidelines as a direct implication of our model. Our first high even today. We would like to mention that such consideration is reopening, followed by effective contact tracing spatiotemporal anomalies are present not just in the US but also and ensuring public compliance. We then discuss the in other countries such as Canada, Russia and India [5] which implications of the mathematical results on people’s behavior witnessed high case growth despite being in lockdown. In order and eventually provide conclusive points aimed at strengthening to better understand the epidemiology of the transmission of the arsenal of resources that are helpful in framing public health COVID-19, we have constructed a delay differential equation policies. The knowledge about pandemic and its association with model. Here we present its practical implications which tries to public health interventions is documented in the various encapsulate a myriad of factors associated with the current literature-based sources. In this study, we explore those resources scenario. to explain the findings inferred from delay differential equation model of covid-19. 2 MATHEMATICAL MODELING TO UNDERSTAND THE EPIDEMIOLOGY KEYWORDS Since many decades, mathematical modelling has been used Delay differential equation, Contact tracing, Socio-behavioral as an integral tool in recognizing the trend of disease progression theories, Lockdown, Reopening during pandemics. For example, using a simple model explaining the transmission dynamics of the infectious disease between the susceptible, infected and recovered population ( SIR Epidemic Models) Kermack and McKendrick proposed and later 1 INTRODUCTION established a principle – the level of susceptibility in the The national (USA) and global spread of Coronavirus Disease population should be adequately high in order for that epidemic 2019 (COVID-19), following its origins in Wuhan, China in at to unfold in that population. Such mathematical models can give least December 2019 and possibly earlier still [2] has been impressionable insights in explaining the epidemiological status alarmingly rapid and deadly. From the 25 individual national of the population, predict or calculate the transmissibility of the forecasts received by CDC, predicts that there is possibility of pathogen and the potential impact of public health preventive the total reported COVID -19 deaths is between 160,000 and In M. Gaur, A. Jaimes, F. Ozcan, S. Shah, A. Sheth, B. Srivastava, Proceedings of the Workshop on Knowledge-infused Mining and Learning (KDD-KiML 2020). San Diego, California, USA, August 24, 2020. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). KiML'20, San Diego, California, USA © 2020, Copyright held by the author(s). KDD KiML 2020 Sharma et al. practices [6]. However, a significant body of evidence suggests that decisions should be made regarding the parameters to be included, being contingent on the impact of the precision of predictions. Several policy questions about the containment of this outbreak have been considered in our recently proposed simple non-linear model [1]This paper delves into the practical solutions that can be devised utilizing the directions of our models’ outcome. In generating interpretable results gathered from epidemiological models, we have used the examples of six types of cities [1]: 1) City A – Moderately effective contact tracing in a hard lockdown. This city has R (reproductive number) <1 and drives epidemic to extinction in time. 2) City B – Less effective contact tracing in a hard lockdown. It starts off R >1, but reached R =1 at 15% infection level. The epidemic ends at 30% infection rate and takes a very long time to get there. 3) City C – Less effective contact tracing (Like City B) with milder restriction on mobility. It proceeds rapidly to herd immunity. 4) City D – Combination of City B and City C. Starts with mild restriction on mobility and progresses towards restriction. The duration of the epidemic as well as of the final case count is between CITIES B and C. 5) City E - Starts off like City A, it reopens with very effective contact tracing and drive the epidemic to extinction in time. 6) City F – Starts off like CITY A, it reopens with less effective contact tracing and suffers a second wave. Pragmatic implications of our work are as follows: KDD KiML 2020 Sharma et al. 3 REOPENING CONSIDERATIONS, ROLE Mr X as a potential case, having been exposed to a known case OF TESTING yesterday. Then, it can be that Mr X contracts the virus ten days from now, in which situation he will report negative if tested The unemployment situation generated as a result of today or tomorrow, but will still amount to a spreading risk ten lockdowns is currently forcing countries and states to partially days later if he is at large then. This also means that secondary reopen their economies even though many of them have not yet contact tracing, i.e. finding Mr. X’s contacts, must go ahead got the virus under control. The reopening is easiest in City A irrespective of his test results. Indeed, the medical authorities are regions where cases have slowed down to a trickle. With every well aware of this loophole. new case being detected, swift isolation of all potential secondary, tertiary and maybe even quaternary cases, both The US Chamber of Commerce has given out state by state forward and backward, should prove possible while the rest of reopening guides for small businesses which are mandated to be the economy functions in a relatively uninhibited way. Even one followed across the US. Continued following of federal, state, mass transmission event can restart an exponential growth tribal, territorial and local recommendations is of paramount regime and force a rollback to a fully locked down state. importance. Reopening beyond a skeletal level is impossible in City B regions which are still in the ascending phase. The ascent implies that Prior to resuming work, all workplaces should have a contact tracing is already inadequate, and on top of that if carefully chartered exposure control, mitigation and recovery mobility increases then the region might turn into City C, plan. Although essential guidance is specific for each business, overstress healthcare systems, and become a massacre. An there are certain measures that can be generally adopted across ascending B-City has little option other than to contact trace as all workplaces. hard as possible and wait for partial herd immunity to kick in. 1) Reopening in phases – The US government has laid down Only when that happens and the cases slow down on their own guidelines to open the country in 3 phases. First phase involves can it consider a more extensive reopening like a City A region. continuation of vulnerable individuals to remain at home. When Testing is an important part of the epidemic management in public, people are expected to wear masks, have maximum process no doubt since it enables the authorities to get an accurate physical separation, avoid places with more than 10 people and description of the spread of the disease. As we have already limit non-essential travel. Second phase allows gatherings of 50 discussed, limited testing capacity is giving us a partial or people, some nonessential travel and reopening of schools. Third distorted picture in many regions. There is a widespread media phase involves relaxation of restrictions, permitting vulnerable perception that extensive testing is one of the prerequisites for populations to operate. any kind of reopening process [7], [8]. Much criticism has also 2) Defining new metrics – Post-corona world will witness been levelled at certain countries for having inadequate testing some significant changes in regulatory controls, and behavioral programs (we shall further elaborate the blame aspects later). drift in personal and professional spheres. Cleanliness standards, However, we would like to emphasize that testing is as of yet a safety standards, infection prevention practices with regular diagnostic tool and not a preventive one. Currently, it can show monitoring and inspection for its assurance are some of the new us how the disease is behaving but cannot slow its spread in any terms that will have to be a part of a daily life of the people for way. Test-induced slowing can come only when the capacity at least the next few months. expands to such a level as to be able to preventively test potential super-spreaders such as grocers and food workers every single 3) Organizational changes – To help essential operations to day. We hope that such a development may prove possible in the function, companies and organizations will have to be prepared near future – many Universities for example are making with advanced IT systems (in case of continuation of remote reopening arrangements with provision for very frequent testing working), supply of PPE, setting up travel facilities to avoid of the entire community. public transport, providing behavioral health services, and leave no stone unturned in overcoming biological, physical, and During reopening it is vital to get a true picture of the disease emotional challenges. We can see that the above guidelines are evolution so that we can gauge the effect of any relaxation of broadly conformal to our model predictions. restrictions – whether it keeps the outbreak under control as in City E or brings about the beginnings of a second wave as in City 4 METHODS OF CONTACT TRACING F. Such beginnings are heralded by a rise in the case rate. As we saw, there was no such rise in City E even though R increased As we have already mentioned, contact tracing is probably the after the reopening. If the rise takes place, the relaxation must single most important factor in determining the progression of immediately be rolled back to avert the disaster. Hence, during COVID-19 in a region. We can see from the model that the faster reopening, the testing capacity must be high enough to detect the contact tracing takes place, the better; the more delay we such incipient rises. As per China’s state media reports, with an have, the higher R becomes. Moreover, our model does not aim to reopen the economy, the city of Wuhan conducted 6 account for backward contact tracing. In practice however, a million tests in one week; we present this fact without discussion sufficiently high level of detection might not be possible to or comment. A second reason why testing is still not all that it achieve with forward contact tracing alone. As much as it is could have been is the high false-negative rate during the initial important, contact tracing is also one of the trickiest aspects to stages of infection [9]. Suppose a contact tracing drive identifies handle since it can interfere with people’s privacy. In classical KDD KiML 2020 Sharma et al. contact tracing, human tracers talk to the confirmed cases and 2) Communicating the consequences involved with risky track down their movements as well as the persons they behaviors in a transparent manner – Central and state ministers interacted with over the past couple of days. This method has as well as public health authorities are in constant worked well in Ithaca, USA and in Kerala, India. While it is the communication with the masses. least invasive of privacy, it is also the most unreliable since people might not remember their movements or their interactions 3) Conveying information about the steps involved in correctly. The time taken in this method is also the maximum. A performing the recommended action and focusing on the benefits more sophisticated variant of this supplements human testimony to action – Famous celebrities, in addition to state and central with CCTV footage and credit/debit card transaction histories – governments, spread the messages explaining the required steps this approach is possible only in countries such as USA where cogently and ensuring that it has the maximum reach, especially card usage predominates over cash. The most sophisticated among social media-addicted millennials and similar contact tracing algorithms use artificial intelligence together with populations. location-tracking mobile devices and apps – while they are quick 4) Being open about the issues/barriers, identifying them at and fool-proof, they automatically raise issues of privacy and early stage and working toward resolution – Activating all sorts security. For example, the TraceTogether app in Singapore, of helpline numbers, email addresses, personal offices etc to which worked very well during the initial phases of the outbreak, address any grievances around the topic. has not found popularity with many users [10]. Similarly, India’s Aarogya Setu has also raised privacy concerns [11]. Americans 5) Developing skills and providing assistance that encourages too have expressed their aversion to using contact tracing apps in self-efficacy and possibility of positive behavior change – a recent poll, with only 43 percent of people saying that they Adequate arrangements for people from lower socio-economic trusted companies like Google or Apple with their data. strata, stable and trustworthy financial schemes for middle class, plan to support small business and a means to become a bridge between the affluent class and the needy class are some of the ways to foster positive behavior change and develop natural trust. 5 ENSURING SOCIAL COMPLIANCE – A Other than health belief model, some theories that can be useful BEHAVIORAL PERSPECTIVE are: As the epidemic drags on and on, the continued restrictions on social activity are becoming more and more unbearable. There Theory of Reasoned Action – This theory implies that an is an increasing tendency, especially among younger people who individual’s behavior is based on the outcomes which the are much less at risk of serious symptoms, to violate the individual expects as a result of such behavior. In a practical restrictions and spread the disease through irresponsible actions. scenario, if the health officials want the people to follow a However, City F, a rise in violator behavior can completely particular trend, let us say based on our model, they need to nullify the effects of lockdown over the past few weeks or reinforce the advantages of targeted behavior and strategically months. Here we discuss how public health professionals and address the barriers. For instance, to enforce separation minima policy makers can resort to behavior/psychological theories to even when it is apparently proving ineffective and the cases are ensure compliance among the common people. The most widely increasing, they can use the examples of Cities B and C to used model is Health Belief Model which has been used convince the citizens that violations – and hence violators – can successfully in addressing public health challenges. We briefly be responsible for thousands of excess deaths. Trans-theoretical discuss the utility of this model in the current situation. Model – This model posits that any health behavior change entails progress through six stages of change: precontemplation, Health belief model is a theoretical model which hypothesizes contemplation, preparation, action, maintenance and that interventions will be most effective if they target key factors termination. For instance, it was observed that in March, despite that influence health behaviors such as perceived susceptibility, a rise in cases in New York City (NYC), people were not perceived severity, perceived benefits, perceived barriers to observing social restrictions the way they should have. Now, we action and exposure to factors that prompt action and self- can see that with passing time, the behavior of the masses efficacy. In general, this model can be used to design short and transforms according to the stages of this model long term interventions. The prime components of this model which are relevant in the current scenario can be outlined as Precontemplation – This is a stage where people are follows. typically not cognizant of the fact that their behavior is troublesome and may cause undesirable consequences. There is 1) Conducting a health need assessment to determine the a long way to go before an actual behavior change. This phase target population – The best example is the demarcation of zones coincides with the commencement of cases in NYC. in India depending on the level of risk. Red zone is highest risk, orange zone is average risk and green zone translates into no Contemplation – Recognition of the behavior as problematic cases since last 21 days. Classification is multifactorial, taking begins to surface and a shift begins towards behavior change. into account the incidence of cases, the doubling rate and the When the cases started being reported all over media and the limit of testing and surveillance feedback to classify the districts. major cause of spread began to surface, citizens started paying attention to their activities. KDD KiML 2020 Sharma et al. Preparation – People start taking small steps toward on their course of action. Since the virus is a new one, there is no behavior change like in our case, exhibiting hygienic practices precedent which can act as a model. Even among emerging and ensuring six feet separation minima. infectious diseases, this latest one is particularly unpredictable, since minuscule changes in parameters can cause dramatic Action – This stage covers the phase where people have just changes in the system’s behavior. This phenomenon is best changed their behavior and have positive intention to maintain illustrated by the notional cities, discussed previously. For that approach. In this instance, people continue to practice social example, to get from City A to B, all we did was increase by 50 restrictions and hygiene positively. percent the fraction of people who escaped the contact-tracers’ net. The result was a 30 times (not 30 percent!) increase in the Maintenance – This stage focuses on maintenance and total number of cases. Similarly, the difference between Cities B continuity toward the adopted approach. Majority of people in and D is an 11-day delay (recall that the first seven days in the NYC are exhibiting positive behavior and maintaining it plots are the seeding period, so they don’t count) in imposing the throughout the stages of reopening phases. This is vitally lockdown in D. 11 days out of a 200-plus-day run might not important to ensure that NYC stops at partial herd immunity like sound like a lot. But, that was enough to create tens of thousands City D instead of blowing up again like City C. of additional cases, risk overstressing healthcare systems and at Termination – There is lack of motivation to come back to the same time shorten the epidemic duration by a factor of three. the unhealthy behaviors and some sections of people across the Further uncertainty comes from the fact that the parameter country/world will continue practicing good hygiene (though not values are changing constantly. It is a well- known fact the social restrictions!) in our day-to-day lives. reported fraction of asymptomatic carriers has increased Social Ecological theory – This theory highlights multiple continuously over the last three months or so. Considering the levels of influences that molds the decision. In our case, let us sensitivity of this or any other model to parameter values, such say for example that the decision is to maintain sufficient changes can completely invalidate the results of a model as well physical separation once offices are opened up. To successfully as any decision which was made on their basis. Identifying follow this, there is a complex interplay between individual, potential exposures is much easier in a smaller city than a large relationship, community and societal factors that comes into or densely populated one. It is also more effective if the cases are action. Law enforcement authorities need to take this into mostly from the sophisticated social class who can use mobile consideration. A group of individuals when motivated by one phone contact tracing apps or otherwise keep (at least mental) another to follow the guidelines, builds a good connection within records of their movements and of the people they interacted the society, and in turn there is a high probability to build a with. However, if there is an outbreak among the unsophisticated healthy network within a defined area. A negative interplay at class, then even the most skillful contact tracer might run up different levels of motivation may in turn, prove disastrous and against a wall of zero or false information. In such cases there are cause all efforts go down the drain. A perfect illustration of this limited options that are left to the authorities to proceed in a in the present condition is how various NGO’s are working in conducive manner. conjunction with public health authorities to bring about a change at an individual level by door-to-door campaigning. This propels the behavior of even the most potentially recalcitrant population India went into lockdown on 25 March 2020. At that time, the in the most desirable way i.e. wearing masks and gloves, official figures stated that there were only 571 cases, which made adopting hand hygiene, being cognizant of symptoms arising in the decision appear premature to many people. Indeed, a seven- any member of the family and following quarantine rules in case day delay of lockdown was suggested so that the migrant workers of travel from other states. would have been able to return to their homes. However, when the lockdown was imposed, the testing had also been woefully 6 SOCIAL ATTITUDES AND BEHAVIOUR inadequate, with a nationwide total of just 22,694 tests having In this Section we address another important issue related to been conducted up to that date. If we use the extrapolation the Coronavirus. This is that the widely heterogeneous case technique of inferring case counts from death counts, then using profiles in different regions have often led to “corona contests” the same 1 percent mortality rate and 20 day interval to death, we among these regions. Far too often, the residents of better-off find almost 40,000 assumed cases on the day that the lockdown regions are seen heaping scorn on worse-hit regions. We have began. If we go by this figure, then the lockdown wasn’t really selected a tiny handful of representative media articles, early, and possibly should have been enforced earlier still in castigating the approaches of India, USA and Sweden, to show trouble zones such as Mumbai. Certainly, if the figure of 40,000 the breadth and vitriol of such commentary [12][13][14] cases is true, then one further week of normal life (with huge [15][16].A feature common to almost all opinion pieces like this crowds in trains and railway stations) might have been is that their authors do not have the slightest knowledge of the disastrous. From the vantage point of today, alternate issues involved, either epidemiological or economic. arrangements should definitely have been made much earlier for rehabilitation of the migrant workers. However these Before embarking on criticisms, we should note that policy arrangements would have involved considerable complexity in decisions need to be taken in real time, as the situation evolves. the prevailing situation, and were certainly not as easy as one The authorities do NOT have the benefit of hindsight to decide KDD KiML 2020 Sharma et al. week’s delay in announcing lockdown. Sweden, which has • Efficiency of contact tracing comes at the expense of adopted a controlled herd immunity strategy, has been accused people’s privacy – balancing between the two is a delicate of playing with fire. It is also possible that the Swedish optimization problem. authorities are aware that they do not have the contact tracing capacity required for performing like City A and hence are • In some regions, restrictions such as masks and six-feet attempting something like City D – a faster end of the epidemic separation minima must be maintained for a very long time to than City B at the expense of a higher case count. To make a come. The public health authorities can ensure compliance by comprehensive analysis of their policy, it is crucial to know not resorting to socio –behavioral theories/approaches. only the last intricate detail of the epidemiological aspects but  In deploying advanced contact tracing techniques, also the details of the economic considerations. That is almost significant consideration has to be given for ensuring high impossible. On a different note however, we have seen reports data security and lay down privacy regulations that are [17], [18] stating that the virus has entered into old age homes convincing to the users and similar establishments, causing hundreds of deaths over there. Assuming that these reports are not overturned in the  Control the spread by swift identification and course of time, allowing the ingress of virus into high-risk areas isolation of cases accompanied by tracing and quarantine for is an indefensible action, whatever the overall epidemiological at least 2 weeks strategy.  Empowering of individuals and communities by the government to facilitate efficient capacity building. Finally, extremely important public health factors such as the racial dependence of susceptibility and/or transmissibility have just  Multidisciplinary coordination, strong leadership to started coming to the surface. Another complete grey area is the mobilize communities and take quick decisions coupled with mutations which this new and vicious virus are undergoing and what thoughtful development of operation plans are likely to prove effect they might have on the spreading dynamics. Some reports also considerably efficient in handling this pandemic to the best of reflect that the change in genetic composition due to mutation might our capacity. be the reason behind huge differences in the crude infection rate between countries [19][20]. In the absence of a clear picture about References this, any public health measure is all the more likely to be a random [1] B. Shayak and M. M. Sharma, “Retarded guess with non-zero probabilities of both success and failure. Not logistic equation as a universal dynamic model for the everything about corona is random or outside one’s control though. spread of COVID-19,” medRxiv, p. 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