Human Behavior and Mathematical Modeling COVID-19- another addendum

In my recent posting, I had estimated the expected end of “1st wave” and total estimated deaths as of that point in time. Based on data at that time, it seemed we had passed an inflection point, and would enjoy a basically contained situation with roughly 70,000 cumulative deaths by mid-May. Sadly, I was quite incorrect. In my own defense, so was the CDC. I believe our mutual error was the assumption of rational behavior from our citizens, who- during April- seemed to be mostly adhering to scientific expert recommendation with the required shutdowns aside from essential services. By early May, increasing irrational behavior was evident. As individuals, we observed people socializing unprotected, holding parties despite advice, and so on. And then our local governments allowed restaurants to reopen- for indoor dining. “Yes- we’re open!” (No charge for extra protein in viral form!) signs abounded. CDC and other scientific experts warned that they expected an increase in transmission and fatalities. And the reaction to this advice- denial. The old joke tells us, “De Nial is not just a river in Egypt.” Somehow, individual decisions were based on the incorrect assumption that mathematical and scientific models can be nullified by edict. Highly illogical. Recall the Inquisition of the 15th-16th century, during which the Church rejected all evidence of a heliocentric solar system as heresy, decreeing the geocentric model was the only permissible model- on penalty of death. As we now all realize (hopefully), such decrees may be unpleasant for those who adhere to mathematical and scientific truth, but as we can see, the planets still orbit the sun. Similarly, those who declare COVID-19 to be hyped, political, not especially dangerous, etc. do so not based on mathematical and scientific evidence, but rather based on their own desired conclusion- namely, “We want everything opened NOW NOW NOW!” (stamping feet) Do I dare project future COVID-19 figures at this time? With the daily transmission rate having surpassed 71,000, and still increasing, perhaps we shall see no letup, and one long wave for the next several months? Projection becomes quite complicated when human behavior is a factor. We had recently 4th of July celebrations (despite recommendations to the contrary), theme parks reopening, schools perhaps reopening next month, all such events tending to shift the curve in an undesirable direction. And speaking as a teacher, it is expected that students will not necessarily retain every nitty gritty detail from math and science classes. However, key concepts should be retained, especially logical deduction, algebraic, exponential, and logistic growth functions, the scientific method, etc. We see here that many citizens- in other countries as well- while they covered these in secondary grades, they seem to have either forgotten all of this, or are arbitrarily discarding this because they do not like the conclusions reached therefrom. It is an accomplishment to graduate from high school, college, and so on, but if- and only if- the knowledge acquired is actually applied in our everyday decisions.

Mathematical Modeling of COVID-19 addendum

We are now over a month into the pandemic crisis in the U.S., and - with more data now to work with- it is becoming possible to more easily and accurately extrapolate the end result of this cycle. We seem to have just a few days ago- around April 10- reached the inflection point in terms of total cases, and are just now reaching the inflection point in terms of total deaths. Insofar as that marks the halfway point of the cycle, we can thereby project a total of 1 to 1.1 million total cases in this country, with a resulting 50,000-60,000 American deaths by the time the virus is contained. We can likely anticipate containment around mid-May. Most mathematicians - if asked to project given current data- would likely offer a similar projection. However, we would need the medical professionals and other scientists to provide further data to consider the future beyond that. What is the potential of subsequent waves of infection? How long until there is a vaccine to protect the public from this virus? We can only work with the data we are given.

2020 MathWorks Math Modeling Challenge- Electric Vehicles and the Environment

As mentioned in an earlier post, I (and probably many others with a math background) have a keen interest in the annual math modeling challenge managed by the Society for Industrial and Applied Mathematics. We have had math teams representing our school (California Virtual Academies) competing in this event during the last 5 consecutive competitions. My interest in the topics chosen is not merely as a math team coach, but in considering the major challenges facing our civilization which are hopefully surmountable via a combination of mathematical and scientific knowledge, coupled with proper ethical conduct and implementation by our leadership. The topics covered are tackled by our country's teams, representing some of the most gifted high school students in the United States. Their mathematical modeling yields results which are worthy of our government's serious consideration. Do they have the wisdom to examine these results, or at least consider the basic conclusions of the winning teams? Or will they brush aside the results, and simply develop the legislation based on their party lines' positions? This year's competition- like that of 3 years ago- is related to the oft-covered issue of global climate change. We see this issue in the news almost daily. Climate change is unfolding before our eyes. Very bizarre weather patterns are increasingly manifesting themselves- record heat waves, increasing intensity of severe storms, wildfires, rising ocean levels as our ice caps are melting. Meanwhile, extinction of numerous species is acceleration Long-term concerns include a continuation of the above, coupled with rising sea levels, flooding of human coastal communities. While this is occurring, we are also depleting our nonrenewable resources- especially fossil fuels, the primary culprit of climate change (via increased carbon dioxide in the atmosphere). These facts are undeniable. The argument is no longer one of environmentalism versus denial of the threat of climate change. Instead, the argument is between ardent environmentalism versus those who concede the threat of climate change but quite ironically portray the situation as too hopeless to address, owing to the financial cost of addressing these issues. Moderation and pragmatism - as exemplified (hopefully) by mathematicians- is all too lacking. Whereas the problem of 2017 examined the evidence of climate change as exhibited by rising sea levels, this year's competition instead focuses on a major piece of the solution- namely, conversion of gasoline-powered diesel trucks to electric-powered ones. The competitors were challenged to examine the speed at which diesel-powered trucks would be converted to electric. Next, they were instructed to determine the number of charging stations needed, and the number of chargers needed at each station, to accommodate the needs of semi-trucks along 5 major corridors. These corridors were San Antonio, TX, to/from New Orleans, LA; Minneapolis, MN, to/from Chicago, IL; Boston, MA, to/from Harrisburg, PA; Jacksonville, FL, to/from Washington, DC; Los Angeles, CA, to/from San Francisco, CA. Lastly, they were challenged to prioritize which corridor was most important to develop first. This problem is not a mere theoretical exercise. For those who have been following, the Doomsday Clock- which represents the danger of humanity's self-destruction- this January was moved forward from 11:58 PM to 11:58:20. It is now 100 seconds to midnight. The primary danger to our civilization is nuclear war, followed by climate change. These are interrelated, insofar as climate change would likely lead to competition for resources, leading to a situation in which war is increasingly likely to occur. This is a grave long-term danger that we need to tackle in a reasonable and pragmatic way. It is not a Democratic issue, or Republican issue, but rather an American issue and, indeed a Human issue. At the moment, we are witnessing how humans behave during a comparatively minor crisis. Hoarding and human indecency are manifesting themselves, even as shortage of supply begins to occur. It is not my intention in any way to minimize the impact of tens of thousands of deaths, millions of seriously ill people, and social isolation over a period of many months. Eventually- within the next 12-18 months- this situation will resolve. However, climate change looms ahead as a much bigger crisis which should be regarded as an existential threat. We have resources- not merely financial and technological resources, but also brilliant students to figure out the best methodology to tackle these issues. God willing, our leaders should have the wisdom to turn to our scientists and mathematicians (of all ages) and figure out a pragmatic set of policies to implement their recommendations. Of course, we need policies that will stick permanently, not ones that will be implemented by one party, dismantled by the next administration, while we find ourselves sinking deeper and deeper into a hole. If we learn just one thing from this present crisis, it should be the need for proper planning and working together with our scientists and mathematicians who have been charged with the task of tackling society's greatest threats.

Mathematical Modelling and the Coronavirus covid-19 Pandemic

It would be safe to say that Americans are presently living in a state of anxiety and fear. I am admittedly far from immune to this from my end- on behalf of my entire household and family (and, incidentally, myself). However, it is worthwhile to step back a bit (in many ways) and tackle this- as mathematicians do- from a mathematical perspective. Perhaps then, the conflicting news reports will begin to make some sense. This is the current U.S. data on Coronovirus numbers. This virus- as with any virus - can be modeled as a logistic growth function. A logistic growth function is most commonly used in biology, as any population will initially grow exponentially, but the rate of increase will slow, eventually to 0; at that point, we reach the "carrying capacity." In the case of viruses, that "carrying capacity" would actually be the total number of people infected. After all, viruses needed human hosts to remain "alive" (insofar as viruses are technically not considered alive); once there are no further non-immune hosts available, they would theoretically cease to operate- so to speak. Any physicians reading this are probably cringing at my medical terminology (or lack thereof). Back to the math.... So what is a logistic growth function? And right now, we are still on the first half (or leg, if you prefer) of the graph, during which dP/dT, the rate of increase, is still increasing. As of today, Coronovirus cases are increasing at a rate of 7500 per day. The "inflection point" would represent the midway point of this crisis. At that inflection point, the rate of increase would stabilize, and the daily rate of new cases would begin to decrease. You see, then, that even if today is the inflection point (which seems unlikely), we would still have another 3 weeks until the graph finally plateaued, and the total Coronavirus cases in our country maxed out at 65,000, with the virus declared contained at that point. That would appear be the best case scenario as of this point. Until we actually reach that inflection point, we would extend our estimate of the crisis' duration, as well as the maximum expected number of Coronavirus cases. UPDATED 3/26/2020- The number of Coronavirus cases in the U.S. is now 85,268, with dP/dT of over 17,000 and climbing. We are poised to reach P of 100,000 within hours. The function now resembles an exponential function of the form P = P0r^t, where r is between 1.2 and 1.25. We are evidently not approaching an inflection point. Prepare for reported Coronavirus cases to exceed 200,000 in the best-case scenario. Worst case, we may conceivably head into 7 figures. This happens normally, by the way- with colds, etc. We hear the expression "There's a cold going around." Within a few weeks, much of the population is infected. Why? Because normally we do not shut the country. Colds are normally of minimal danger (aside from for those with severe immune deficiencies); hence, there is no reason to stop business as usual. However, this virus is different. It is far nastier, and with a mortality rate of 4%, allowing 1/2 the population to become infected (which is a figure we hear commonly) in the absence of a shutdown, amounting to roughly 10 million American deaths, would be unacceptable to us. We hear the expression "flattening the curve." This is precisely what is accomplished by this shutdown. Minimizing human interaction (aka “social distancing”) slows the rate of transmission so that the maximum number of Coronacases- and, more importantly, deaths resulting from such, is minimized. There is a price paid, however- increased duration. To save lives, this shutdown increases the duration before the "carrying capacity" point is reached. Hopefully we all would concur that increasing the duration is worth saving many millions of lives. Also, we hear about hospitals' capacity. By slowing the spread, this also - hopefully- decreases the cases of severe Coronavirus patients who are unable to receive adequate treatment due to shortages of beds, medical supplies, etc. We hear many officials indicating figures of 9-11 more weeks. This is a probably fairly accurate estimate of the time remaining until containment is attained. One official grimly indicated 18 months, punctuated by multiple waves. This would make sense when considering the expectation that a vaccine to eliminate COVID-19 would likely take 18 months to develop, and meanwhile- even after containment is achieved- some people might potentially bring the virus back into our country, and it would then resume spreading to Americans not previously infected, and then another round of this. Hopefully, with our government wiser from the experience, the response would be more prompt, decisive, and hence more effective than this round. And this, in a nutshell, is the mathematical representation of the Coronavirus pandemic. If you prefer to hear the non-mathematical details- regarding food shortages, people acting irrationally, the occasional touching story of people reaching out to help others, etc., this will pop up in front of you in today's headlines. No reason for me to provide more of this here. However, if you are reading this, please stay safe. And as Mr. Spock would say, "Live long and prosper!"