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COVID-19’s mathematics

“Policy makers and enforcers act and respond depending on what they see.

Dean Dela Paz



In a little over a week the compulsory quarantine imposed over Luzon might end and as expected, those who’ve religiously complied are looking forward to returning to some modicum of normalcy. A few suggested that the quarantining continue but on an optional and selective basis as practiced in some countries that have aggressively tested a good deal of the population. Others fear that the one-month period was not enough and are suggesting an extension of at least two weeks. Others still foresee selected quarantine pockets where the pandemic remains uncontrolled or has reached alarming “hot spots” proportions.

The simplest logic supports a two-week extension if the virus has a 14-day incubation period. The first 14 days should have drawn out all who were infected previous to the lockdown. The next 14 days would have addressed those who, during the lockdown’s first cycle, were infected by the tens of thousands who we saw had actually violated their quarantines.

The extension of two weeks, or a third cycle of 14 days is needed considering the number of violators that we continue to see. The one-month lockdown assumed everyone would comply. The key was in compliance and a statistically controlled and limited population. Hence the border checkpoints. Unfortunately, not only were borders porous, quite a number did not strictly follow the quarantine.

For some the question of extensions is being answered using understandable biases. Policy makers and enforcers act and respond depending on what they see and that’s a function of the lenses they wear. The skew depends who the decision maker is, his decision criteria, his expertise and ultimately, his objectives.

How those are received and appreciated are pretty much the function of these same coefficients. Political scientists (not those cranially constricted congressmen) are generally cognizant of the downsides that diversity produces despite categorizing the mix as democratic.

The diversity of these factors and the evident disparateness due to the number of combinations and permutations can create a “lose-lose” proposition. Add to the emergent discombobulation toxic, obstructionist, partisan politics that does not seem to be relenting even at this time of crisis.

Academicians and our best and brightest epidemiologists and doctors are struggling to track the behavior of the virus and presumably since government has declared that science will lead the way, we are hoping that this indeed is the truth. So far, save for the lost month since having the first death outside China to the point we imposed a lockdown last 15 March 2020, it does seem that the government has allowed science to lead the charge.

The logic of a minimum one-month lockdown validates that. To check its infection rate try to number-crunch using binomial expansions, exponential progressions, factorials and Euler’s number.

Unfortunately by using the arithmetic we can still only determine the infection rate and percentage mortality. It’s basically binomial theorem. The current mathematics will not definitively determine whether the lockdown is working or whether to extend or lift it notwithstanding mortality ratios as indicators.

A minimum model should have the number of susceptible, the infected asymptomatic, the symptomatic, the morbidity and the recovered as variables. Add also the time frame and work on the assumption that susceptibility to COVID-19 is homogenous and that immunities are produced. On those two assumptions already we know that susceptibility is selective while immunity remains dependent on convalescent plasma experiments.

Lessened deaths to infections help but what seriously constrains decision-making is the incompleteness of data and the critical lack of an accurate denominator that measures the susceptible, asymptomatic and symptomatic. This requires random sampling and substantial testing which have not yet been done due to understandable constraints.

Unfortunately, that denominator is critical in the decision to lift the quarantine or extend it.

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