President Trump has canceled the U.S. economic contribution to the O. M.S. accusing them of failing to adequately communicate the pandemic. Europe is considering asking China to explain its lack of information. Political and geostrategic issues aside, explaining a pandemic is not that easy, and modeling it less so.
Epidemiologists, scientists, sociologists, mathematicians, etc., are trying to help understand this new pandemic. Without undermining the work of these experts, I intend to put forward a robust and simplified technical base.
The variables that most influence the evolution of Covid19 seem to be its transmission speed, and the protection and/or containment measures that allow this speed to be reduced. On this basis, I propose my estimates for the future. If the management of the remainder of the pandemic is correct, I would consider it a “minor” evil to have in Spain an impact on the GDP of 13%, a peak of net infections of 350,000 people, and, unfortunately, the number of deaths above 44,000.
The building blocks of a pandemic (S, I, R)
Epidemiological models can be very complicated, but many of them are based on a block diagram already described in 1927 by Kermack and McKendrick in “A contribution to the mathematical theory of epidemics“.
This means that during an epidemic, we move from one state (block) to another. In its most simplified version, there are three blocks that we will go through. First, there is the block of the Susceptible to be infected (Block S). From there, we go to the block of the Infected (Block I). From the latter, we will reach the block of the Recovered (Block R). I never liked too much the word recovered because if someone died, it would also leave Block I and go to the block of the “recovered”.
In this model, you can only be in one of these three blocks. Therefore, the sum of all blocks is equal to the total number of people in that geography.
| Total population (N) = Population in Block (S) + Population in Block (I) + Population in Block (R) |
Or what is the same (to simplify):
| N = S + I + R |
The key factor: the basic reproductive number (R0)
At the start of the pandemic, we’d all be in Block S. Well, not all of us. We need at least one person who’s already infected and can infect others.
The stay in each block is not static. It passes from one to another at a certain rate or speed. That speed will depend on the net between those who are infected and those who recover:
Contagiousness: The ability of an infected person to infect others is called the Transmission Rate. We will call it ß.
Recovery: An infected person stops being infected when he or she is no longer able to spread the disease. The ability to get out of being infected is called the Recovery Rate. We will call you γ.
The ratio between the two is called the basic reproductive number or R0:
If R0 is greater than 1, the infection will spread.
If R0 is less than 1, the infection will die out on its own at some point.
Therefore, in a simple pandemic evolution model, controlling R0 over time (Rt) and lowering it from 1 is key to control and eradicate the pandemic. In the absence of a vaccine or similar, efforts are usually directed at controlling the Transmission Rate ß, since the Recovery Rate γ would remain constant.
Covid19: Calculation of R0,ß,γ.
A person remains infected from the time he or she can infect another (with or without symptoms) until he or she is no longer able to infect. This is called the recovery period T. In Covid19, it looks like T=15 days.
The Recovery Rate is defined as the inverse of the period T:
| γ = 1 / T |
Therefore, if Period T is 15 days, the Recovery Rate (γ) of Covid19 is:
| γ = 0,0667 |
The R0 of Covid19 is being established by experts based on global data in approximately:
| R0 = 2,2 |
Finally, having both factors, we can calculate the Transmission Rate (ß) as R0 * γ:
| ß = 0,1467 |
Bending the Covid19: Confinement and Protection.
In the Covid19 scenario, with no vaccine in the short term, there are only two generic ways to decrease the reproductive number over time (R(t)). Either confine people or protect people who are not confined.
Both confinement and protection can be graduated from nothing to everything. This would be the Degree. The objective of the Degree of Containment (GC) and Degree of Protection (GP) is to reduce the Transmission Rate. As the Recovery Rate γ is constant, we are influencing the value of R(t) and, therefore, the reduction of the pandemic.
Both strategies reduce the Transmission Rate over time ß(t), which in this case is equivalent to reducing the R(t) since the Recovery Rate remains constant.
In fact, at each point in time, the original basic reproductive number could be reduced by a percentage that will depend on which Degree of Confinement (GC%) and which Degree of Protection (GP%) we apply. The formula would be:
As we see, R(t) <= R0 so the infection rate = ß = R(t) *γ will also go down.
Protection is preferred over Confinement, as the latter stops the economy. Only if you do not have sufficient means to be able to protect people, you have no choice but to confine people until they can be adequately protected.
Scenarios
From here, we could establish different scenarios.
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Scenario 1: The Covid19 without protection or confinement.
Spain has 46.65 million inhabitants (N), which we could consider equal to the initial Block S minus the initial infected we had or imported from outside.
With these data, if nothing had been done and the pandemic had been left to evolve as it pleased, the expected results would have been shown:
This can be seen in the graph, where the right axis (blue curve) marks the total number of deaths, and the left axis (orange curve) the impact on GDP. The growth has an exponential form week by week until its stabilization by having reached the maximum level of possible infected people.
If the entire population is infected, the pandemic can no longer grow, and the Growth Rate drops to zero. As there are no new infections, Block I empties at the Recovery Rate until it reaches zero. This is called having reached the level of intrinsic group immunity.
In this scenario, the peak of people in Block I occurs five months after the start (23 weeks) and reaches almost 25 million people. This can be seen in the graph comparing the evolution over time of R0 with the net number of people infected (Block I). It should be borne in mind that the pandemic most likely began well before any known cases were recorded. If it were back in January, we would be talking in this case about reaching a peak in mid-May.
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Scenario 2: Non-Confined Protection
Imagine that when Covid19 was detected, Spain would have had sufficient means of protection (respirators, masks, gloves, protective equipment, tests, etc.). In that scenario, most people would have been protected, and no confinement would have been necessary, the result would have been:
Scenario 3: COVID19 from now on, estimated deaths and impact on GDP
In Spain, the necessary means of protection were initially not available. Nor is there any prospect of having a vaccine in the short term. Therefore, to protect human life, we only have to skillfully manage the Degrees of Confinement and Protection. The objective is to significantly reduce the number of deaths without increasing too much the negative impact on the GDP. The challenge is to bring the R(t) below 1 and to let the contagion dynamics itself work in our favor by helping to eliminate the pandemic.
To avoid runaway growth in the number of deaths, ideally, the choice would be to choose Protection. However, as we did not have sufficient means of protection, we needed a powerful Shock Confinement that would reduce the R(t) to well below one.
This confinement is tremendously expensive. If it is total confinement, it would cost us about 1.9% of GDP per week. Therefore, as soon as possible, and when the protective measures allow us to do so, we have to replace confinement with protection.
After confinement (total or partial), the re-start of the economy is neither immediate nor easy. It will be gradual, probably throughout the rest of the year. With this in mind, the quote-unquote scenario could be “optimal”:
Conclusion
The management of the Covid19 is the result of political decisions, taken with the great added difficulty of having partial data and few absolute certainties. However, politicians do have access to multiple sources of information that give them a global vision that each expert does not have. And most important of all, they can get things done.
When a politician claims to have done what the experts have told him, it sounds more like paraphernalia than reality. He makes the decisions. Listening to everyone but making them himself. This brings with it a great responsibility, and these decisions have consequences.
I wish we had had the means of protection to stop the pandemic and its toll on human lives. Severe containment and its tremendous impact on GDP could have been avoided.
If we handle with finesse the elements at our disposal and get people to collaborate, we can mitigate the catastrophic scenario. Still, it will be very hard.
English version of the article published in Spanish at:
