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To better understand how it works, it is explained how it is applied to a current issue such as COVID19 (note coronavirus is a family of viruses, COVID19 is a particular coronavirus that was presented in late 2019). It is explained how

• get the information,

• how models are formed,

• use existing models,

• adapt the models to the situation

• analyze problems with the data that can be obtained

• adapt model to use data with problems

• calculate key model factors

• integrate behavior of people and authorities

• use the models to find a better strategy

>Model

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To show how this other physics works, it is shown in a simplified way how a model to study the COVID pandemic19 is structured and how the work is used to advise in decision-making. It also explains the difficulties they are having and how they can be addressed.

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The following video shows how the virus spreads, how it penetrates the cell and how it replicates to attack other cells again.

Data for modeling can be obtained from:

General global data on infected, dead, tests, measures, etc.

Our World in Data

Data from Chile (MINSAL)

MINSAL Chile

Data by state and commune in the United States:

New York Times

Google mobility data:

COVID-19 Community Mobility Reports

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The first step is to get to know the topic by

• read generic information to get an overview
• contact experts who can contribute to a first vision of the subject
• look for more detailed information on the key issues for the model
• search for existing models
• generate your own model that meets the information requirements to be obtained
• review the model with experts who can point out possible conceptual and / or parameter errors

In this particular case there are two key issues that should be modeled:

• the times that the different faces take and the possibility that the person can infect others

• the mechanisms and the probability of contagion per day

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In the case of COVID19 the main contagion is by droplets (drops that carry the virus) that are expelled by the infected. Depending on the size of the drops, they fall at different speeds to the ground. This can be modeled with Stokes' law for the displacement of spheres in a viscous medium with the asymptotic speed (the maximum reached by falling) being equal to\\n\\n

$v=\displaystyle\frac{2\rho}{9\eta}a^2$

where \ rho is the density of water, \ eta the viscosity of air and a the radius of the drop. Since the speed of fall is proportional to the radius squared of the drop, smaller droplets fall faster, while smaller ones can stay in the air for a long time (mist type).

If it is assumed that the drop is expelled at a height of 1.5 m, the fall time can be calculated with the fall speed. With a drop expulsion speed of 0.1 m / s and the fall time, the range can be calculated if there were no diffusion processes. As if there is diffusion, it can be assumed that the ranges of small drops are totally overestimated.

If the literature is consulted, it will be seen that the droplets that are generated when speaking are between 2 and 100 um with a higher concentration between 4 and 8 um (The size and the duration of air-carriage of respiratory droplets and droplet-nuclei, JP Duguid , J. Hyg. (Lond.) 44, 471-479 (1946)). Therefore, the current 1 meter recommendations are too limited. If studied in more detail, it will be seen that droplets change to a diffusion mode that is more limited in range than indicated. For this reason, assuming a distance of 2 meters is more realistic and it is considered that the drops remain in the air for several minutes or even hours.

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Seeing how limited the use of social distancing is, the use of a mask becomes key. common masks captures a good part of the droplets emitted by the wearer of the mask and therefore are a protection for others and not for the wearer of the mask. Since the porosity is not less, they do not protect against aspiring droplets that are already in the environment.

If real protection is needed, you should use a mask of type N95 that has pores between 65-125nm in size and therefore lets only a few droplets pass. On the other hand, there is a danger that droplets reach some of the mucosa (wet areas) of the body, so a eye protector (visor) is useful. In addition, it is required not to touch your mouth, nose or eyes since you can have viruses on your hands and thus reach mucosa . Hospital personnel also wear suits so that viruses do not remain attached to clothing . Finally there is the washing that takes about 20 seconds for the soap to dissolve the outer layer of the virus and thereby destroy it.

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Once we know the probability of contagion we must estimate the number of infected with whom we contact and with this we have the possibility of contagion. Here we must distinguish between the number of daily C contacts and those of people with whom we can potentially have N contact. To estimate the size of this group or network of contacts from which the real contacts originate, you should look for a proxy , that is, a variable that is a good measure of what we are looking for, not being exactly the variable that we would seek to know. In the case of communities, and bearing in mind that for a pandemic we must monitor the use of hospitals, the number of people we can group per hospital can be assumed as size. For this, it is enough to consider the size of the population and divide it by the number of hospitals.

In the case of Valdivia, there are approximately 170 thousand inhabitants and two clinics with ICU beds (the German Clinic and the Regional Hospital). In this sense, Valdivia can be divided into two groups or communities that form networks through which the pandemic can spread: the middle to upper class that tends to use the services of the German Clinic and the second group that uses the services of the Regional Hospital with an N average of about 85 thousand people.

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Within the community with which we usually have contacts are those people who are currently infected and actively infecting I . From the relationship between this number and the number of people in the community, it is estimated that a person with whom we have contact is infected and can infect us.

To estimate the number of active infected it is necessary to measure the diagnosis of the population. This can be done by trying to cover the majority or via sampling and extrapolating to the entire community. Therefore it is always necessary to know the number of tests carried out so that the proportion of positive cases divided by the number of diagnoses gives an estimate of the total number of infected. For this reason the phrase that is heard 'if more is found, more is found and therefore it does not make sense' since you should always buy the number of positives with the number measured, so the increase in measurements only increases the precision.

Note: if you want to keep an outbreak under control, it may be necessary to systematically search for the infected to quarantine it. In these cases they diagnose it from all people and multiple times.

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On the day one meets with a small group of people that we call C contacts and with whom there is sufficient proximity to be able to infect (distance less than one meter for a long time). These vary from day to day and are a small subgroup of the N community of people. Studies have shown that the average number varies with age and is made up of people with whom one lives, a friend with whom one meets, a colleague from where one works or studies and contacts for personal services employed.

Graphic of 'Mixing patterns between age groups in social networks', S.Y. Del Valle a, J.M. Hyman b, H.W. Hethcote c, S.G. Eubank, Social Networks 29 (2007) 539-554

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The probability of a person being infected can therefore be estimated by considering\\n\\n- all the $C$ contacts you have per day\\n\\nIf the contacts are multiplied with the probability that a person is an active contagion I / N , we obtain\\n\\n- the contagious number with whom you have contact $C I/N$\\n\\nIf the average number of infected people with contacts is multiplied by the probability of contagion \ beta , which gives the probability of daily contagion\\n\\n

$\beta C \displaystyle\frac{I}{N}$

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To calculate how the disease spreads, we can use epidemiological models of the SIR type (susceptible, infected, recovered or resolved). In this, it is first estimated how the number of susceptibles S varies, equating it to the multiplication of the susceptibles with the probability of contagion:\\n\\n

$\displaystyle\frac{dS}{dt}=-\beta C\displaystyle\frac{I}{N} S$

\\n\\nThe negative sign reflects that the susceptible number is decreasing due to the infection. Secondly, we must consider the recovered population R or that we will define as resolved by the effect that there are deaths. In this case, the SIR model assumes that the variation of the resolved is proportional to the existing infected.\\n\\n

$\displaystyle\frac{dR}{dt}=\gamma I$

\\n\\nwhereby the variation of the infected is calculated by adding the new infected and subtracting the resolved\\n\\n

$\displaystyle\frac{dI}{dt}=\beta C\displaystyle\frac{I}{N} S-\gamma I$

\\n\\nThe problem in the SIR model is that the solved ones are taken at random from the infected which does not correspond to the real process in which there is a process of generation of symptoms, development of the disease and finally recovery or resolution with characteristic average times. Therefore we will work with an alternative expression\\n\\n

$\displaystyle\frac{dI}{dt}=\beta C\displaystyle\frac{I}{N} S-\displaystyle\frac{dR}{dt}$

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If we try to apply the model for the Chilean case, we see that the local data presents serious anomalies:

• In the daily infected there are two jumps that cannot be a real situation and in fact if the associated information is studied, it is noted that in two situations the criterion was changed
• there is a jump in additional deaths that also comes from a change in the source of information of data compiled by hospitals to that of the civil registry

The problem of these changes originated when Chile studied the excess deaths , that is, the number of deaths observed this year with respect to the trend of the previous year. Hence, it was determined that not all the deaths by COVID19 that were occurring were being recorded because there were deaths that occurred in the homes and not in the hospitals. For this reason, reports from hospitals were transferred to those of the civil registry. On the other hand, it was recognized that he had died for other reasons in which COVID19 had contributed indirectly. This adjusted the criteria to identify the dead.

The problem with these changes is that it makes the historical information questionable, thus losing the initial conditions in solving the equation of the model to be applied.

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The seriousness of the problems with the average data in Chile is that it does not allow us to reliably estimate the hospital need that will arise in the future . If there are not enough respirators, the situation is reached in which it is necessary to decide which patient to attend and which patient must literally be left to die due to insufficient infrastructure. In these cases, the probability of survival is evaluated and priority is given to patients who have a better prognosis (variant of the traditional triage).

The problem is that since the consequence of the infection takes about 14 days , any action we take today will take this time to take effect. For this reason it is key to have models that allow us to assess how the current situation will evolve against possible actions that we take today in order to select the one that is probably the most appropriate .

It is like piloting a boat from a position at the stern trying to see that the bow is on the right track.

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From physics, the problem can be solved. As a first step, with excess deaths and curve jumps, a correction factor k (t) can be estimated, which multiplied by the certain infected I_m allows us to estimate the probable number that actually exists:\\n\\n

$I(t) = k(t) I_m(t)$

\\n\\nOn the other hand, the reduction of infected by resolution can be estimated by the number of infected that we reduce today is similar to the infected that were generated a time ago and the duration of the disease. As the time to overcome the disease \ tau is of a given order, it is not a defined value but rather a time range so the factor \ gamma :\\n \\n

$\displaystyle\frac{dR}{dt} = \gamma I_m(t-\tau)$

\\n\\nIn this way the equation can be rewritten as\\n\\n

$\displaystyle\frac{dI_m}{dt} = \gamma I_m(t)\left(\displaystyle\frac{\beta C}{\gamma}-\displaystyle\frac{I_m(t-\tau)}{I_m(t)}\right)$

\\n\\nwhere it was assumed that we were at the beginning of the pandemic and the number of susceptible S is of the order of the entire population\\n\\n

$S\sim N$

\\n\\nThe factor\\n\\n

$R_0=\displaystyle\frac{\beta C}{\gamma}$

\\n\\nIt is called the reproductive factor and characterizes how the disease is spreading since it compares how \ beta C spreads with the possibility that the chain is cut depending on < tex> \ gamma . This can be calculated accordingly by solving for the evolution equation of the infected:\\n\\n

$R_0=\displaystyle\frac{I_m(t-\tau)}{I_m(t)}+\displaystyle\frac{1}{\gamma I_m(t)}\displaystyle\frac{dI_m}{dt}$

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Once you have the reproductive factor, it can be associated with factors that describe how countries reacted at the level of people. One of the parameters that allows this to be done is the mobility factors generated by google and which shows how the internet presents fewer searches in some concepts and greater in others.

With a model of this type, it is possible every time from the behavior of people to infer the spread and with it how it spreads and eventually it is possible to control the pandemic.

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Once you have the relationship between how the community behaves and with it how it affects the spread of the pandemic, you must study how effective the governments' measures are. For this, the information can be used to build an AI system that gives us behavior in the face of government actions.

With this, there is a system in which it can be used to predict how the actions of the rulers influence people and how they act according to the spread of the pandemic.

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It only remains to leave three messages for the road:

• Be curious with data. Every time you find one, explore if it contains any interesting information. In particular, see if it surprises you and you would have expected other behavior. If there is a discrepancy, why is that? What did you suppose is not?

• Every time you see an interesting process think about how you would model it. What variables would you use? What relationships will you assume?

• Schedule. Discover a library that allows you to assemble powerful tools with little effort and time. How could I access the data in bulk? With which algorithm would it solve the models it works with? How would you structure an AI system? How would I train him? would you check and I would finally use '

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Video: The Other Physics: methods