Formulas+Code: Who are the people shielded in the green zone?

[apascualgarcia]

@jordan-klein @Jennifer-Villers @ecam85 @Chamsy-Sarkis

We would need to present the formulas used for the following description and a script to compute it, to generate rapidly new scenarios for different assumptions (I copy and paste from your report after the meeting):

Adults (13-50) with comorbidities some family members if an arrangement cannot be found for the kids. We have decided to establish the rule that no more than 20% of the camp can be shielded (otherwise it would be impossible to reach immunity).

We could start with a 20% but it is important to show how the numbers belew fit within a given threshold:

In a camp of 2000 people,

Note that if I remember properly, the population in camps follow a log-normal distribution with mean 6000 (Jordan which was the exact values?). Irrespective of the precise values, we will need to test our simulations for at least three population sizes (mean and upper and lower CI) so this should be an input variable and the rest of values should be rescaled accordingly.

we estimated that 119 are elderly and 125 are adult comorbid.

how?

Hence, up to 156 healthy adults (spouses of comorbids) and kids (of comorbids) can be shielded with them. Among those 156 healthy people, we arbitrarily estimated that 70 would be adult spouses and 86 would be children.

Families have on average more thann 2 kids and you are roughly assuming here 2 adults + 2 kids, does it make sense to split a family in two? I guess one may think that older kids can stay with relatives or alone but this should be explained and look for a way to implement it. Otherwise I think it may make more sense to less complete families.

[Jennifer-Villers]

Hi Alberto,

Thank you for opening this issue. I agree that a general script allowing changes would be a good idea. I have answered some of your points in the text below:

@jordan-klein @Jennifer-Villers @ecam85 @Chamsy-Sarkis

We would need to present the formulas used for the following description and a script to compute it, to generate rapidly new scenarios for different assumptions (I copy and paste from your report after the meeting):

Adults (13-50) with comorbidities some family members if an arrangement cannot be found for the kids. We have decided to establish the rule that no more than 20% of the camp can be shielded (otherwise it would be impossible to reach immunity).

We could start with a 20% but it is important to show how the numbers belew fit within a given threshold:

In a camp of 2000 people,

Note that if I remember properly, the population in camps follow a log-normal distribution with mean 6000 (Jordan which was the exact values?). Irrespective of the precise values, we will need to test our simulations for at least three population sizes (mean and upper and lower CI) so this should be an input variable and the rest of values should be rescaled accordingly.

Chamsy wanted us to focus on smaller (informal) camps as their operating mode is completely different from the larger camps. The large camps are usually much closer to cities with a lot of camp people mixing with people from the outside. I don't think that our current model is that suitable for larger camps. If you want to create a distribution, perhaps we could look at the sizes of informal camps as they are usually smaller than formal camps.

we estimated that 119 are elderly and 125 are adult comorbid.

how?

Jordan used data available from Syrian camps in Jordan to estimate the proportion of people in each age category . We just applied those numbers to a population of 2000.

Hence, up to 156 healthy adults (spouses of comorbids) and kids (of comorbids) can be shielded with them. Among those 156 healthy people, we arbitrarily estimated that 70 would be adult spouses and 86 would be children.

Families have on average more thann 2 kids and you are roughly assuming here 2 adults + 2 kids, does it make sense to split a family in two? I guess one may think that older kids can stay with relatives or alone but this should be explained and look for a way to implement it. Otherwise I think it may make more sense to less complete families.

This was a long discussion with Chamsy. We estimated that a lot of comorbid adults will be older than 40 years old and have only adult kids (who would not join). Chamsy also anticipated that kids older than 12 years old would probably stay with a cousin or other family arrangements. Of course these 70 and 86 numbers are just rough estimations and will vary from one camp to another but we had to start somewhere.

[apascualgarcia]

Chamsy wanted us to focus on smaller (informal) camps as their operating mode is completely different from the larger camps. The large camps are usually much closer to cities with a lot of camp people mixing with people from the outside. I don't think that our current model is that suitable for larger camps. If you want to create a distribution, perhaps we could look at the sizes of informal camps as they are usually smaller than formal camps.

The distribution I mentioned (6K) was for informal camps only as far as I remember. We should otherwise have an idea of the new distro and model at least three values.

Chamsy wanted us to focus on smaller (informal) camps as their operating mode is completely different from the larger camps. The large camps are usually much closer to cities with a lot of camp people mixing with people from the outside. I don't think that our current model is that suitable for larger camps. If you want to create a distribution, perhaps we could look at the sizes of informal camps as they are usually smaller than formal camps.

I see, we need to find a way to formalize/justify this explicitly to adapt it to changes in pop. sizes.

[apascualgarcia]

@Jennifer-Villers @jordan-klein

In issue #12 the estimated fraction of population with comorbidities we agreed to be raised to 17% and Jordan brought a link to a file that does not exist. In the link you mentioned above it is just of 10%

[jordan-klein]

@apascualgarcia @Jennifer-Villers The probability distribution of the population of the informal camps is as follows: ln(N) ~ Normal(6.886, 0.611)

The proportion of the adult population with comorbidities is indeed ~17%, the population structure is here (same as the null model).

Echoing @Jennifer-Villers, after a long discussion with Chamsy we decided that the maximum capacity of the green zone should be 20% of the camp, and given the estimated size of each class in a camp of 2,000, we would expect an estimated 70 non-comorbid adults and 86 children to join relatives in the green zone. I would suggest we generalize this to camps of different sizes by converting these values into proportions, ie the proportion of the population made up of non-comorbid adults in the green zone is .035 and the proportion of the population made up of children in the green zone is .043. Please see the population structure I have for the intervention models for reference.

[Jennifer-Villers]

@apascualgarcia Sorry for the long silence. I am slowly trying to catch up.

I double checked what the average population of the informal camps is and I got 1200 with a median of 950, based on this data set (idps_in_camps_syria_april_2020.xlsx) that Chamsy shared with us when we started the project: https://drive.google.com/drive/folders/1hnyjceF21uVsyUX5CTS8k1_D6NFaxfH4

[apascualgarcia]

Thanks @Jennifer-Villers, great this is consistent with the numbers that @jordan-klein provided. Apparently the distribution has a long right tail so I think it make sense to start modelling the population size you suggested (2000) even if it is above the average, since these are camps more difficult to handle. If we have time we can then simulate a couple of sizes more.

Jordan has expanded this script to incorporate the criteria to split the population. I see now more clearly the reasoning, which is that shielding all elderly plus all comorbid adults in the green zone still leaves space to shield more relatives, and you decided that this number was 20%.

What I still do not understand are the criteria behind this choice:

% # 55% of remainder of green zone capacity will be allocated to child family members of adults aged 13-50 with comorbidities

green_rem_chil <- .55*green_rem

% # 45% of remainder of green zone capacity will be allocated to non-comorbid adult family members of adults aged 13-50 with comorbidities

green_rem_ad <- .45*green_rem

How did you end up with these numbers, 55% and 45%?

Cheers

[Jennifer-Villers]

How did you end up with these numbers, 55% and 45%?

These numbers were decided arbitrarily based on the discussion that we had with Chamsy. He estimated that most adults 13-50 with comorbidities are between age 40 and 50, so they don't have younger children but may still want to bring their healthy spouse (we did not assume that every adult 13-50 with comorbidities would bring a spouse because some of them may have an elderly spouse or an adult spouse with comorbidities as well). Adults with comorbidities of age < 40 may not be able to find arrangements with family members for their kids and would bring them to the green zone.

There is no strict rationale for these numbers. They will change based on the family compositions of the adults 13-50 with comorbidities: an information that unfortunately we do not have. So we made a guess.

[apascualgarcia]

@Jennifer-Villers , @jordan-klein

The problem is that 45% and 55% are so close to 50% that a 5% accuracy sounds very ad-hoc (I would simply say 50% if there is no further explanation).

Here an attempt to provide some more accurate numbers. Let me call P(comorbid) the probability of being an adult with comorbidities and P(married) the probability of being married. Then the probability that an adult brings to the shielded zone an spouse with no comorbidities is P(married)*(1-P(comorbid)). Therefore, the number of adults that will end up in the green zone is:

Frac_age2_green =  Frac_age2*P(comorbid)*( 1 + P(married)*(1-P(comorbid)))

The variable P(married) is possibly near one, but I'm sure Chamsy will have an idea. The next question is how many kids they bring. The following numbers I bring are just guesses, but for some of them I think we know the numbers or Chamsy may know them. Let us assume that a woman has her first kid with 18 years old on average. I think we know that the mean number of kids per couple married is 7. So if we assume that there is a birth every 2/3 years we get the following numbers:

Woman age 40: (Kids < 18) = (5-6); (Kids < 13) = (3-5)
Woman age 50: (Kids < 18) = (0-3); (Kids < 13) = (0-2).

Therefore, we need to estimate only the fraction of women that will be 40/50 and if we consider that all under 18 or all under 13 (I chose 13 because is the limit for age 1) will be shielded.

What do you think?

[Jennifer-Villers]

The problem is that 45% and 55% are so close to 50% that a 5% accuracy sounds very ad-hoc (I would simply say 50% if there is no further explanation).

I agree with that.

Here an attempt to provide some more accurate numbers. Let me call P(comorbid) the probability of being an adult with comorbidities and P(married) the probability of being married. Then the probability that an adult brings to the shielded zone an spouse with no comorbidities is P(married)*(1-P(comorbid)). Therefore, the number of adults that will end up in the green zone is:

Frac_adults_green = Frac_adultsP(comorbid)( (1-P(married)) + P(married)*(1-P(comorbid)))

I like the idea but I am not sure I understand what Frac_adults_green mean. Is it supposed to be the total fraction of adults shielded (with and without comorbidities) or only the fraction of healthy adults brought by a spouse with comorbidities? Basically, when I replace the proportions with their actual value, I end up with a smaller number of adults than the number of adults with comorbidities.

The variable P(married) is possibly near one, but I'm sure Chamsy will have an idea. The next question is how many kids they bring. The following numbers I bring are just guesses, but for some of them I think we know the numbers or Chamsy may know them.

Yes, according to Chamsy, their society is very traditional. I checked in the data set (idps_in_camps_syria_april_2020.xlsx) what is the proportion female-headed households. If the head of household is a woman, it usually means that the husband has died. I think that this could be a reasonable proxy for the proportion of unmarried adults (assuming that women are a lot more likely to be widowed than men). According to this, P(married) = 0.9112.

Let us assume that a woman has her first kid with 18 years old on average. I think we know that the mean number of kids per couple married is 7. So if we assume that there is a birth every 2/3 years we get the following numbers:

Woman age 40: (Kids < 18) = (5-6); (Kids < 13) = (3-5)
Woman age 50: (Kids < 18) = (0-3); (Kids < 13) = (0-2).

Therefore, we need to estimate only the fraction of women that will be 40/50 and if we consider that all under 18 or all under 13 (I chose 13 because is the limit for age 1) will be shielded.

What do you think?

Can you please clarify the part about the children? Are you talking about women age < 40 vs. women age between 40 and 50?

It would only make sense to shield children under 13 (not 18). Chamsy was very clear about that in our conversation. At age 16, a lot of girls are already married and kids between 13-16 are independent enough to stay with a cousin or alone.

Also, I think that we should keep in mind that the idea is not to allow every single adult with comorbidities to bring their children. The idea is to first ask them to try and find arrangements with other family members and only if they don't find any solution, they would be allowed to bring their children to the green zone. We can also imagine that a few married couples may accept to be separated and that the healthy one would keep the children while the spouse with comorbidities would be shielded.

[apascualgarcia]

I like the idea but I am not sure I understand what Frac_adults_green mean. Is it supposed to be the total fraction of adults shielded (with and without comorbidities) or only the fraction of healthy adults brought by a spouse with comorbidities? Basically, when I replace the proportions with their actual value, I end up with a smaller number of adults than the number of adults with comorbidities.

Sorry, the formula was wrong, I updated it. It is the total number of adults shielded:

Frac_age2_green =  Frac_age2*P(comorbid)*( 1 + P(married)*(1-P(comorbid)))

Can you please clarify the part about the children? Are you talking about women age < 40 vs. women age between 40 and 50?

It was just a couple of examples because you mentioned these two ages in your estimations. There would be between 0 and 5 kids per couple, and the final number will be biased towards 0 or 5 depending on the age of women given the assumptions.

It would only make sense to shield children under 13 (not 18). Chamsy was very clear about that in our conversation. At age 16, a lot of girls are already married and kids between 13-16 are independent enough to stay with a cousin or alone.

Great, then just estimate those

Also, I think that we should keep in mind that the idea is not to allow every single adult with comorbidities to bring their children. The idea is to first ask them to try and find arrangements with other family members and only if they don't find any solution, they would be allowed to bring their children to the green zone. We can also imagine that a few married couples may accept to be separated and that the healthy one would keep the children while the spouse with comorbidities would be shielded.

Ok, this variability could be simulated a posteriori changing the % of total population shielded once we give a first estimation, but I think it is important to start with some short of reproducible recipe with some numbers to justify our guesses.

[jordan-klein]

@apascualgarcia @Jennifer-Villers, why don't we just keep the capacity of the green zone at 20% of the camp's pop, calculate frac_age2_green, and then frac_age1_green = .2 - frac_age2_green - frac_age3_green, especially if the idea re Chamsy is to encourage people to bring as few children as possible into the green zone?

EDIT: I committed changes in line with this, updating the class_structure of the models with shielding. Updated script with option to manually set green zone capacity (I use 20%) here and updated class structure for shielded models here.

Let me know your thoughts, I'm comfortable with this construction since we limit the capacity of the green zone to a reasonable level and prioritize adults in the green zone being able to bring spouses, with the remainder allocated to children they bring. The method for estimating number of non_comorbid spouses that will be brought into the green zone by @apascualgarcia is reasonable, while any estimates we try to get for the number of children that will be brought into the green zone will rely on data we do not have and/or many arbitrary assumptions. If Chamsy suggests we allocate for space in the green zone to children (of course with the tradeoff of a larger green zone), we can just adjust the variable in the script "green_cap".

[Jennifer-Villers]

@apascualgarcia @jordan-klein

Thank you for updating the formula, it works much better!

I am fine with Jordan's proposition. I think that it makes a lot of sense.

Regarding the proportion of unmarried adults, I made a mistake in my calculation. Since 0.0888 is the average proportion of female-headed households, it means that 0.9112 households have two adults in it, which makes the proportion of married adults P(married) = 2 0.9112 / (0.0888 + 2 0.9112) = 0.95

This assumes that men-headed households all contain two adults (meaning that only women are widowed), a hypothesis that could be supported by death rate data for men vs. women in Syria since the beginning of the conflict.

EDIT: if instead of assuming that only women are widowed, I assume that they are 3.5 x more likely to lose their husband (based on the death rate for men being 3.5 x higher than for women in Syria), I get this:

• 0.0888 = proportion of female-headed households (based on the data set)
• 0.0254 = proportion of man-headed households where the wife has died (3.5 x less than the number of female-headed households)
• 0.8858 = proportion of households with a couple.

P(married) = 0.8858 2 / (0.8858 2 + 0.0888 + 0.0254) = 0.94

[jordan-klein]

@Jennifer-Villers @apascualgarcia Working off of your ideas, I used a slightly different method to estimate the proportion of the population that is not vulnerable but will accompany their spouses to the green zone. The idea is this:

We're not interested in the probability that an adult brings a spouse with no comorbidities to the green zone, but more generally the probability that an adult aged 13-50 with comorbidities has a spouse in a non-vulnerable population group that they would bring into the green zone with them, let's call this P(bring_sp). We make the assumption (as discussed with Chamsy) that virtually all men aged 13-50 are married to women aged 13-50, but some women aged 13-50 can be married to men over 50. By the law of total probability, we have:

P(bring_sp)=P(bring_sp|spouse aged 13-50)*P(spouse aged 13-50)+P(bring_sp|spouse aged over 50)*P(spouse aged over 50) where P(bring_sp|spouse aged 13-50)=P(age2=no_comorbid), P(spouse aged 13-50)=2*37_M_13/(37_M_13+37_F_13), P(bring_sp|spouse aged over 50)=P(age3 not in green zone)=0, and P(spouse aged over 50)=(women married to older men)/(37_M_13+37_F_13).

Following this, we have: P(bring_sp)=P(age2=no_comorbid) * 2*37_M_13/(37_M_13+37_F_13). I get Pr(bring_sp)=0.8480556, which is a bit higher than what I would get using @Jennifer-Villers's estimation of P(married). Script is here and classes_structure for shielded is here. @apascualgarcia @Jennifer-Villers let me know if you prefer this approach, relying on the assumption that virtually all men aged 13-50 are married to women aged 13-50, or @Jennifer-Villers' estimation of P(married); I am ultimately agnostic towards which we use.

[apascualgarcia]

why don't we just keep the capacity of the green zone at 20% of the camp's pop, calculate frac_age2_green, and then frac_age1_green = .2 - frac_age2_green - frac_age3_green, especially if the idea re Chamsy is to encourage people to bring as few children as possible into the green zone?

We may end up doing this but I would like to show the rational behind the estimation of 20% (if it is the final value), and it is actually not that difficult. There is an easy way to estimate the fraction of age1 that would be shielded:

We can say that most kids in age1 will have their moms within the age2 population. Assuming that all married women have kids and the estimation of P(married) of @Jennifer-Villers:

frac_mothers = P_married * frac_age2 / 2

Therefore, distributing the kids uniformly we have

Nage1=frac_age1 / frac_mothers

which leads to 1.6 kids per mother on average. Now simply estimate the number of married woman in the green subpopulation:

frac_mothers_green = (frac_age2_green * P_married)/2

And which is the fraction of the total population that their kids represent

frac_age1_green = frac_mothers_green*Nage1

Summing up all fractions for age1, age2 and age3 getting in the green zone I obtain that 26.7% of the population would be shielded. If then we say that the number will be lower because they will be encouraged to leave their kids in the other zone or whatever is fine, but at least show how was the estimation made "mechanistically". You will find the script here. After looking at @jordan-klein estimation I think my estimation of age2 is not totally correct, I follow the rational but I do not completely follow your computation Jordan, what is the variable 37_M_13?

[Jennifer-Villers]

@apascualgarcia Hi Alberto, After having a quick look at your calculation to estimate the fraction of kids, I think that something is missing. I expect that there should be a negative correlation between having comorbidities and the number of young kids you have (in your calculation kids seem to be distributed evenly independently of the age of the parents):

• more people between age 40 and 50 are expected to have comorbidities (compared to younger adults)
• people between age 40 and 50 are not expected to have children under the age of 13 anymore.

I don't think we have the necessary data to estimate the number of shielded kids more precisely but I expect your estimation to be more of an upper limit than an average.

@jordan-klein I have the same problem as Alberto to follow your computation.

[jordan-klein]

@apascualgarcia @Jennifer-Villers

why don't we just keep the capacity of the green zone at 20% of the camp's pop, calculate frac_age2_green, and then frac_age1_green = .2 - frac_age2_green - frac_age3_green, especially if the idea re Chamsy is to encourage people to bring as few children as possible into the green zone?

We may end up doing this but I would like to show the rational behind the estimation of 20% (if it is the final value).

20% is based on our discussion with Chamsy and the desire to minimize the proportion of the camps that need to be put in the green zone so that they are manageable. I would be comfortable using this rationale to justify the shielded population structure, more comfortable than I would be estimating the number of shielded children relying on a bunch of shaky assumptions.

We can say that most kids in age1 will have their moms within the age2 population. Assuming that all married women have kids and the estimation of P(married) of @Jennifer-Villers:

frac_mothers = P_married * frac_age2 / 2

Therefore, distributing the kids uniformly we have

Nage1=frac_age1 / frac_mothers

which leads to 1.6 kids per mother on average. Now simply estimate the number of married woman in the green subpopulation:

frac_mothers_green = (frac_age2_green * P_married)/2

And which is the fraction of the total population that their kids represent

frac_age1_green = frac_mothers_green*Nage1

This approach is rough, I agree with @Jennifer-Villers that it may be workable for an upper limit, but I'm not sure if it can be for much more than that. It is important to specify that the interpretation of the value Nage1 that we're searching for , that we would multiply by the number of women aged 13-50 with comorbidities to find the fraction of children that should go in the green zone, is "children aged 0-12 per women aged 13-50 with comorbidities". We definitely cannot make the assumption that the population aged 13-50 with comorbidities is evenly distributed in this age interval. The calculation is also not exactly right, we have the precise population by sex in each age group (which I have been adjusting for in my calculations). I would also note that this likely overestimates the number of children women in the green zone have by a lot; with a high mortality population such as this one, it is likely that significantly fewer than all children have a mother who is alive. I can try to see if I can use data on "child headed households" to estimate orphan-hood.

Summing up all fractions for age1, age2 and age3 getting in the green zone I obtain that 26.7% of the population would be shielded. If then we say that the number will be lower because they will be encouraged to leave their kids in the other zone or whatever is fine, but at least show how was the estimation made "mechanistically". You will find the script here. After looking at @jordan-klein estimation I think my estimation of age2 is not totally correct, I follow the rational but I do not completely follow your computation Jordan, what is the variable 37_M_13?

I have some time tomorrow to work on estimates for the Nage1 variable, but I am dubious as to how useful it would be given these limitations/shaky assumptions we would need to make to overcome them. I'm comfortable taking the reigns on the demography-centric parts of the model, so I can compute it and post for feedback on whether we think it may be useful. @apascualgarcia @Jennifer-Villers 37_M_13 is males aged 13-50 in demographic notation.

[Jennifer-Villers]

@jordan-klein The percentage of child-headed households is only 1.34% and households are considered child-headed if the person in charge is 18 and younger (not 13 and younger), so I don't know if that aspect would change our calculations a lot. However, I agree that Alberto's calculation is likely to be an overestimation as we would expect the majority of adults with comorbidities to not have children under the age of 13 anymore.

Out of curiosity, where is the 37 coming from in your demographic notation of males aged 13-50? I had guessed the M_13 part but not the 37.

[jordan-klein]

@Jennifer-Villers thanks for pointing this out- this means we would have to make additional assumptions I would not be comfortable making about the age distribution of child head of households/orphanhood. I really do think our least bad option is to set a capacity for the green zone and allocate the remainder to children without making our own estimates of "children aged 0-12 per women aged 13-50 with comorbidities".

In demographic notation, n_N_x, where x is the age at the beginning of the age interval and n is the length of the age interval, N is the total pop in the age interval, M is male and F is female.

[apascualgarcia]

I expect that there should be a negative correlation between having comorbidities and the number of young kids you have. (in your calculation kids seem to be distributed evenly independently of the age of the parents): more people between age 40 and 50 are expected to have comorbidities (compared to younger adults) people between age 40 and 50 are not expected to have children under the age of 13 anymore.

In age 2 we are considering women between 13 and 50. It is true that the older they are the more likely it will be that they have comorbidities. However:

1. Women tend to be younger than men and since the probability of having a couple with comorbidities in both members is much lower than having only one of the members of the couple with comorbidities, I would expect that many women are shielded because their partner have comorbidities, so they will be young and fit to have young kids. Since Jordan says these numbers are available for men and women, let's have a look at that.

2. Given the mean number of kids per family, women of different ages may have the following mean number of kids (I explained the details of this calculation above, and this is possibly and underestimation because many will possibly give birth before being 18): Woman age 20: (Kids < 13): (0-1) Woman age 30: (Kids < 13): (5-6) Woman age 40: (Kids < 13) = (3-5) Woman age 50: (Kids < 13) = (0-2).

This numbers are in general higher than the average of 1.6 kids < 13 I came out with, and it is lower from the 2.2 kids <13 that Chamsy provided, so I don't think it is necessarily an overestimation.

3. Even if they have comorbidities, some do not prevent for having more kids.

4. I agree orphans may be a relevant number to look at.

20% is based on our discussion with Chamsy and the desire to minimize the proportion of the camps that need to be put in the green zone so that they are manageable.

In the document you provided after the meeting with Chamsy you said

We have decided to establish the rule that no more than 20% of the camp can be shielded (otherwise it would be impossible to reach immunity)

What is the maximum number of people that can be shielded to reach heard immunity is something to be tested. And if there is a strong argument to say that 20% can be managed but 25% or 30% cannot I would like to hear that. I would say that if, for instance, 30% of the population should be shielded considering comorbidities+spouses+kids<13, separating a 10% of the population just because we stick arbitrarily with 20% is what may generate a real management problem.

I am not looking for a precise number here, I just want to justify that the numbers we provide are reasonable and that we can show why they are reasonable.

I would be comfortable using this rationale to justify the shielded population structure, more comfortable than I would be estimating the number of shielded children relying on a bunch of shaky assumptions.

"bunch of shaky assumptions" --> Man, try to be more delicate with the tone of your criticisms, it's Saturday, 2:49AM and I am working on this instead of having beers or sleeping, so please take care of my ego.

The approximation is rough, indeed it is. But it is more than setting ad hoc a parameter which is what we had 18 messages above. And I insist, it is not about the derivation of an exact number, an upper bound would be enough.

New proposal:

To me it is clear that this number lies between 20-30%. And I also see that it would be interesting to see how this threshold affects herd immunity. So I think it may be better to invest time in simulating and analysing more scenarios than in digging more into this question. I propose these scenarios:

• Shielding only age 3.
• Shielding age3+age2+spouses.
• Shielding age3+age2+spouses+kids up to 20%
• Shielding age3+age2+spouses+kids up to 25%
• Shielding age3+age2+spouses+kids up to 30%
• Shielding age3+age2+spouses+kids up to 35%

We will understand better the system and the effect of the interventions, and it is not needed to provide nothing more than a bunch of shaky assumptions to roughly justify these numbers. What do you think?

[jordan-klein]

See my comments on slack. Also script and new folder of classes_structure files for different shielding scenarios.