Parameters for infectious compartment

[apascualgarcia]

This issue is relevant for: @Jennifer-Villers and @jordan-klein: they are handling these parameters. @JudithBouman2412: A new term may get into the computation of R0 from the critical compartment.

Intro An optimistic scenario rises the number of beds in Isolation Centers + Hospitals to 1500 beds for 4M inhabitants, which is ~4 beds for 10K. Since the informal camps are 2K, in a global outbreak the camp will have access to <1 bed, so we can assume that the existence of these facilities can be neglected.

As a consequence, all cases should be handled within the camp. This opens a challenge to adapt the parameters of the infectious compartment to this new scenario.

Problem (1): Now we have the following parameters that should be merged into a single compartment:

• Fraction of infectious hospitalized.
• Average duration of infection A/I
• Average time from symptoms onset I to hospitalization H
• Average time from hospitalization H to critical care, here considered as death D
• Average time from hospitalization H to recovery R

Proposed Solution Consider a new compartment including critical symptoms that mimics "hospitalization", I will call it "C" for "Critical". The parameters would be:

• Fraction of infectious hospitalized: Fraction of I --> C
• Average time from symptoms onset I to hospitalization H. Rate I --> C.
• Average time from hospitalization H to critical care. Rate C --> D.
• Average time from hospitalization H to recovery R: No recovery considered, all die.

Problem (2) Determine which of these parameters should be age/comorbidity-dependent.

[jordan-klein]

@apascualgarcia

Agree with the proposed solution for problem 1.

For problem 2:

Of these parameters, the one I've worked on is fraction of infectious hospitalized. I currently have it as age but not comorbidity dependent, using data from the Spanish ministry of health, the largest sample size/highest quality data on age-specific rates of hospitalization. The data I've been able to find on fraction of cases hospitalized by age and comorbidity is from the US centers for disease control but the estimates are much higher than what I've seen in other literature and the data seem to be of poorer quality. I can either:

1. Keep my estimates for this parameter as is using only the Spanish data with the parameter only age-dependent, or

2. Use the US data for the 4 adult classes (13-50, over 50, comorbid yes/no) and the Spanish data for children, assuming no children are comorbid.

@Jennifer-Villers has worked on estimates for the other 3 parameters you mention.

[apascualgarcia]

@jordan-klein

From your current estimates, what we were suggesting after Jennifer sharing the paper about Nigeria spread is that Syrian ages should map older Western ages (10 years older) while you are mapping roughly the same ages. Regarding issue #12, commorbidities-age 2 could have the same values than age 3.

[jordan-klein]

@apascualgarcia

Hm, rather than making that assumption I'm inclined to use the US data for adults. The estimates are high compared to the other literature, the age groups run older than the ones in our model (19-64 & 65+ vs 13-50 & 51+), and they actually have data on comorbidity by age.

Edit: I updated this parameter as described. parameter doc parameter values

[Jennifer-Villers]

@jordan-klein Do they somehow adjust for the fact that most covid cases are never tested/diagnosed? Maybe that could explain why their numbers are so high. That is what I liked about the ICL study: they corrected for under-reporting.

[jordan-klein]

@Jennifer-Villers Re the ICL data: upon further investigation I found the study was based on a small sample size pre-print from China a few months ago that has been withdrawn. So the Spanish data seems to be the best source of age-specific only proportion requiring hospitalization.

In the US data, they do not correct for under-reporting, which I agree seems like it may explain why their numbers are so high and indicate their data is of poorer quality. What I do like about the US data however is that they report proportion requiring hospitalization by age and comorbidity, rather than just age, and their numbers are on the higher end of the plausible.

Their proportion requiring hospitalization in the 19-64 age group (maps to the 13-50 age group in our model) without a comorbidity falls between those of the 30-39 and 40-49 age groups in the Spanish data. Their proportion requiring hospitalization in the 65+ age group (maps to the 51+ age group in our model) without a comorbidity is approximately that of the 70-79 age group in the Spanish data. And comorbidities increase the age-specific proportion requiring hospitalization by about 3.

I can of course use the Spanish data, but the US data is in line with @apascualgarcia 's suggestion that Syrian ages map to older Western ages and allows us to incorporate differential hospitalization rates for population classes with comorbidities into our model without relying on additional assumptions.

[Jennifer-Villers]

@jordan-klein I agree with all your points. It seems reasonable for our purpose to go with the US data, thanks a lot for this extensive research.

[apascualgarcia]

@Jennifer-Villers and @jordan-klein,

I had a look at the values for the hospitalized/critical care/death data that Jennifer collected and there is the following problem. There are parameters for the interval Symptoms onset to hospitalized and Symptoms onset to critical, but there are no data from the time interval between the time in which the pacient is hospitalized and the time in which she becomes critical. This interval for us would be the rate in which those in the critical compartment take to basically die. And similarly to what happend with the presymptomatic period, we cannot simply generate random values for one, for the other and substract, because we may end up with unfeasible (negative) values.

So I think a solution could be to consider this model:

S --> E
E --> P
P --fa--> A 
P --(1-fa)*(1-fv)--> I
P --(1-fa)*fv-->V    (v stands for seVere, because C is used for contact matrix)
A --> R
I --> R
V --> D

So basically to detemine from the presymptomatic compartment the fractions of assymptomatic, those symptomatic that will survive and those that will die. Then we can take for the symptomatic surviving the same rate than for the assymptomatic for recovery, and for those dying the interval between symptoms onset and critical care in hospitals.

Does it make sense?

[Jennifer-Villers]

@apascualgarcia Hi Alberto, Thank you for thinking about all of this. Your proposition seems reasonable to me.

However, I wanted to stress that a similar problem exists for the latency period, which is the difference between the incubation period and the pre-symptomatic period for which you fitted a Gompertz distribution (thank you for that!). Do you have an idea of how to circumvent that problem too?

[apascualgarcia]

@Jennifer-Villers Hi Jennifer,

For the presymptomatic period it is no longer a problem because we already found the distribution. I can generate an incubation period, then the presymptomatic period and the exposed period will simply be the remainder of the incubation period. Here there is not any issue because the presymptomatic period is strictly smaller than the incubation period. Whereas for the hospitalization, the time from onset to critical is often shorter than the one from onset to hospitalization.

[Jennifer-Villers]

@Jennifer-Villers Hi Jennifer,

For the presymptomatic period it is no longer a problem because we already found the distribution. I can generate an incubation period, then the presymptomatic period and the exposed period will simply be the remainder of the incubation period. Here there is not any issue because the presymptomatic period is strictly smaller than the incubation period. Whereas for the hospitalization, the time from onset to critical is often shorter than the one from onset to hospitalization.

Ok, I think that I finally see your point. Is it because the confidence intervals of "onset to hospitalization" and "onset to ICU" are too big? Then, yes, I believe that your proposition could solve the problem (sorry it took me so long to figure it out).

[apascualgarcia]

@Jennifer-Villers Exactly, we have E--->I and P-->I and it happens that max(P-->I) << min(E-->I) so we can always define E-->P>0 taking the difference, whereas for the hospitalization intervals both highly overlap so this strategy does not work.

[jordan-klein]

@apascualgarcia @Jennifer-Villers I agree with this approach, if we treat V conceptually as "cases that are currently or are symptomatic and will become severe" rather than only "cases that are currently severe."

[apascualgarcia]

@Jennifer-Villers @jordan-klein Following Jordan comment, I realized that splitting immediately after P the infectious compartment in three parallel pathways, the total time in which we have infectious people would be around would be shorter than it should. I had a new look at all parameters that you guys estimated and when there is an infection, there are roughly 7 days until the pacient either recovers or get into a hospital. Once in the hospital, it takes another 7-10 days to either recover or die. So the most natural map I can see would be:

(W=Western, S=Syrian) Infectious (W) = Infectious (S) (7 days) Hospitalized (W) = Medium symptoms (S), will recover but they take 10 days more (the W interval Hospitalized to recovery). What we change with espect to W are not the rates, but the fraction of those that will become severe. Hospitalized (W) = Severe symptoms (S), those that will not recover. The added time from infectious is ~3days, which is the time from hospitalized to critical care.

So the model would look like

S --> E E --> P P --(1-f)--> A P -- f --> I I --g(1-h)--> M I --gh-->V
A --> R I --(1-g)--> R M -->R V --> D

It looks more complicated, but we have all the fractions f, g, h, and rates. You can find the model in manuscripts/seairqd_class_syria/SEAIRQD_byClass_Syria_V2.pdf

[Jennifer-Villers]

@apascualgarcia Thank you, Alberto, for the update.

I am wondering if you're not overestimating Syrian's ability to recover from symptoms that would bring western people to the hospital. I can tell you that during the peak of the pandemic, people whose symptoms were not life-threatening were not accepted to the hospital. My husband almost lost a colleague in New York city because the paramedics thought his symptoms were not serious enough to go to the hospital. Fortunately he insisted and upon arrival at the hospital the doctors told him he would probably have died if he hadn't made it to the hospital on time. Blood clots obstructing irrigation of the lungs and brain is the number one cause of death in younger people and I believe it would be the number one cause of death for Syrian refugees as well, especially if a lot of them already suffer from hypertension. It does not require ICU to save someone from a blood clot but it requires hospitalization.

To sum up, I don't think that what is considered "hospitalized" in our countries can be considered "medium symptoms" in Syria. I think that their chances of dying without the hospital are high, even if they don't need ICU and ventilators.

I believe that your previous version of the model had more chances of capturing the reality than the one you're proposing now.

[jordan-klein]

@apascualgarcia I agree with @Jennifer-Villers. I do not see the need for adding a "medium symptoms" compartment (M) since we don't expect any cases requiring hospitalization to recover. I propose something similar to your previous approach that takes into account the additional time for which we expect cases that will require hospitalization (V) to be infectious:

S --> E E --> P P --(1-f)delta_PP--> A P --f(1-h)delta_PP--> I P --fhdelta_PP--> V V --alpha*V-->D A --> R I --> R

Where f is proportion symptomatic, h is proportion of cases that will require hospitalization, 1/alpha is time from onset of symptoms to ICU. The V compartment therefore represents all cases that will die without hospitalization but are still alive, in the camp, and infectious (~10 days as opposed to the ~7 days for A/I).

Please let me know what you think as I'm currently working on manuscript edits.

[Jennifer-Villers]

@jordan-klein That totally looks like what I had in mind.

[apascualgarcia]

@jordan-klein and @Jennifer-Villers Hi guys I think I didn't explain myself properly, it is not about the conceptual meaning of "M" but about its role in the model.

Jennifer, I am not overestimating as soon as we play with the proportions lying in each compartment, which is the strategy we agreed to follow, namely inflating those values mapping the proportions to older age intervals. What is not realistic either is to assume that all cases that would be hospitalized in Western countries will die in Syria, what we agreed to assume is that severe cases would all be dying, and to increase the fraction of severe cases.

Jordan, the model you propose is exactly the same I proposed above and, as I said, when I faced the challenge of parameterizing it with the parameters you provided I realized that 1) the map is tricky because there are no neat correspondences between parameters and the model and 2) it underestimates the time that we have infectious in the camp. Let me explain why again.

In western countries you reported that there are three classes of symptomatic:

• Compartment I. Symptomatic that do not require hospitalization, proportion P1 and time to recovery T1=7 days.
• Compartment H. Symptomatic that do require hospitalization, proportion P2 and time to recovery T2= 7 days to get into the hospital + 10 days of recovery = 17 days.
• Compartment V. Symptomatic requiring intensive care, proportion P3 and time to recovery intensive care T3=7+3 days = 10 days (in our case all will die).

If we select the model only with infectious (7 days) and severe (10 days to die) there will be a fraction that would spend up to 17 days being infectious around that dissapears. In addition, you estimated P1, P2 and P3 and you already inflated these values. If compartment H dissapears, how would you map P1, P2, P3 to the new model? Are you suggesting that P2 will die? This seems to me a too strong assumption.

My proposal is to keep the (inflated) values you already estimated for P1, P2, and P3 and create an M compartment mimicking the H compartment, and it is not about the meaning it is about keeping in the model those infectious cases that will take longer. If you think the model with only I and V should prevail, please present how the parametrization would work.

[jordan-klein]

@apascualgarcia in line with our previous conversation today, I revised the model

[apascualgarcia]

Thanks @jordan-klein I do not fully understand the model now, I think we do not have enough data to parameterize it. I think it would be better to discuss it in "person". Could you please commit the document you are using to generate the model diagram? I would like to plot the alternative model so that we can discuss both together.

A technical note on git, to modify files edited by multiple authors please rename files or create a git branch to track the different versions.

[Jennifer-Villers]

@apascualgarcia Hi Alberto, I agree that we should discuss all of this in person. On my side there was no misunderstanding, it is just that we have diverging views on the severity of the hospitalized compartment in western countries. I understand that one of your main concern with our previous version of the model is that severe people may not die that fast and remain infectious longer. I don't believe that hospitalized people in western countries remain infectious for the entire duration of their hospitalization and I will try to find literature on the subject today. Please give me some time to do the research before we chat. I hope this way that we will be able to address most of your concerns.

[apascualgarcia]

@Jennifer-Villers Sorry Jennifer, you missed a conversation between Jordan and me yesterday, I will try to give you an update. The last model Jordan proposed is not the one above but this one. Mine would differ a little bit, I would like to create a diagram.

I understand that one of your main concern with our previous version of the model is that severe people may not die that fast and remain infectious longer.

Not only that, the main difference I see is if all hospitalized cases in Western countries would be dying or not. We agreed in that all ICU cases will die but not in that all hospitalized will die. The second question is what you mentioned, for those hospitalized and survying, for how long they will remain infectious. For the first question, the solution I discussed with Jordan yesterday was the following:

• Consider three infectious boxes as in western countries. Not hospitalized, hospitalized and severe.
• The fraction that goes into hospitalized and severe is larger (we all agreed on that).
• The intermediate compartment is the problematic one. Should we consider them to die, to recover, or something in between? Since there is no way we can know this, the solution we found yesterday is to simulate both extremes and provide upper and lower bounds, so we would maintain that intermediate compartment.

For the second question, whether hospitalized cases remain infectious or not for a longer period, I talked to a colleague who is doing the modelling of beds occupancy in public hospitals in Zürich. What she says is that it is unknown for how long people is infectious. In their models, they become non-infectious if it is assumed that the barriers used are effective and the hospital personnel is not infected. As a rule of thumb, the more symptomatic they are the more infectious they are considered, at least for symptoms like caugh.

@Jennifer-Villers, @jordan-klein What I would like to propose is that each of us prepares a diagram of the model (s)he thinks it is the most appropriate AND how it would be parameterized from the data we have. I think we should close this question asap, today if possible. Both the code and the estimation of R0 are in standby for this question, so let me know when you would be ready, from my side I would need just to plot the diagram so I can do it almost at any time.

[Jennifer-Villers]

@apascualgarcia @jordan-klein As planned, I did some literature research on the duration of the infectious period.

The most extensive study on the subject is this one from Canada. They analyzed samples from 90 patients and here are their conclusions:

• Positive cultures of the virus were only observed up to 8 days post symptom onset (they tried to cultivate virus collected up to 21 days post symptom onset).
• They determined that for every one day increase in time between symptom onset and test, the odds ratio of being cultured positive was decreased by 37%.

The limitations of this study:

• they could only successfully cultivate viral samples from 26 patients (not 90)
• they don't specify the clinical severity of the symptoms of the patients but they specify that immunocompromised individuals and children may be underrepresented in their study.

Another source of information on the subject is the US CDC. Their key findings are the following:

1. Viral burden measured in upper respiratory specimens declines after onset of illness (CDC unpublished data, Midgely 2020, Young 2020, Zou 2020, Wölfel 2020).
2. At this time, replication-competent virus has not been successfully cultured more than 9 days after onset of illness. The statistically estimated likelihood of recovering replication-competent virus approaches zero by 10 days (CDC unpublished data, Wölfel 2020, Arons 2020).
3. As the likelihood of isolating replication-competent virus decreases, anti-SARS-CoV-2 IgM and IgG can be detected in an increasing number of persons recovering from infection (Wölfel 2020).
4. Attempts to culture virus from upper respiratory specimens have been largely unsuccessful when viral burden is in low but detectable ranges (i.e., Ct values higher than 33-35[1])(CDC unpublished data).
5. Following recovery from clinical illness, many patients no longer have detectable viral RNA in upper respiratory specimens. Among those who continue to have detectable RNA, concentrations of detectable RNA 3 days following recovery are generally in the range at which replication-competent virus has not been reliably isolated by CDC (CDC unpublished data, Young 2020).
6. No clear correlation has been described between length of illness and duration of post-recovery shedding of detectable viral RNA in upper respiratory specimens (CDC unpublished data, Midgely 2020, Wölfel 2020).

[Jennifer-Villers]

@apascualgarcia

I have also tried to answer some of the points you made yesterday:

• We agreed to assume is that severe cases would all be dying, and to increase the fraction of severe cases. We agreed to assume that only critical cases would die when we thought that non-critical cases that need hospitalization would have access to it. The lack of access to a hospital is, to my point of view, a game changer and our model should change accordingly.

• We agreed to inflate the proportions lying in each compartment by mapping them to older intervals. I thought that the age-inflation was meant to reflect the hardship of their life conditions that could weaken their health and resistance, not to reflect the absence of hospitalization. I would be fine with matching the Syrian ages to western ages without any age inflation, but I am not fine pretending that most people who need hospitalization but not ICU would recover without any access to the hospital (it is unlikely given the type of symptoms people are hospitalized for).

• It underestimates the time that we have infectious in the camp I am not sure about that for two reasons:

1. People usually don’t remain infectious for the entire duration of their hospitalization (see literature review in my previous comment).
2. The reason hospitalized people in western countries live so long with the disease (up to 17 days from symptoms onset) is because they are at the hospital and receive care. Their lifespan is artificially prolonged thanks to hospitalization. The same people with no access to any hospital-like care would likely die within an average of 10 days (not 17), which is what we saw in the news in Italy and NYC when people delayed going to the hospital.

My key point regarding hospitalization is that it is usually a question of life and death, not a question of ‘needing more time to recover’. Those people who recover at the hospital would have been very likely to never recover (hear “die”) if they had stayed at home without hospital care.

If it was up to me, I would build two models:

• One with access to hospitalization (people are removed from the infectious pool, whether they live or die). Hospitalization can mean portable clinics built last minute, as long as it provides care and is outside of the camp.
• One without (people die within an average of 10 days from symptoms onset, this one is the same proposed by Jordan and the one you proposed before)

I could also be okay with one of the last propositions you made together with Jordan (although I am not clear on all the parameters yet--we can discuss that during the meeting).