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Applying Chemical Reaction Engineering to Epidemiology

  • 1.  Applying Chemical Reaction Engineering to Epidemiology

    Posted 03-29-2020 11:59
      |   view attached

    I am sitting at home being a good citizen and waiting the 15 days that we have been requested by he President.  I am retired after 40 years in the industry but still do a bit of consulting and the shutdown has drastically affected that work.   As I recall a great Chemical Engineer once said We Chemical Engineers are not smarter than the rest of you, we just know how to look it up faster, or something to that effect. (former head of Chem. Engr. Dept at University of Texas Dr. McKetta). So as most inquiring minds are prone to do, I have been doing some research on the SARS-CoV-2 (aka COVID-19 or the coronavirus).  Besides reviewing a lot of articles on the CDC site which includes the ones related to the use of Hydroxychloroquine and Azithromycin (Z-Pack) by both the Chinese and the French.  Good reports on in-vitro tests and a limited clinical trial. Both with good reports. Then I read an editorial by Dr. Fauci in the March 26th New England Journal of Medicine in whcih he seems to now believe this is not going to be more than an outbreak like a severe flu. Further in the latest briefing I watched Dr. Birx seems to indicate that the data they are now seeing seems to be showing that the current models being used to project the "pandemic" seems to be overestimating the number of cases by a pretty large margin.

    Sort of made me wonder if the reaction by the government of practically shutting the economy down was a bit of overkill. In a telephone townhall with my Congressman, former Chair of the Homeland Security Committee, Michael McCall, and a noted invectious disease doctor in Austin, Dr. Mark Escot, it was stated that Texas was relying on models done by the University of Texas. I believe from my research that this model is based on the work of Dr. Laren Meyers wh has published a number of papers on the issue.  One which caught my eye was in 2007, entitled "CONTACT NETWORK EPIDEMIOLOGY: BOND PERCOLATION APPLIED TO INFECTIOUS DISEASE PREDICTION AND CONTROL". Not only does Dr. Meyers work through "a brief overview of compartmental models, the dominant framework for modeling disease transmission, and then contact network epidemiology, a more powerful approach that applies bond percolation on random graphs to model the spread of infectious disease through heterogeneous populations."   In Dr. Meyer's article it states: "In chemistry, the mass-action law states that the rate of a chemical reaction is proportional to the product of the concentrations of the reacting substances. In epidemiology, the mass-action assumption states that the number of new cases of disease in a time interval is proportional to the product of numbers of infected and susceptible hosts in the previous time interval."

    This sounds a lot like the kinetics we Chemical Engineers studied in college. The epidemiologists have developed their models along the same basis, first using chain-binomial modeling, then a more flexible approach called compartmental modeling.  This compartmental model has been used to predict how much "Immunization" is required to reduce the reproductive rate for an infectious disease to below one. e.g. One person passing on a virus to at least one other person. At below that rate the spread will eventually die out.  "Extensions of this basic model have been used to predict the minimum coverage necessary to drive specific diseases to extinction. For example, measles and whooping cough-two of the most contagious diseases-are thought to require 90-95% coverage, chicken pox and mumps 85-90% coverage, polio and scarlet fever 82-97% coverage, and smallpox 70-80% coverage."  [R. M. Anderson and R. M. May, Infectious Diseases of Humans, Dynamics and
    Control, Oxford University Press, Oxford, 1991.]

    The original SARS virus proved some of those models wrong. Seems that the calculated case count was much lower than the initial projections (sound familiar).  "Shortly after severe acute respiratory syndrome (SARS) was first recognized outside of Asia, epidemiologists estimated its basic reproductive rate (Ro) to be between 2.2 and 3.6 for this virus.  These estimates are well above one and similar to rates measured for new subtypes of influenza. Despite this high estimate and worldwide susceptibility to SARS, the disease did not spark a global pandemic."

    "The discrepancy between the high R0 estimates and the limited spread of SARS might be explained by effective public health intervention that reduced the basic reproductive rate of the disease. Consider, however, the transmission of SARS in
    China during its initial four months of spread before the implementation of extensive public health measures. Case counts were much less than expected during this period, as suggested by a simple calculation. The expected total number
    of cases of a disease is predicted to increase by a factor of Ro for every generation of disease transmission, where a generation is the average time between an individual becoming infected and their infecting others. The average generation time (γ) for
    SARS was estimated to be 9.7 ± 0.3 days. The cumulative number of SARS cases after D days of transmission is predicted to be approximately:"

    D/γ             1 − RoD/γ+1
    Σ  (Ro)i =___________              [10]
    i=0                     1 − Ro

    "For R0 ranging between 2.2 and 3.6, this then suggests that the first four months of SARS spreading in China should have produced somewhere between approximately 30,000 and 10 million cases. China ultimately reported only 782 cases
    during this initial outbreak, which, by equation (10), suggests that the reproductive rate of SARS was actually closer to 1.6.
    Why do the initial estimates of Ro seem incompatible with the observed epidemiology in China? The basic reproductive rate has two critical inputs: (1) intrinsic properties of the pathogen that determine the transmission efficiency per contact and the duration of the infectious period, and (2) the patterns of contacts between infected and susceptible hosts in the population. While the first factor may be fairly uniform across outbreaks, the second may be quite context dependent, varying both within and among populations. The problem with the SARS estimates stems from the mass-action assumption of compartmental models-that all susceptible individuals are equally likely to become infected. When this assumption does not hold, the models may yield inaccurate estimates or estimates that do not apply to all populations. The Ro estimates for SARS were based largely on outbreak data from a hospital and a crowded apartment building, with anomalously high rates of close contacts among individuals. It may thus be inappropriate to extrapolate estimates for Ro from these specific settings to the population at large. Contact rates in the general community may be much lower and, therefore, so may be the rate at which SARS spreads."

    "The transmission efficiency of SARS varied considerably. A few individuals were responsible for a large proportion of disease transmission In contrast to the mass-action assumption of standard compartmental models, contact patterns may vary within a community. Consider two scenarios: a community in which all individuals have approximately the same number of contacts and a community in which a very small number of individuals have enormous numbers of contacts while all other individuals have only one or very few contacts. The basic reproductive rate of disease (Ro) can be identical for the two communities, while
    the resulting epidemiology will differ significantly."

    "While the mass-action assumption laid the groundwork for major advances in epidemiological theory, it may be inappropriate when contact patterns are heterogeneous. To overcome this limitation, mathematical epidemiologists have developed
    several methods to explicitly consider heterogeneity in contact patterns including more complex deterministic and stochastic compartmental models with multiple demographic groups, branching process models, dyad models, Reed-Frost chain-binomial models, and individual based models."

    What Dr. Meyers has coonsidered in 2007 was "a recent addition to this toolkit, contact network epidemiology, which is an analytical framework that explicitly and intuitively captures the diverse interactions that underlie the spread of diseases (Figure1)"

    "Figure 1. Compartmental and contact network models. Mass action models assume that all individuals in a group are equally
    likely to become infected, while contact network epidemiology considers diverse contact patterns that underlie disease transmission. The disease spreads along the arrows (top) and the edges (bottom).
    (S=susceptible, I=infected, and R=recovered.) "
     

    "The methods of contact network epidemiology can be divided into three steps. First we attempt to build a realistic network (graph) model of the contact patterns at an appropriate temporal and spatial scale. Second, we mathematically predict the spread of disease through the population based on intrinsic features of the pathogen and structural properties of the network. Third, we manipulate the network to model control strategies and analyze the epidemiological impact of such manipulations."

    Without going into the derivation that Dr. Meyers has done in the paper (which I encourage all who have read this far to go find and read, including all the references that I have failed to include).  What I was impressed with was that some of the same issues that were discussed with the earlier models and now the later models of overpredicting are the same as are discussed in Levenspeil's Chemical Reaction Engineering, particulary with respect to gas phase reactions.  Not all collisions result in a reaction.  In Epidemiology not all contact results in an infection.  While there are other mitigations that epidemiologist must consider, such as possible acquired immunity due to exposure to a similar type of coronavirus, or interference due to patients taking drugs that may interfere in the absorption of a virus' rouge RNA due to interference in the DNA polymerase process, it still seems to me that these can be accunted for much like things that inhibit chemical reactions. 

    Maybe while we are taking this respite from or normal day to day activities and trying to reduce the concentration of reactants in our society so as to reduce the number of contacts which spead the virus, some of those who are more adept at using the kenetics we were taught in college in their practice may want to look into how the Contact Epidemiologist are now modeling this and see if there is a way to help them tighten up their models. One thing we need to remember is that the method of slowing the transmission has one glaring deficiency.  For every person who stays in and does not get exposed and eventually does not either succumb or recover keeps the concentration of susceptible people high.  The curve plateauing and going back down is based on the reduction in the number of susceptible people (reduction in concentration of initial reactant) but are we changing the rection from a batch reaction to more of a plug flow reaction?  Are we really going to reduce the death toll or are we just extending the duration of the disease?  Also are we shifting the order of the reaction by limiting the available reactant?
     
       



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    Marc Young PE
    Managing Partner
    AC Engineering, LLC
    Sealy TX
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    Attachment(s)

    pdf
    MeyersAMS07.pdf   532K 1 version


  • 2.  RE: Applying Chemical Reaction Engineering to Epidemiology

    Posted 03-29-2020 21:17
    Edited by Aaron Sarafinas 03-29-2020 22:15
    For an excellent discussion of an interdisciplinary process modeling approach on this, check out @Joe Hannon's "QbD with Scale-up Suite" blog entry on "Coronavirus projections" at http://blog.scale-up.com/2020/03/coronavirus-projections.html.  This is a powerful example of how a Process Scheme should precede a model, even for Coronavirus projections.  He introduced a "mixing parameter" that he described as
    The effect of reduced movement/ contact of citizens is included as a mixing parameter, ranging from 1.0 with free movement to 0.0 with no movement at all.  [Because infection behaves like an un-premixed chemical reaction, classical chemical engineering concepts like intensity of segregation are relevant and the rate of reaction depends quite linearly on the number of infectious people that are moving around/ mixing.]

    Joe used the capabilities of DynoChem and regressed the model parameters for the number of cases in Ireland, made some predictions of future cases, created some interesting contour plots of parameter sensitivities, then also looked at the process requirement of hospital beds needed.

    I saw that Joe made a follow-up post with a second iteration on the model, adding in the data from Italy, with more interpretations and conclusions at:  http://blog.scale-up.com/2020/03/coronavirus-projections-model-2.html

    Sensible process modeling thinking can be applied to complex systems, but we need to remember to listen to the experts in the field and incorporate their perspectives in our models.

    Hope that you all stay healthy.


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    Aaron Sarafinas
    Principal
    Sarafinas Process & Mixing Consulting LLC
    Warminster PA
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  • 3.  RE: Applying Chemical Reaction Engineering to Epidemiology

    Posted 03-31-2020 09:53
    Thank you, Aaron, for your post.

    Public health is a tricky field and perhaps the trickiest part is that when public health workers do their job, they don't get credit for the pandemic that didn't happen.  Instead, they are criticized for creating inconvenience and wasting resources for nothing.    Perhaps their budgets are cut.

    The success of containing the outbreak of SARS is a shining example of not giving public health practitioners their due.  From https://www.who.int/whr/2003/chapter5/en/index5.html:
    "The rapid containment of SARS is a success in public health, but also a warning. It is proof of the power of international collaboration supported at the highest political level. It is also proof of the effectiveness of GOARN [the Global Outbreak Alert and Response Network] in detecting and responding to emerging infections of international public health importance. At the same time, containment of SARS was aided by good fortune. The most severely affected areas in the SARS outbreak had well-developed health care systems. Had SARS established a foothold in countries where health systems are less well developed cases might still be occurring, with global containment much more difficult, if not impossible.  Although control measures were effective, they were extremely disruptive and consumed enormous resources -- resources that might not have been sustainable over time."

    SARS was contained in less than a year, due to a massive public health effort.  Perhaps this is unfortunate -- perhaps it fostered the delusion that public health experts don't earn their keep or deserve our respect.



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    -Kirsten

    Kirsten Rosselot
    Process Profiles
    Calabasas, CA United States
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  • 4.  RE: Applying Chemical Reaction Engineering to Epidemiology

    Posted 03-31-2020 11:19
      |   view attached

    Aaron

    One statement you said has kind of stuck with me a few days and I wanted to make a response.  Your statement "Sensible process modeling thinking can be applied to complex systems, but we need to remember to listen to the experts in the field and incorporate their perspectives in our models."  sort of came across as maybe we as chemical engineers needed to stick to our own mending and let the heath care experts take care of this.  If that was your intention, then I could not disagree with you more. If it was not, then let me apologize in advance. 

    This pandemic is an all hands on deck event.  What I am concerned about is that health care has been a bit of a take whatever measures you can to avoid catching something no matter what the cost and avoid risk at all cost. Of course our legal profession and our tort system has helped lead to this outcome.  We here in the United States have seen this blow up our health care cost as Doctors in their efforts to avoid litigation by ordering too many tests at the expense of our heath care system.  This has lead to a reluctance to try anything that has a modicum of risk in treating patients.  I believe from reviewing the modeling efforts the health care profession is still trying to err on the side of no risk.  An example is the current effort to just reduce exposure to try to keep the peak hospital beds and ICU beds form running short.  While prudent social distancing is a good practice during and type of outbreak and the normal annual flu outbreaks come to mind.  However employing draconian measures of asking people to shelter in place, shut down all schools,   

    What I see is that as chemical engineers, particularly process engineers are excellent at staging reactions so they do not exceed the capabilities of the available vessels in continuous flow processes.   We are the experts at doing that.  And like it or not the viral infection is really a chemical substitution reaction that takes place in the lungs particularly with respect to the ACE-2 receptors in the lung alveoli.  The infection rate is the rate of reaction, It is figuring out how to spread this out so that we fully utilize the bed space for the time it takes to allow the virus to run its course and yet limit the fatalities that may be the most efficient process.  An example is the current projections for my home state of Texas.  See the attached IHME (University of Washington) healthdata projections. Note we have adequate bedspace based on their baseline projection.  We jsut may be a bit short on ICU space.  Yet I cna tell you that from the other models I have reviewed there is no consideration for drug therapy intervention.  While many reviled our President for suggesting use of HCQ+ Z pack it clearly is a good choice.  It is a published fact that it acts as a ACT-2 inhibitor that stops the RNA replication which is the primary mechanism for the virus to spread in the body.  The issues were that some could not take it for the side effects.  Yes there are some. But there is not enough of the drug to treat everyone so combine there and the medical community claims foul.  It is not even considered  as a mitigation. As engineers, we would work around this by removing reactants that could negatively react with a process to prevent such action.  If given the opportunity to have input on the "process of the epidemic treatment" we might be able to help them do it more efficiently with less undesirable side effects. I think you get my drift.  

    It is important that there is collaboration with all that can make a contribution.  The problem is that it is difficult for the polticians to understand really who are the experts in each phase so they tend to give credence to only one group.  I find it refreshing that Dr. Fauci and Dr. Brix on the Corona Virus taskforce does not always agree with each other.  It shows that they are allowing a more inclusive discussion to be held.  

    My current belief is that we are just setting ourself up for a second peak possibly higher than the first by removeing too many form the early exposure. The reservoir of unreacted reagents are just being held up in separate vessels which will eventually be dumped back into the main vessel. This is not an efficient reaction process. If we think of it in these terms we can help solve for a more efficient and less deadly process.

    We as chemical engineers must not let this become the next CHINA SYNDROME.  Note that the last one was caused an accidents like Three Mile Island whch lead to severe problems for this country and the world for a number of years. It has set back nuclear industry in the US permanently. It lead to more fossil fuel use that many now are concerned about the resulting CO2 emissions.  For those of us that lived through the 70's and early 80's we know what an impact that had on the US economy. Lets not allow our country to be paralysed once again by such an impact. we must not allow this to become China Syndrome II. I think it is imperative we speak up and let the government and medical research community know how we can help them.  Remember, those that don't know, don't know they don't know.        



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    Marc Young PE
    Managing Partner
    AC Engineering, LLC
    Sealy TX
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    Attachment(s)



  • 5.  RE: Applying Chemical Reaction Engineering to Epidemiology

    Posted 03-31-2020 20:26
    I think you misunderstood me, @Marc Young.  Chemical engineers can both contribute their know-how to understanding the outbreak AND recognize the expertise of public health professionals who have made epidemics their specialty.  I feel that a collaborative, interdisciplinary approach, valuing different perspectives, is usually a superior alternative when trying to understand complex systems.  When I said "Sensible process modeling thinking can be applied to complex systems, but we need to remember to listen to the experts in the field and incorporate their perspectives in our models" I am referring to such an interdisciplinary collaboration.


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    Aaron Sarafinas
    Principal
    Sarafinas Process & Mixing Consulting LLC
    Warminster PA
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