Effect Measure

Tomorrow we begin a blog experiment, one we already judge has failed. In January Marc Lipsitch and his team at the Harvard School of Public Health published a splendid paper using a mathematical model to investigate the spread of antiviral resistance in the control of pandemic influenza. When we read it our first thought was to write a substantial blog post about the results. The paper was published in PLoS Medicine almost the same week as another mathematical model on spread through the air traffic system by Colizza et al. and the Colizza paper seemed to get most of the newswire notice. But the Lipsitch paper is important in several respects. It has extremely interesting results of interest to planners or anyone else interested in pandemic influenza. And it is instructive. The Harvard team are expert modelers and subject matter experts. This is modeling done the right way and PLoS Medicine is an Open Access journal, so the entire paper was available for free download. Readers could follow the explanations with the original paper in hand. So we decided to go ahead and explain it in detail.

Why consider this an “experiment”? The experiment was to see if a paper that used a coupled system of non-linear ordinary differential equations as its main technical tool could be explained sufficiently so a lay audience could understand what was involved and how the model worked. In that way they would have a better appreciation for the findings and some understanding of an important tool, mathematical modeling. We took it as a personal challenge, and that part of the experiment succeeded, we think. We have been teaching a long time and it is our experience you can teach just about any subject to non-technical audiences if you take the time and effort. Some of the posts might take more focus and attention than most readers can afford or desire to devote to them, but we think most everyone who reads this site could make their way through the explanation if they invested the effort.

That’s where, we judge, the experiment fails. The blog format is both flexible and constraining. Readers come for short, usually stand alone, posts about something they’re interested in or just to see what’s being said in the blogosphere, a venue that has become surprisingly influential. They don’t come for a connected series of sixteen posts on a single specialized scientific paper.

Yes. Sixteen posts. This surprised even us. We read the original paper in an hour or two and it seemed straightforward. It wasn’t until we set out to explain it in detail — enough detail so a lay reader could see what was going on in almost every paragraph, figure and equation — that we began to realize how many moving parts there were that we took for granted. Even the figures took a couple of paragraphs each, sometimes a whole post for one figure. We’ve spent between almost forty hours writing this series. We wouldn’t do it again. We got a great deal out of it ourselves, for to teach is to learn twice. But it is a cost-benefit question for both reader and writer.

However we did do it, and it would be a waste to just delete the final drafts. We’re not forcing anybody to read them and some of you, no doubt, will do so with interest, and we hope even with pleasure. If we want most people who read us to keep coming here, we will have to keep posting in the usual blog style, though. We’ll also keep doing that to the best of our abilities.

We took a risk we don’t think paid off. Live and learn. First post, tomorrow.

Table of contents for posts in the series:

What is a model?

A modeling paper

The Introduction. What’s the paper about?

The essential assumption.

Sidebar: thinking mathematically

The model variables

The rule book

More on the rule book

Finishing the rule book

The rule book in equation form

Ready to run the model

Effects of treatment and prophylaxis on resistance

Effects of Tamiflu use and non drug interventions

Effects of fitness costs of resistance


A few words about model assumptions

Conclusion and take home messages


  1. #1 traumatized
    March 20, 2007


  2. #2 JJackson
    March 20, 2007

    Good go for it!

    A while a go (old site) you wrote a series of posts confusingly called Turkish Mutations (I think) explaining how AI gains access to the cell a2,3 a2,6 etc. These were great and I doubt these posts will fail in your objective. I, and I suspect others, are very willing to put in the time to try and improve our understanding and modelling is a great place to start. It is ubiquitous and the conclusions are often quoted but without an explanation of the method or how chaotically the model behaves depending on the parameters chosen as inputs.
    Richard Feynman was asked to try and explain Quantum Electro Dynamics (QED) by a non scientist friend but felt it was too difficult to do justice to for a lay audience. It was a matter of considerable regret to him that Alix Mautner died before he figured out how to give this lecture but he did so in a memorial lecture and the book based on it is readable and extraordinary. He felt a full understanding of physics could not be gained without equal understanding of math but was equal convinced that a fair understanding was attainable by everyone and was worth having.

  3. #3 Melanie
    March 20, 2007


    Yes, the blog format is constraining. But so are symphonies, string quartets and poetry. That having been said, I join JJackson to encourage you to bring us what you found. You are a gifted teacher who has taught me so much technical information in this space that I didn’t ever think I’d be able to understand. You’ve already invested a great deal in this series, so put it out and let’s dicker, as needed in the comments threads. I’m speaking as a math phobic who is always trying to overcome my shortcomings.

  4. #4 gilmore
    March 20, 2007

    It is better to have learned and forgotten, than to have never have learned at all. . .

  5. #5 andy
    March 20, 2007

    I’m a theoretical physicist with an interest in mathematical epidemiology, and read the paper but with some difficulty. I hope your that your “lay explanation” will clarify some parts I found confusing. I can hardly wait! Thank you so very much for your efforts — I assure you they have not been wasted.

  6. #6 R Hayes
    March 20, 2007

    Do you write for the many, or the few?

    In this forum, for the many, obviously; but how many of the many does it take for the effort to be worthwhile?

    It might be that those of your readers who read and benefit from the exposition are a crucial “market segment”; it depends on what your payoff is — and that might not be clear-cut or static.

  7. #7 MFoley
    March 20, 2007

    I agree with the above posts. As an economist with an interest in simulations I find a lot of good ideas in the math-epi field. I am probably able to get through these papers on my own, but having your guidance will greatly increase the range of insights I expect to gain. Let’s see those posts!

  8. #8 Chris
    March 20, 2007

    I think your little experiment shows a great deal about the concise and precise writing style that is expected of scientists. I still remember my first big science write-up in undergrad. I thought I put in some extra time and thought that I did a pretty good job of making it short and to the point. Imagine my surprise when my prof handed it back with a note that said “good, but it should be about half as long”.

    This condensed style we cultivate also leads to more jargon, and makes most of the science literature incomprehensible to those with no training or familiarity with the field. As a result, we’ll always need people like Carl Zimmer and Carl Sagan who popularize science without distorting its claims. Thanks for joining the ranks of people making science more accessible.

  9. #9 marquer
    March 20, 2007

    With regard to that Colizza paper, it says, right in the front matter,

    Like all mathematical models, this model for the global spread of an emerging pandemic influenza virus contains many assumptions (for example, about viral behavior) that might affect the accuracy of its predictions.

    Seems to me that the largest single assumption that is made by Colizza, et al, is that the neuraminidase-inhibitor antivirals are going to work to slow down the spread.

    There are serious reasons to suspect that any emergent panflu may be largely or completely resistant to Tamiflu and Relenza. It’s purely Panglossian to expect otherwise. And I am enough of a grouchy old engineering type that I instinctively dismiss any planning or modelling effort which does not include worst-case scenarios from the outset.

    With regard to air travel, I carry a folded N95 mask whenever I fly, tucked in my cabin baggage. If there is an obviously sick person in proximity to me, it is a sensible prophylaxis. Imperfect, but nevertheless much better than going entirely unprotected. Even if what the other person is infected with is not a lethal panflu, I prefer not to sit in foreign hotel rooms sick with even an annoyance-level head cold. I’ve done that. Ugh.

    I note en passant that the entire cohort of passengers and cabin crew could be provided with this level of protection, or better (N100) for a tiny cost. A set of fifty such masks costs, in bulk, about fifty bucks, and masses about 1kg, and fits in a space the size of a shoe box. Fifteen such boxes stowed in otherwise unused corners of the aircraft (like the avionics bays) would protect even a 747- or A380-sized population.

    The fewer people who get infected on the plane, the slower the spread at the destination once they get off. Not rocket science.

    I note as well that airliner environmental controls, just as in automobiles, have two settings: input of outside air, and recirculation of inside air. Airline operations staff invariably dictate that the cabin air be set for max recirc — because it’s cheaper that way. Outside air has to be bled off the engines, warmed, and compressed to a breathable density, which cuts fuel economy.

    So the passengers and cabin crew rebreathe each others’ exhalations for hours. The health statutes for decent treatment of prison inmates mandate a higher fresh air flow than is provided to an airline passenger! (The cockpit crew get max fresh outside air at all times, which tells you certain things.)

    If the panflu side of the public health apparat had a clue, their contingency plans for managing the early stages of a breakout would include mandating that the airlines use maximum outside ventilation on those flights which were permitted to operate. Again, this isn’t a perfect guarantee against infection. What it would likely do would be to reduce the number of persons likely to become infected. Which, given the epidemiological mathematics, is important.

  10. #10 revere
    March 20, 2007

    R. Hayes: The many or the few? It’s not so much a question of that. It’s a cost benefit calculaation with respect to my time and effort and how much benefit would accrue. It literally too, me more than 40 hours to write and rewrite the posts (not that you’ll know it from reading them; they’re not that good). I just don’t have the time to do this and I judge most people will not have the time to read all of them. I tried to make them semi-independent, but several of them are so specific to the paper that it wasn’t possible to do that entirely. They will go too fast for some, agonizingly slow for others. It’s tne nature of the form I am writing in. I certainly take as much or usually much more time explaining things to far fewer people when I teach, so it’s not that kind of accounting.

    marquer: IMO N100s would be a waste of money. N95s for cabin crews would not be properly fitted and so much of their protection would be wasted, too. They are probably better than nothing, but I’d rather have Tamiflu. You can read the posts (or not) and make up your own mind. The models will do one thing: help you set out your assumptions, which I recommend for your mask statements.

  11. #11 Steph
    March 20, 2007

    For what it’s worth – those explaining-the-science posts are my favorite ones! Thanks for taking the trouble and time. I for one really appreciate it.

  12. #12 JDBallenger
    March 20, 2007

    Self-deprecating comments on style from the Reveres aside, this is an important effort and should be applauded. If nothing else, I expect the forthcoming posts will be entertaining.

    The Revere efforts will probably be the only detailed lay explanation of mathematical epi modelling on the web – yes, from a cost / benefit perspective the short term return is poor, but over the longer term we will all be better informed.

    All I can say is thanks – it will probably inform my research and that of many others, so in that regard it is most certainly not a failed experiment.

  13. #13 MFoley
    March 20, 2007

    Since the cost for providing this service is so concentrated onto one individual while the benefits are very large but diffused across many readers, it is unlikely this can be sustained in its present structure. This would be a shame since it is likely very beneficial, a perfect example of a “public good”. In grad school we formed “journal clubs” where we would each take it in turn to present advanced-lay-reader presentations of recently published work to each other in our areas of special interest. This leveraged our resources wonderfully, and exposed us to many more articles we would never otherwise have read. Is there some way we could form a kind of on-line version of this among ourselves?

  14. #14 Tom DVM
    March 20, 2007

    How exactly does one model something (nature) that is beyond our perception and capabilities?

  15. #15 revere
    March 20, 2007

    Tom: You mean like religion (modeled like an old man with a beard in the sky), quantum mechanics (probability functions), proteins (ball and stick models), atoms (solar systems), etc., etc. What exactly did you mean by “exactly”?

  16. #16 sharpstick
    March 20, 2007

    I shut the office door and forward phone calls when you do the “explaining the science posts”. I’m looking forward to them.

  17. #17 Rob
    March 20, 2007

    Whoa. I hear you when you say it’s not easy. I did quite a bit of journalistic writing for scientific professionals back before my hair turned grey. You have to first find the floor, and then explain your way up to the ceiling–all without letting your reader turn the page. I’m looking forward to this.

  18. #18 M. Randolph Kruger
    March 20, 2007

    Mar-Q. M-95’s are designed to keep virus in and not out. Funk in the air would be blown about but the airplanes are now fitted with an M-95 filter on the return air. Not good enough though as evidenced by the SARS outbreak. Yeah, they had them on there then too but it was for TB more than anything else. . Your eyes, skin and the mask itself would be pretty good points for the stuff to collect in and on. How do you take an M-95 off safely pray tell? .

    Revere is the modeling thing going to be modeled on that QuickTime movie that was produced about a year ago? The movie for those who just joined us had H5N1 or a pandemic flu running thru the US and it changed a green map, to yellow, then red, then bright red and then slid back down the scale after four months (single wave event). There were white areas before the start of the pandemic indicating few or no people. Markedly absent were the white areas showing where the dead would be stacked up as it progressed and of course when it had finished with us. If it maintains its current yearly rate of 83% it would create a lot of “white” areas that werent there before. So that was something that I noted. It also just made one single assumption that we wouldnt be doing squat and just letting it happen. Now we have the antiviral thing that Revere is setting up here.

    I know they didnt put it in because they didnt and dont know what the CFR’s would be until it breaks. So does this antiviral blanket throwdown create fewer CFR’s in your opinion or does it do what its doing now which is save the mild cases and not do a thing for the major Revere? I say that because I see that the virus is becoming resistant to Amantadines, Rimantadines in all of the sideline news… did I miss any ‘dines or are there others out there? That original model would likely still stand and be modified by all of the factors that they could likely be cranking into it it such as lack of food, antivirals, masks? (if they worked), etc.

    So whats your best guess of what antivirals will really be able to do? I just havent seen anything that indicated that any of them working but that doesnt meant that it wont.

  19. #19 Tom DVM
    March 20, 2007

    Faith-based science?

    You can’t model what you can’t understand or control.

    Therefore, you can’t model nature.

    Models are ‘toys for boys’…an interesting parlour game for the sophisticated…in my opinion.

  20. #20 Tom DVM
    March 20, 2007

    …but a heck of a way to get research funding.

  21. #21 revere
    March 20, 2007

    tom: It’s not an easy way to get research funding. Getting research funding today is painfully difficult, more so for modelers than many others. I’ll discuss what models are tomorrow. Read it if you wish.

  22. #22 Tom DVM
    March 20, 2007

    Revere. There is quite a difference between biochemistry molecular models and disease epidemiology models. I don’t know anything about quantum mechanics or God. /:0)

    My personal opinion of this type of modelling is completly separate from the interest with which I will study your analysis.

    Thanks again.

  23. #23 Miso
    March 21, 2007

    “There are serious reasons to suspect that any emergent panflu may be largely or completely resistant to Tamiflu and Relenza.”

    could you supply more information with regard to resistance to Relenza? I am not aware of any discussion of a viable Relenza resistant mutation.

  24. #24 marquer
    March 21, 2007

    Miso, if one looks at the (now depressingly long) list of drugs which have lost their utility due to evolved resistance, it is evident that in many cases, drugs with a similar mechanism of action frequently end up being rendered generically useless by adaptation to one drug in the class. Uncle Darwin’s scythe has a wide blade.

    That has long been seen in antibiotics, and holds true for antivirals as well. Amantadine and rimantadine, with comparable biochemical mechanisms, used to work on H5N1. Now neither one do. The culprit seems to have been primarily amantadine overuse.

    Oseltamivir and zanamivir are both neuraminidase inhibitors. And oseltamivir is being used now in reckless, not well thought out or clinically overseen ways. There are already signs that response to its administration during H5N1 progression is not as strong as would have been thought. Ready to bet on either or both drugs as the last line of defense? It seems a chancy wager.

    It would be frankly a reassuring thing to have a third class of antiviral in the formulary right now, unrelated to either of these two groups. That does not (yet) exist.

    Revere and Randy, on the mask issue: most of what I know about respirators comes from their use in the context of IDLH industrial chemical hazards. Pandemic flu might kill you in a few days if you get a whiff of it. The chemicals I’m referring to are ones that will kill you in sixty seconds, guaranteed or your money back, if the respirator fails.

    Contemplating panflu risks are almost calming by contrast. But, on the other hand, industrial chemicals don’t replicate uncontrollably in biological hosts. They stay put.

    Is an N95/N100 just the thing to protect against an aggressive airborne pathogen? No. Not at all. Totally enclosed hoods with their own supplied oxygen would be preferred. In an airliner context, ones with provision to be fed off of outside air. And that did not dump exhaled air to the cabin.

    But that is fantasy. Too expensive, too complex. And many laypersons are frightened to put on heavy head-covering respiratory kit — it makes them claustrophobic. It does for me, too, except that I know the alternative is certainly worse. N95s exist right now, they are cheap, and can be proliferated widely as a means of slowing down (*not* preventing entirely) initial pandemic infections. The innocuous little quarter-face masks don’t freak out civilians. You can even make them in cute pastel colors.

    And while they don’t work ideally well, they nevertheless work.

    I don’t think that the increment of protection from N95 to N100 is large. But the incremental cost of manufacturing to an N100 standard is tiny. Might as well.

    With regard to fit, a badly designed mask will not fit *anyone*. I’ve suffered through wearing some of those. But a mask with multipoint attachments, a flexible nose clip and an exhale valve will fit most people well enough to accomplish some protection. That’s all that is being recommended here: partial, temporary, imperfect protection. This is not a magic bullet. But in a situation where nothing else is a magic bullet either, we have to stack up layers of improvised partial solutions.

    Magic bullets are great — if they arrive in time. I refer interested parties to Arthur C. Clarke’s classic short story Superiority for a lesson in over-reliance on said timely arrival.

    Note also that air leaks around the periphery of a lightweight mask can be almost totally ameliorated with a few lengths of impermeable medical tape. I know because I have had to have recourse to that when the only protection to hand was a crappy mask with a bad fit, which had to be made to do the job via rude field expedients.

  25. #25 marquer
    March 21, 2007

    Oh, and I forgot to mention — no, Randy, not the M95 military mask! The N95 civilian aerosol mask is what I had referred to. Just one M95 probably occupies the size and mass spec which I had listed for a box of fifty N95s. And it probably costs several times more for one M95 than for that lot of fifty as well.

    It would be far better protection. But the capacity isn’t there to make zillions of those heavy complex costly masks as early first-pass response items. Not to mention that Grandma would never put one on.

  26. #26 cpg
    March 21, 2007

    “There are serious reasons to suspect that any emergent panflu may be largely or completely resistant to Tamiflu and Relenza.”

    ‘Oseltamivir and zanamivir are both neuraminidase inhibitors’

    You didn’t answer miso question about your statement.

    Relenza is structurely different than Tamiflu even though they are both neuraminidase inhibitors.

    Resistance to Relenza has not be been proven in ANY strain of H5N1 currently circulating. Quite the opposite it has been proven to work were Tamiflu and Amantadine have not.

    So your comment is in fact false based on available evidence and I like you to retract it or provide facts to support it.

  27. #27 JJackson
    March 21, 2007

    I too am unaware of any in vivo Relenza resistance. I am more pessimistic than the modellers on how often Tamifu resistance will occur; we have had human H5N1 in 12 countries and resistance has emerged independently in 3 of them. Another problem is getting it used within the 24 to 48 hour time window after symptom onset as per the packet: Indonesia recently published the good news that the average time to delivery had been reduced from 5.7 to 5.2 days. Late application, in the absence of any alternative, can not help in the battle to reduce resistance. The ion channel blockers readily produce resistant strains but are cheaper, might they have a role in combination therapy to slow the emergence of Tamiflu resistant strains. Has anyone seen a model with Amantadine in the mix?

  28. #28 revere
    March 21, 2007

    JJ et al.: Resistance is not all or none. A contribution of the paper is to consider various degrees of resistance. But the paper won’t settle the questions or doubts people have. I am going through it both for its substance and its method, so you can see what is involved and have a better idea of what this kind of science is about. If you’ve alrady made upyour mind about antiviral I hpe you will still get something out of learning about modeling.

  29. #29 Miso
    March 22, 2007

    Perhaps the modelling would have been more informative if the known differences between Tamiflu and Relenza were accounted for. Instead Tamiflu characteristics, particularly resistance, MAGICALLY became neuraminidase inhibitor characteristics. Relenza doesn’t even get mentioned by name, and yet if Tamiflu and Relenza had been modelled individually, wouldn’t that have been more useful?
    Call it a conspiracy theory but I think alotting Relenza it’s own characteristics generated an embarassing model. One that does not vindicate the worlds rush to stockpile Tamiflu.

  30. #30 revere
    March 22, 2007

    Miso: Nothing in the model structure depends on this being Tamiflu, or, for that matter, a neuraminidase inhibitor. The variables here are rate of emergence of resistance (and it could as well be Relenza), fitness cost (which may be zero or something much greater) and transmission rates. Tamiflu is the only oral agent at the moment, so when it comes to dispensing ten of millions of doses, self administered, it is the natural example, but the model doesn’t require it. Perhaps you should read the series and then see what you think. Relenza and Taiflu are very similar and it is not by any means obvious (to me, anyway) that you cannot get resistance to Relenza, too. Suppose that resistance is much less common, say 100 or 1000 times less common. Then you are in the domain of this paper, which asks what the effect of just such rare emergences might be. So everywhere it says Tamiflu, feel free to substitute Relenza.

  31. #31 Tom DVM
    March 22, 2007

    Unfortunately, influenza has effectively harnessed its instability.

    It’s rapid replication rate and error rate in replication has allowed it to evade every technology, treatment(antivirals) and defense(vaccination), that we have developed against it.

    It took decades to develop significant resistance to antibiotics while it takes weeks or days to develop equivalent resistance to antivirals, due to genetic instability and replication rate.

    H5N1 has been with us for ten years. The signposts (significant antiviral resistance and vaccine failure) are there for all to see.

    Whether we choose to put our faith in technology and fail to read them is a uniquely human failing.

    I think it would improve our chances for survival, on many levels, if we admitted that current technologies and infrastructure shortcomings, leave us more at risk then they were in 1918.

  32. #32 Miso
    March 22, 2007

    “Relenza and Tamiflu are very similar and it is not by any means obvious (to me, anyway) that you cannot get resistance to Relenza, too.”

    “So everywhere it says Tamiflu, feel free to substitute Relenza.”

    I didn’t say you can’t get resistance to Relenza. I said that Tamiflu resistance already exists, was predicted, and there are mutations that have not occurred yet but will also confer resistance without reducing viability in the virus. Viable resistance to Relenza was not predicted, and although it has not (reportedly) been used in the field against bird flu, when used in the laboratory it has been effective against Tamiflu and Amantadine resistant strains.

    Why don’t you at least read:
    Oseltamivir Resistance – Disabling Our Influenza Defenses by Anne Moscona, M.D. (http://content.nejm.org/cgi/content/full/353/25/2633)

    and then tell me the NIs are interchangeable.

    I didn’t tell the authors what to call their model, but having called it a model of NIs, they not only missed an opportunity to highlight the diferences, they ignored them.

    No need for Relenza, no need to develop i.v.Relenza, we’ve got Tamiflu in convenient capsules. Well I tell you what, tell me where I can get some zanamivir so I can make up my own i.v. Relenza, and good luck to you.

  33. #33 revere
    March 22, 2007

    Miso: It’s not about Relenza or Tamiflu. It’s about modeling and what we can learn from it. If you want to learn something. And don’t have a one track and closed mind. And don’t perseverate. BTW, there is at least one report of resistance in flu B to Relenza and we can expect more as more is used. But Relenza sounds great. I’d like to have some. I’m not against it. I’m not pro Tamiflu. It’s just that these posts are about something else.

  34. #34 Miso
    March 22, 2007

    Well researched revere,

    An immunocompromised 18-month-old girl developed influenza B infection following bone marrow transplantation for juvenile chronic myelocytic leukemia. She was treated with 6 mg of ribavirin every 12 h by continuous aerosolized delivery. When her clinical condition deteriorated, approval was obtained from the US Food and Drug Administration for individual use of a new influenza NA inhibitor, zanamivir , and treatment was started 6 days after the diagnosis of infection. Zanamivir was administered by nebulizer at a dosage of 16�32 mg in 1�2 mL of sterile water every 6 h, the highest dosage tested in preliminary clinical trials . Treatment with zanamivir was discontinued when her clinical status worsened. During the 2 weeks she was treated with zanamivir, she shed virus, which was detected by routine nasopharyngeal swabs for virus. The child died of respiratory failure 2 days after zanamivir treatment was discontinued.”


    “There is no evidence of zanamivir resistance in viruses isolated from normal healthy patients after treatment with the drug. The only case of in vivo zanamivir resistance is that of an 18-month-old immunocompromised child, who acquired an influenza B virus infection and failed to respond to ribavirin treatment. The child was subsequently treated with zanamivir and after 12 days of treatment a virus containing an R152K NA mutation was isolated. This virus also contained a mutation in the HA protein, T198I, which had appeared prior to the NA mutation. In contrast, resistance to oseltamivir occurs in 1%-4% of adults and 4%-8% of the paediatric population.


    Sir Lancelot: Look, my liege!
    [trumpets play a fanfare as the camera cuts briefly to the sight of a majestic castle]
    King Arthur: [in awe] Camelot!
    Sir Galahad: [in awe] Camelot!
    Sir Lancelot: [in awe] Camelot!
    Patsy: [derisively] It’s only a model!


  35. #35 cpg
    March 26, 2007

    I notice with pleasure the splitting of the model into two. One theoretical, the other practical.

    I was going to post about seeing the wood from the trees re Modeling, but now we have a good compromise.

    Can we now talk on this blog about the resistance of antivirals from a practical perspective based on existing facts

    Can we then inter-twine the thoeretical with the practical when the right time presents itself.


    I think this is the meaning of what you have just presented ???

  36. #36 greensmile
    April 6, 2007

    congratulations. You got all the way through it. We will all pass around links to this for quite a while.

    I should thank you twice. I have had half a mind to try blogging on math modelling…it was something I did and enjoyed at a number of points throughout my career. But I have to admit it is not nearly as much fun to write about as it is to design, code and run…I never even wrote the first post.

    You have spared me the trouble of actually demonstrating the difficulty by trying it myself.

  37. #37 revere
    April 6, 2007

    greensmile: Thanks. Much appreciated.

  38. #38 Pete G Kinnon
    August 12, 2008

    To return couple of points relating to generalities of the initial post.

    “The experiment was to see if a paper that used a coupled system of non-linear ordinary differential equations as its main technical tool could be explained sufficiently so a lay audience could understand what was involved and how the model worked. In that way they would have a better appreciation for the findings and some understanding of an important tool, mathematical modeling.”

    It seems to be often overlooked that mathematics is simply a language. While, unlike the natural languages, it is largely synthetic, all of its expressions having direct application to the real world must, in principle, be expressible in natural language.
    In practice, of course, translation of a page of equations into natural language may be a formidable task requiring hundreds of pages of output.
    Similarly, describing a rose using the language of mathematics, although perhaps not impossible, requires a vast output to achieve even a modest representation.
    Such considerations form part of a book I am currently writing (with the general reader in mind) and I would be interested to hear opinions on this.

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