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croot
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Joined: July 23rd, 2006, 8:30 pm

Dissecting the efficiency of certain types of applied mathematics

March 16th, 2012, 2:46 pm

Disclaimer:I am not, nor do I even know, any of the authors of the following study:Optimal control strategies for tuberculosis treatment: a case study in AngolaIn fact I have not even read the paper, only the posting Comments on arxiv:"We apply optimal control theory to a tuberculosis model given by a system of ordinary differential equations. Optimal control strategies are proposed to minimize the cost of interventions. Numerical simulations are given using data from Angola. "Post:Well I wanted to discuss with the OTers around this point in space-time: -I am apriori sympathetic to most keywords in the paper's title: I like optimal control and doing things well, I'm damn sure interested in beating tuberculosis - a family member had it and was cured (phew!) , and I am for helping Angola and such places that certainly need it.-BUT then I get this nagging doubt about the effectiveness of "Numerical Algebra, Control and Optimization" in this pursuit. I can disclose that I am a total ignoramus in every aspect of this except the optimal control bit: I have never cured anyone from any disease in Africa or anywhere, except maybe recommending a hot drink against a cold. Still I get that sad feeling that maybe the effectiveness of the mathematics can be disputed.To make this a really pointless discussion, I will commission first thought before opening the paper:-ODE system is presumably some kind of Volterra equation: is there a parameter for "rate of human deaths per Koch unit"?-minimize the cost of interventions? Are we talking the cost of transport onsite + cost of vaccine? Is space discretized into a finite number of vaccination wards to which the sick flock of their own will, or is there a jab van chasing people all through the streets? I naively thought vaccines were the most expensive part of a vaccination campaign but maybe it IS transports+logistics .-other usual qualms about how are the model parameters estimated, what if i add variables changing my ODE system to a nonholonomic one will that affect propagation, and thus conclusions of the study, wildly?
 
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Paul
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Joined: July 20th, 2001, 3:28 pm

Dissecting the efficiency of certain types of applied mathematics

March 16th, 2012, 3:09 pm

I share your concerns.It depends how experienced the researchers are. Do they have a wide range of experience? If so, they will have the same worries we do, so maybe we shouldn't be worried.I know someone at the UN who does modelling in this sort of area. But what he (and this is true for most at the UN) does is econometric-type stats for these sorts of problems. That could be better or worse. In an ideal world I'd have an experienced applied mathematicians overseeing lots of different modelling approaches.P
 
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SierpinskyJanitor
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Joined: March 29th, 2005, 12:55 pm

Dissecting the efficiency of certain types of applied mathematics

March 16th, 2012, 3:23 pm

What an incredibly useful idea croot. This forum is definitely well positioned to help on these matters.If you need volunteers for any "model validation" stuff, then you can unconditionally count on me.best regards,Serp
 
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croot
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Joined: July 23rd, 2006, 8:30 pm

Dissecting the efficiency of certain types of applied mathematics

March 17th, 2012, 4:05 pm

To foster more collaborative interdisciplinary miscegenation of ideas, here is the link btw just in case http://arxiv.org/abs/1203.3255After a squint at the insides.. -I had wildly overestimated the 'spatial component' transporting vaccine to people and discovering the sick, instead it appears they have unfolded it into several dimensions of "being sick".-The hypothesis that the population stays constant was a startler, but it seems standard and 'controlled for' in the numerical experiments.-The squared u's in the cost function seem weird.. why is incremental cost proportional to certain squared fractions of population :sAcademic judge says: "These ODE's are a pretty tame kind of nonlinear .."Grant-agency judge says: "I hear child soldiers are all the rage this year, can this research account for the effect of child soldiers?"Luckily Angola has enough high mountain areas to set up sanatoria.
Last edited by croot on March 16th, 2012, 11:00 pm, edited 1 time in total.
 
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Traden4Alpha
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Joined: September 20th, 2002, 8:30 pm

Dissecting the efficiency of certain types of applied mathematics

March 17th, 2012, 4:36 pm

QuoteOriginally posted by: crootTo foster more collaborative interdisciplinary miscegenation of ideas, here is the link btw just in case http://arxiv.org/abs/1203.3255After a squint at the insides.. -I had wildly overestimated the 'spatial component' transporting vaccine to people and discovering the sick, instead it appears they have unfolded it into several dimensions of "being sick".Spatial domain epidemiological models are really hard because the models bear limited resemblance to geographic space. Also the spatial models for logistics and for disease transmission are independent of each other. Grid models don't work well.QuoteOriginally posted by: croot-The hypothesis that the population stays constant was a startler, but it seems standard and 'controlled for' in the numerical experiments.That's probably OK given that the change in population over the infection/treatment cycle is essentially constant. Modeling diseases with multi-year incubation periods or extreme rates of mortality might require a non-constant population model.QuoteOriginally posted by: croot-The squared u's in the cost function seem weird.. why is incremental cost proportional to certain squared fractions of population :sDiseases show network effects -- it the number of person-to-person connections, not the number of persons that modulate new infections and quarantine costs. Thus, costs can scale with N^2.
 
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SierpinskyJanitor
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Joined: March 29th, 2005, 12:55 pm

Dissecting the efficiency of certain types of applied mathematics

March 17th, 2012, 4:56 pm

my wife and I went to the painful process of actually reading the whole article. Unfortunately we found not only misconceptions as far as basic epidemics are concerned ( as verified by her who happens to be a geneticist specialised in these sorts of things ) but also far-fetched assumptions around the mathematical model used - also, the final conclusions are basically unoriginal and not very enlightening. That multiple combined strategies should be adopted is something extremely basic and hardly worth researching about, more noticeable so when the authors reach the LaPalissean conclusion that: "Results justify the need for intervention in tuberculosis treatment".Anyway, this has been published on arXiv though under no peer-reviewing whatsoever, so our suggestion to the authors would be to submit it elsewhere instead. IMO this subject matter deserves a more serious treatment, it seems, the authors are just plugging in a well known model to real-data.
Last edited by SierpinskyJanitor on March 16th, 2012, 11:00 pm, edited 1 time in total.
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