bhobba
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morrobay said:Thanks, The compound interest formula, final=initial (1+%)^n is exactly how I am solving for the R0 from initial and final infections: 17(R0)^6 = 231. Then (R0)^6=13.58 and 6(logR0) = log 13.58. therefore log R0 =.1888 so R0 is 1.54 I just am asking if this is valid for solving R0. Note 6 infection periods from 24 days/4 day max.infectious period from initial infection.
OK then let's go carefully through the math. We want to find the infinitesimal R0 similar to the force of interest idea for compound interest. You are using that after 6 days on the average 1 person infects 13.58 people. So we know that e^(6*R0) = 1+ 13.58 = 14.58. This means 6*R0 = ln 14.58 = 2.68 or R0 = 2.68/6 = .45 to two decimal places. You just need to understand the concepts involved which is largely basic differential equations and really everyone should be taught it at HS. They have wide applicability in many situations - infection spread and compound interest are just two. It allows one to think clearly about concepts like R0 and compound interest rates. This is done by treating time as continuous and working in terms of parameters based on doing that. People sometimes say - how do we know time is continuous. The answer is we do not. By modeling situations as if it is we can use calculus which allows progress to be made in a clear and precise way. As you probably know there is all sorts of philosophical ideas about what science is - Wittgenstein, Kuhn, Popper, Poincare, Feynman (he was sort of anti-philosophy - which interestingly is a philosophy in itself) etc. I recently read a book on an introduction to the subject that examined carefully a number of different views. It glossed over a view called the modelling view saying not a lot of work has been done on it. Philosophers might not have done a lot of work on it, but mathematicians and scientists use it all the time, and IMHO it is the correct view - but that is another story not really suited to this forum.
On another forum a question was once posed - before leaving school what is the most important thing students should understand. My answer was basic calculus. I was laughed at. But you have just witnessed how it resolved the confusion you had about R0. Another good one is if you go a bit further than basic calculus into real analysis (where calculus is studied with full logical rigor and not intuitive ideas like an infinitesimal period of time dt) and use it on Zeno's paradoxes. The solution is then clear. One of the fundamental axioms of real numbers often used in real analysis is the Least Upper Bound Axiom (LUB). It says - Every non-empty subset of real numbers that is bounded above has a least upper bound. In modelling the tortoise and hare race by real numbers the LUB axiom applies. Now obviously it has an upper bound where the race has finished. But we know there is a least upper bound. Below that the race is still going, above it, it has finished. So that must be when the race ends. Many many people, and some even post here about it, are totally unaware of this and think it is still unsolved. Some people think even the calculus explanation does not solve it - you really need physics.
https://www.forbes.com/sites/starts...esolves-zenos-famous-paradox/?sh=6ed441b033f8
But we are now getting way off topic - if you want to pursue it further then start a new thread.
Thanks
Bill
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