|
Handshaking Problem :(
Link |
by
  
on 2009-01-29 17:29:51 (edited 2009-01-29 17:34:12)
|
|
(I dont know if this actually applies to physics, but its is math though D:!) For the past two days in honors bio, we've had this interesting discussion on the transmission of disease through the shaking of hands, and the exchanging of fluids. In an experiment, to which we had no idea of what we were doing, we had test tubes holding a clear liquid. We "traded" liquids with four members of the room by taking a dropper and taking out half of our liquid, them taking out half of theirs, etc. Then our teacher came around and dropped an indicator into the tubes to see who had the "disease". (I had it, lol, if you're wondering). We were then asked to try and find out who could've been the original vector or carrier of the "diseased" tube. The infected stood up. Then we interviewed our infected peoples, and we determined that a person who would have harbored the disease would have transmitted it to all four of the people he or she traded with us. It was believed this would be a sure-fire way to finding the person, but we were left an an impasse when four of us, including me, were left standing, and some of us had traded with each other. etc. Next, after we had sat back down in our desks, we were asked the question, "Assuming that there is only one vector of the disease, and you knew the size of the group, and the number of 'transmissions', could there be a formula that can tell you how many people are infected at each 'stage' of transmission?" We set about this task. The first equation we came up with was i = g - (1)2^t, where i is the infected, g is the group, and t is the transmission/trade. This equation, however, only gave the number of people who survived infection. So, we took that equation, and came up with i = g - (g - 2^t), which would, indeed, find out the number of infected people. Then, everything got screwed up. One of my table members, who is in a math level one step higher than me, mentioned that this would only find the maximum amount of possible infections. She presumed that there should be a minimum value as well, and that there was most likely an equation for that too. Therefore, the equation should be i ≤ g - (g - 2^t). She lost me at the word minimum, but she and my other table partner came up with a table: Stage: 1 2 3 4 5 6 7 8 Total: 1 2 4 4 8 8 8 8 I'm not entirely sure what her intentions were in the table. This was supposed to note that a person cannot infect the same person twice? Ugh. I definitely did NOT understand this. However, we all noticed that there was a pattern to the way the table was written, which I have highlighted. It took one term to get two, two terms to get four, and four terms to get eight. When my group members continued this pattern, it was determined that it would also take eight terms to get sixteen, and sixteen to get thirty two, etc. We tried to determine a formula for this pattern we noticed, but we could not place one. It's not arithmetic, and its not geometric. Of course, my teacher will not offer us input into our little dilemma. He even offered to quit our studies and our test, and continue with the problem until June. Eww. Summing it all up, these are my questions that I am looking to answer: Is there a formula to the pattern in the table? If there is a pattern, and is it even applicable in this situation? Is there a maximum and minimum value for this situation? Is the equation g - (g - 2^t) applicable? Am I in over my head? What formulas do you suggest WOULD apply to the situation? Thanks! -Ichigo. :D |
|
Re: Handshaking Problem :(
Link |
by Hidden Text
on 2009-01-29 18:18:05
|
|
its a factorial response mechanism but to catch the back half of the dilema ergo the fact that a person cannot re-infect the same person you have a minimalization factor ie you have a Sum of a factorial over a 1-sum of factorial...diesease pattern and transmission is like a computer worm, it cannot travel backwards if the sendee is on the same list as a sender...ie...i email you...you email gendou...gendou emails me...but i cannot catch the worm again due to it already infecting my computer at least...i think its factorial response mechanisms...any public descent among the peanut gallery? |