結果又回到公共衛生的老本行-其實也不算"老本行"~只是大學四年修過且被當過很多次~
但說真的~印象中還真的沒學到這一塊-以數學模型估算感染的傳遞影響力...
...若公共衛生沒學到... 那... 怎管制疾病...
但是因為紅蔥頭我小時不努力~數學給它半知半解~當然微積分則更...不敢說明~
卻啊~到了四時多才發現數學的妙用-用"簡明的語言"來說明複雜問題的趨勢~...
只好到這時問東問西~甚至借來高中數學慢慢理解~
而以下呢~則是最近頗改興趣的領域~ 特別記錄一下~
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The Kermack-McKendrick model is an SIR model for the number of people infected with a contagious illness in a closed population over time. It was proposed to explain the rapid rise and fall in the number of infected patients observed in epidemics such as the plague.
It assumes that the population size is fixed (i.e., no births, deaths due to disease, or deaths by natural causes), incubation period of the infectious agent is instantaneous, and duration of infectivity is same as length of the disease. It also assumes a completely homogeneous population with no age, spatial, or social structure.
The model consists of a system of three coupled nonlinear ordinary differential equations,
where
 is time,  is the number of susceptible people(易受感染),  is the number of people infected(被感染病人數),  is the number of people who have recovered and developed immunity to the infection(產生免疫力的人),  is the infection rate(感染的機率), and  is the recovery rate(復原的機率).The key value governing the time evolution of these equations is the so-called epidemiological threshold,
Note that the choice of the notation
 is a bit unfortunate, since it has nothing to do with  .  is defined as the number of secondary infections caused by a single primary infection(研究的限制); in other words, it determines the number of people infected by contact with a single infected person before his death or recovery(端視傳染力強不強).
When
 , each person who contracts the disease will infect fewer than one person before dying or recovering(疾病到控制), so the outbreak(爆發) will peter out ( ).
When
 , each person who gets the disease will infect more than one person(不只傳染一位~所以不易控制), so the epidemic will spread ( ).  is probably the single most important quantity in epidemiology. Note that the result  derived above, applies only to the basic Kermack-McKendrick model, with alternative SIR models having different formulas for  and hence for  .
The Kermack-McKendrick model was brought back to prominence after decades of neglect by Anderson and May (1979). More complicated versions of the Kermack-McKendrick model that better reflect the actual biology of a given disease are often used.
1.大部份資料來自(Most sentence was taken from- http://mathworld.wolfram.com/Kermack-McKendrickModel.html If copyright infringement, please sent me an e-mail. I will take this article off as soon as possible. 2.http://dufu.math.ncu.edu.tw/calculus/calculus_eng/node137.html
DG
**If copyright infringement, plase let me know. I will take this article off as soon as possible.**
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(資料2稱為基本再生率)
