论文标题
修改了SIR模型，产生了逻辑解决方案
Modified SIR Model Yielding a Logistic Solution
论文作者
论文摘要
大流行模型遭受了一个不切实际的假设：从传染性类别中删除的率与传染性个体的数量成正比。这意味着感染率的变化同时改变了去除速率。一个更现实的假设是，在感染后，在特定时间间隔中删除了一个人。提出了一个简单的修改后的SIR模型，该模型实现了此延迟，从而产生了一个构成模型的单个延迟微分方程。适用于大流行的该方程的解决方案是a+b l（t）的形式，其中l（t）是逻辑函数，而a和b是常数。尽管经典的SIR模型通常是对大流行行为的过度简化，但它具有启发性的是，大流行论的许多基本动力和描述符清楚而简单地定义。通常用描述性地使用逻辑模型，就像仅适用于易感和感染类别以及它们之间的转移率一样。本模型提供了一个完整但修改的SIR模型，具有更简单的逻辑解决方案，更现实，同样具有启发性。
The SIR pandemic model suffers from an unrealistic assumption: The rate of removal from the infectious class of individuals is assumed to be proportional to the number of infectious individuals. This means that a change in the rate of infection is simultaneous with an equal change in the rate of removal. A more realistic assumption is that an individual is removed at a certain time interval after having been infected. A simple modified SIR model is proposed which implements this delay, resulting in a single delay differential equation which comprises the model. A solution to this equation which is applicable to a pandemic is of the form A+B L(t) where L(t) is a logistic function, and A and B are constants. While the classical SIR model is often an oversimplification of pandemic behavior, it is instructive in that many of the fundamental dynamics and descriptors of pandemics are clearly and simply defined. The logistic model is generally used descriptively, dealing as it does with only the susceptible and infected classes and the rate of transfer between them. The present model presents a full but modified SIR model with a simpler logistic solution which is more realistic and equally instructive.
