论文标题
SIR流行模型中的精确和近似分析解决方案
Exact and approximate analytic solutions in the SIR epidemic model
论文作者
论文摘要
在这项工作中，获得了一些新的精确和近似分析解决方案的SIR流行模型，该模型是根据无量纲的变量和参数配制的。使用Lambert W功能（主要和二级分支），使用这种方式，使用这种方式与感染群体（i）明确相关。还获得了未捕获该疾病的人群部分的简单准确关系。使用R0-> Infinity Limiting Case（Logistic Cerve）的简单函数（基本乘法数）（基本乘法数）（基本乘法数）（基本乘法数）（基本乘法数）（基本乘法数）（基本乘法数）（基本乘法数）的任何值（基本乘法数）（基本乘法数）的明确时间依赖性以及流行曲线的显式依赖性以及流行曲线的显式依赖性。还表明，对于I0 << S0，比率I0/S0变化对种群演变曲线的影响相当于时间变化，其形状和相对位置不受影响。
In this work, some new exact and approximate analytical solutions are obtained for the SIR epidemic model, which is formulated in terms of dimensionless variables and parameters. The susceptibles population (S) is in this way explicitly related to the infectives population (I) using the Lambert W function (both the principal and the secondary branches). A simple and accurate relation for the fraction of the population that does not catch the disease is also obtained. The explicit time dependences of the susceptibles, infectives and removed populations, as well as that of the epidemic curve are also modelled with good accuracy for any value of R0 (basic multiplication number) using simple functions that are modified solutions of the R0 -> infinity limiting case (logistic curve). It is also shown that for I0 << S0 the effect of a change in the ratio I0/S0 on the population evolution curves amounts to a time shift, their shape and relative position being unaffected.
