论文标题
改良的SIR模型的精确封闭形式解决方案
Exact closed-form solution of a modified SIR model
论文作者
论文摘要
提出了从人口中删除恢复的个体的改良SIR系统的封闭形式的确切分析解决方案。在这个动态系统中，发现$ s（t）$和$ r（t）$ r（t）$的易感和恢复的个体是广义的逻辑功能，而感染性的$ i（t）$均由广义逻辑功能时间给予指数，所有这些功能都具有相同的特征时间。分析了此修改后的SIR系统的动力学，并执行了一些流行病学相关数量的确切计算。根据其各自保守数量的零，提出并解释了此修改后的SIR模型与原始SIR ONE之间的主要区别。此外，还表明，具有时间依赖性传输速率的修改后的SIR模型也可以以封闭形式解决某些现实的传输速率函数。
The exact analytical solution in closed form of a modified SIR system where recovered individuals are removed from the population is presented. In this dynamical system the populations $S(t)$ and $R(t)$ of susceptible and recovered individuals are found to be generalized logistic functions, while infective ones $I(t)$ are given by a generalized logistic function times an exponential, all of them with the same characteristic time. The dynamics of this modified SIR system is analyzed and the exact computation of some epidemiologically relevant quantities is performed. The main differences between this modified SIR model and original SIR one are presented and explained in terms of the zeroes of their respective conserved quantities. Moreover, it is shown that the modified SIR model with time-dependent transmission rate can be also solved in closed form for certain realistic transmission rate functions.
