论文标题
SIR模型的分析近似解决方案
An analytic approximate solution of the SIR model
论文作者
论文摘要
SIR（D）流行病学模型是通过先验方程系统定义的，而不是通过基本功能解决的。在本文中，这些方程式被成功地替换为近似方程，其解决方案在基本功能方面明确给出，从而起源于广义逻辑函数：它们确保{\ em Exact}（在数值意义上）无效的值，例如，不适合使用，例如适合于数据外观的拟合；此外，它们推出了一个有用的功能，实际上，至少在非常严格的近似值中，也归{\ em Exact}方程的（数值）解决方案所有。工作中的新颖性是：使用简单的，分析的几何考虑，获得近似方程的方式；最终近似解决方案的简单且实用的表述；上述有用的功能，以前从未透露过。该作品的方法和结果被证明是在众所周知的非二维参数的范围内具有鲁棒性的，称为{\ em碱性繁殖比}，涵盖了至少所有已知的流行病病例，从流感到麻疹：这是在类似作品中看起来并没有太多讨论的观点。
The SIR(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, originating, piece-wisely, from generalized logistic functions: they ensure {\em exact} (in the numerical sense) asymptotic values, besides to be quite practical to use, for example with fit to data algorithms; moreover they unveil a useful feature, that in fact, at least with very strict approximation, is also owned by the (numerical) solutions of the {\em exact} equations. The novelties in the work are: the way the approximate equations are obtained, using simple, analytic geometry considerations; the easy and practical formulation of the final approximate solutions; the mentioned useful feature, never disclosed before. The work's method and result prove to be robust over a range of values of the well known non-dimensional parameter called {\em basic reproduction ratio}, that covers at least all the known epidemic cases, from influenza to measles: this is a point which doesn't appear much discussed in analogous works.
