A birth–death process is considered as an epidemic model with recovery and transmittance from outside. The fraction of infected individuals is for huge population sizes approximated by a solution of an ordinary differential equation taking values in [0, 1]. For intermediate size or semilarge populations, the fraction of infected individuals is approximated by a diffusion formulated as a stochastic differential equation. That diffusion approximation however needs to be killed at the boundary {0}∪{1}. An alternative stochastic differential equation model is investigated which instead allows a more natural reflection at the boundary.

中文翻译：

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流行病建模：扩散近似与允许反射的随机微分方程

生死过程被认为是一种具有外部恢复和传播的流行模型。感染个体的比例是针对庞大的人口规模，通过常微分方程的解来近似，取值[0, 1]. 对于中等规模或半大型人群，感染个体的比例通过公式为随机微分方程的扩散来近似。然而，该扩散近似需要在边界处被杀死{0}∪{1}. 研究了另一种随机微分方程模型，它允许在边界处进行更自然的反射。