Ordinary differential equation (ODE) models of cancer growth are often used to predict tumor growth and form the basis for more complex models used in personalized medicine. Unfortunately, ODE models provide predictions of the average behavior of the cell population neglecting the fact that cells are discrete objects subject to discrete events. This kind of stochasticity can dramatically change the time course of tumor growth, particularly when the cell population is small. Here, we investigate stochastic versions of seven common ODE models of cancer growth to determine the role of stochasticity in eradicating tumors via chemotherapy. We find that stochasticity leads to differences in predictions among the different models of both the level of chemotherapy needed to cure a tumor and the time it takes to achieve a cure. Our results highlight the need for more investigation of which model provides the best description of cancer growth.

癌症生长的普通微分方程（ODE）模型通常用于预测肿瘤的生长，并为个性化医学中使用的更为复杂的模型奠定了基础。不幸的是，ODE模型忽略了细胞是经受离散事件的离散对象这一事实，提供了细胞种群平均行为的预测。这种随机性可以极大地改变肿瘤生长的时间进程，特别是在细胞数量较小的情况下。在这里，我们研究了七个常见的ODE癌症生长模型的随机版本，以确定随机性在通过化学疗法消灭肿瘤中的作用。我们发现，随机性导致在不同模型之间的预测差异，即治疗肿瘤所需的化学疗法水平和达到治愈所需的时间。