关键词: 系统生物学, 随机微分方程, 数值模拟, 算法

Abstract: Many phenomena in systems biology, such as the biochemical reaction process, the evolution of ecosystems, the spread of infectious diseases, can be described by stochastic differential equations (SDEs). Considering the influence of randomness, stochastic differential equation models can describe the evolution of variables over time more accurately than deterministic differential equation models. However, the analytical solutions of most stochastic differential equations cannot be obtained. Even though some of them can be obtained, the forms of the solutions are usually extremely complex. One therefore requires proper numerical methods to approximate their solutions on computers. These stochastic differential equation models in systems biology usually have the properties of high dimension, high nonlinearity, and the solutions being located in a specified region. It is difficult to simulate them numerically. This paper reviews the numerical simulation algorithms of several typical models in systems biology (biochemical reaction models, ecosystem models, infectious disease models, population genetics models, cell differentiation models), and briefly introduces their advantages and disadvantages.

Key words: Systems biology, Stochastic differential equation, Numerical simulation, Algorithm