:
Reconstruction of gene regulatory networks (GRN) plays an important role in understanding
the complexity, functionality and pathways of biological systems, which could support the design of
new drugs for diseases. Because differential equation models are flexible androbust, these models have
been utilized to identify biochemical reactions and gene regulatory networks. This paper investigates
the differential equation models for reverse engineering gene regulatory networks. We introduce three
kinds of differential equation models, including ordinary differential equation (ODE), time-delayed
differential equation (TDDE) and stochastic differential equation (SDE). ODE models include linear
ODE, nonlinear ODE and S-system model. We also discuss the evolutionary algorithms, which are
utilized to search the optimal structures and parameters of differential equation models. This investigation
could provide a comprehensive understanding of differential equation models, and lead to the
discovery of novel differential equation models.
Bayesian Inference of High-Dimensional Cluster-Structured Ordinary Differential Equation Models with Applications to Brain Connectivity Studies
