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**Several indicators of critical transitions for complex diseases based on stochastic analysis.**
*(English)*
Zbl 1397.92376

Summary: Many complex diseases (chronic disease onset, development and differentiation, self-assembly, etc.) are reminiscent of phase transitions in a dynamical system: quantitative changes accumulate largely unnoticed until a critical threshold is reached, which causes abrupt qualitative changes of the system. Understanding such nonlinear behaviors is critical to dissect the multiple genetic/environmental factors that together shape the genetic and physiological landscape underlying basic biological functions and to identify the key driving molecules. Based on stochastic differential equation (SDE) model, we theoretically derive three statistical indicators, that is, coefficient of variation (CV), transformed Pearson’s correlation coefficient (TPC), and transformed probability distribution (TPD), to identify critical transitions and detect the early-warning signals of the phase transition in complex diseases. To verify the effectiveness of these early-warning indexes, we use high-throughput data for
three complex diseases, including influenza caused by either H3N2 or H1N1 and acute lung injury, to extract the dynamical network biomarkers (DNBs) responsible for catastrophic transition into the disease state from predisease state. The numerical results indicate that the derived indicators provide a data-based quantitative analysis for early-warning signals for critical transitions in complex diseases or other dynamical systems.

### MSC:

92C50 | Medical applications (general) |

60H30 | Applications of stochastic analysis (to PDEs, etc.) |

60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |

### Keywords:

critical transitions; complex disease; stochastic analysis; stochastic differential equation
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\textit{G. Wang} et al., Comput. Math. Methods Med. 2017, Article ID 7560758, 10 p. (2017; Zbl 1397.92376)

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