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Mathematical Models of Panic Disorder

机译：恐慌症的数学模型

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摘要

The dynamics of panic attacks in both functional individuals and panic disorder patients are qualitatively evaluated by using coupled nonlinear differential equations. Each panic attack is described by two variables, fear and physical symptoms. Different thresholds for these variables are defined for functional individuals, patients in the acute phase, and patients in the chronic phase. Integral lines, vector fields, and time series of solutions, based on the proposed coupled nonlinear differential equations, are shown. The efficacy of treatment and severity of each panic attack are also evaluated. Under our hypothesized condition, it is shown that particular pharmacological treatment could change the final states of patients in the acute phase, but could not change either the final states of patients in the chronic phase or those of functional individuals. Our model is consistent with the well-known major features of panic attacks, and sheds new light on the dynamics of panic attacks.
机译：通过使用耦合的非线性微分方程定性评估功能性个体和恐慌症患者的恐慌发作的动力学。每次恐慌发作都由两个变量来描述，即恐惧和身体症状。为功能个体，急性期患者和慢性期患者定义了这些变量的不同阈值。显示了基于所提出的耦合非线性微分方程的积分线，向量场和解的时间序列。还评估了治疗效果和每次惊恐发作的严重程度。在我们的假设条件下，已表明特定的药理治疗可以改变急性期患者的最终状态，但不能改变慢性期患者或功能个体的最终状态。我们的模型与恐慌攻击的众所周知的主要特征相一致，并为恐慌攻击的动力学提供了新的思路。

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