Mathematical models of panic disorder

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.