Nonlinear dynamics of runaways among children and adolescents: disruptive disorder or step toward a suicide attempt?

The aim of this study is to analyze the decision-making process whereby susceptible adolescents end up choosing the option to run away or attempt suicide. Our basic hypothesis is that this transition is largely based on cooperative mechanisms. The runaway state is regarded as a potential precursor of the suicidal one. A mathematical model incorporating these processes is developed from which the time evolution and the values of the susceptible, runaway and suicidal populations are evaluated in terms of a number of key parameters. It is shown that for appropriate ranges of parameter values the interactions present in the system eventually end up counteracting both runaway and suicidal attempts. Quantitatively this is shown by the existence of stable solutions of the model equations in which the populations of both suicidal and runaway individuals end up being zero, although in some cases a significant temporary enhancement can take place. But as the parameters are varied beyond these ranges the system starts sustaining non-trivial stable states, in which the populations of suicidals or runaways are maintained at non-zero levels. This hints at prevention strategies and crisis management such as separation from the environment and specific treatment different from those dispending traditional adolescent psychiatric units.