Mathematical and computational modeling of suicide as a complex dynamical system

Background: Despite decades of research, the current suicide rate is nearly identical to what it was 100 years ago. This slow progress is due, at least in part, to a lack of formal theories of suicide. Existing suicide theories are  instantiated verbally, omitting details required for precise explanation and prediction, rendering them difficult to effectively evaluate and difficult to improve. By contrast, formal theories are instantiated mathematically and  computationally, allowing researchers to precisely deduce theory predictions, rigorously evaluate what the theory can and cannot explain, and thereby, inform how the theory can be improved. This paper takes the first step  toward addressing the need for formal theories in suicide research by formalizing an initial, general theory of suicide and evaluating its ability to explain suicide-related phenomena.
Methods: First, we formalized a General Escape Theory of Suicide as a system of stochastic and ordinary differential equations. Second, we used these equations to simulate behavior of the system over time. Third, we evaluated  if the formal theory produced robust suicide-related phenomena including rapid onset and brief duration of suicidal thoughts, and zero-inflation of suicidal thinking in time series data.
Results: Simulations successfully produced the proposed suicidal phenomena (i.e., rapid onset, short duration, and high zero-inflation of suicidal thoughts in time series data). Notably, these simulations also produced theorized  phenomena following from the General Escape Theory of Suicide: that suicidal thoughts emerge when alternative escape behaviors failed to effectively regulate aversive internal states, and that effective use of long-term  strategies may prevent the emergence of suicidal thoughts.
Conclusions: To our knowledge, the model developed here is the first formal theory of suicide, which was able to produce – and, thus, explain – well-established phenomena documented in the suicide literature. We discuss the  next steps in a research program dedicated to studying suicide as a complex dynamical system, and describe how the integration of formal theories and empirical research may advance our understanding, prediction, and  prevention of suicide.