Nonlinear Model of Population Dynamics in Suicide

Abstract

This paper proposes a nonlinear model and estimates time series for populations involved in the phenomenon of suicide using demographic information from DANE and epidemiological bulletins from Sivigila for the department of Tolima. Vulnerable populations, susceptible populations, those in treatment, and populations that have completed psychological treatment against suicide are introduced, and projections for these populations are estimated up to the year 2034. Linear and nonlinear relationships are established between populations involved in the suicide phenomenon, allowing the definition of initial conditions and parameter estimation using the Levenberg-Marquardt method to obtain population series until the year 2034 under the dynamic evolution of a nonlinear model using Matlab R2021a software. As a result, assumptions are established between state variables that allow bounding and estimating the proportionality constants. A causal diagram of the dynamic interaction of state variables with respective assumptions is proposed, enabling the formulation of the mathematical model of the dynamic interaction of suicide, which is normalized to obtain estimates of population series projections. Finally, it is concluded that the Tolima department shows an increasing trend in suicide cases, where 99.84% of the vulnerable population is exposed to triggering factors, and less than 0.11% receives treatment, with an effectiveness rate below 0.05%. Public health entities are encouraged to develop strategies to reduce mortality rates due to this cause.