Abstract

GRANADA DIAZ, Héctor Andrés; NOVA MARTINEZ, Manuel Arturo  and  OLIVAR ROBAYO, Luis Eduardo. Effect of relapse and recurrent mental health treatments on the population dynamics of suicide risk. Ciencia en Desarrollo [online]. 2025, vol.16, n.1, pp.123-134.  Epub Jan 20, 2025. ISSN 0121-7488.  https://doi.org/10.19053/uptc.01217488.v16.n1.2025.17611.

This paper proposes a function for the risk rate of suicidal behavior, whose formulation is based on the relationship between risk, the occurrence of suicide attempts and the number of suicides. It is shown that the distribution of suicide attempts by age in Colombia adjusts to a Burr-type distribution function. Vulnerable, non risk, susceptible in treatment and untreated populations are characterized, and time series are estimated based on Colombian statistics from Dane, Minsalud and Sivigila. We propose a nonlinear dynamic model to investigate the relationships between these populations and use it to estimate a projection of population dynamics. The steady state is analyzed using numerical techniques, identifying scenarios such as stable focus, stable nodes and saddles. The conditions to reach a transcritical bifurcation that guarantees the coexistence between equilibrium points are established, and its dynamic evolution is examined on three-dimensional vector fields. The results suggest that implementing effective treatment policies could lead to a decrease in the risk rate, furthermore by controlling for parameters related to the relapse rate, the whole population could be resistant to suicide triggers factors.

Keywords : Risk of suicide; Population dynamics; Mathematical model; Treatment; Relapse.

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