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Revista de Matemática Teoría y Aplicaciones

versão impressa ISSN 1409-2433

Rev. Mat vol.28 no.2 San José Jul./Dez. 2021

http://dx.doi.org/10.15517/rmta.v28i2.44746 

Artículo

A simple model with peer pressure: the antisocial behavior case

Un modelo simple con presión de grupo: el caso de las conductas antisociales

Geiser Villavicencio-Pulido1 

Daniel Olmos-Liceaga2 

Lidia Ivonne Blásquez-Martínez3 

1Universidad Autónoma Metropolitana-Unidad Lerma, División de Ciencias Biológicas y de la Salud, Depto. de Ciencias Ambientales, Ciudad de México, México; j.villavicencio@correo.ler.uam.mx

2Universidad de Sonora, Departamento de Matemáticas, Hermosillo, México; daniel.olmos@unison.mx

3Universidad Autónoma Metropolitana-Unidad Lerma, División de Ciencias Sociales y Humanidades, Depto. de Procesos Sociales, Ciudad de México, México; l.blasquez@correo.ler.uam.mx

Abstract

Antisocial behaviors such as consumption of addictive substances and eating disorders are modeled using a SIR model. We propose a function l(y(t)) that describes the relapse-recovery-recycling rate. l(y(t)) describes either strengthening or weakening of convictions of recovered individuals to relapse in antisocial behaviors. We show that a wide variety of functions can induce the existence of multiple equilibria points for R0 1 which is a catastrophic scenario for the susceptible population. Finally, conditions for avoiding a sudden and catastrophic jump in the number of individuals with antisocial behaviors are given.

Keywords: peer presure; antisocial behaviors; backward bifurcation; forward bifurcation.

Resumen

Comportamientos antisociales tales como consumo de sustancias adictivas y desordenes de la alimentación son modelados usando un modelo SIR. Proponemos una función l(y(t)) que describe la tasa de reciclamiento-recuperación-recaída. l(y(t)) describe ya sea el fortalecimiento o debilitamiento de la convicción de los individuos a recaer en conductas antisociales. Mostramos que una amplia variedad de funciones puede inducir la existencia de múltiples puntos de equilibrio para R0 1, lo que constituye un escenario catastrófico para la población susceptible. Finalmente, se dan condiciones para evitar un aumento repentino y catastrófico en el número de individuos con comportamientos antisociales.

Palabras clave: presión social; comportamientos antisociales; bifurcación hacia atrás; bifurcación hacia adelante.

Mathematics Subject Classification: 34A34, 34C40.

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Acknowledgments

We would like to thank the anonymous referee for the careful reading of our manuscript and for providing us with constructive comments, which helped to improve the manuscript.

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Received: December 04, 2020; Revised: May 02, 2021; Accepted: May 19, 2021

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