A simple model with peer pressure: the antisocial behavior case

• Villavicencio-Pulido, José Geiser ^[2] ; Olmos-Liceaga, Daniel ^[1] ; Blásquez-Martínez, Lidia Ivonne ^[3]
  1. [1] Universidad de Sonora

     Universidad de Sonora

     México

     
  2. [2] Universidad Autónoma Metropolitana–Unidad Lerma, División de Ciencias Biológicas y de la Salud, Depto. de Ciencias Ambientales, Ciudad de México, México.
  3. [3] Universidad Autónoma Metropolitana–Unidad Lerma, División de Ciencias Sociales y Humanidades, Depto. de Procesos Sociales, Ciudad de México, México.

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• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 28, Nº. 2, 2021 (Ejemplar dedicado a: Revista de Matemática: Teoría y Aplicaciones), págs. 279-294
• Idioma: inglés
• DOI: 10.15517/rmta.v28i2.44746
• Títulos paralelos:
  • Un modelo simple con presión de grupo: el caso de las conductas antisociales
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• Resumen
  • español

    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.

  • English

    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.

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