12/02/2015, 14:30 — 15:30 — Sala P3.10, Pavilhão de Matemática
Paolo Falsaperla, Dipartimento di Matematica e Informatica, Università di Catania, Catania, Italy
A mathematical model of anorexia and bulimia
Time evolution of pathological and harmful behaviors (such as binge drinking or drug consumption [1, 2]) can be modeled in the context of epidemiological models [3]. In this paper we propose a mathematical model to study the dynamics of anorexic and bulimic populations inspired by the model of Gonzalez et al. [4]. The model proposed takes into account, among other things, the effects of peers' influence, media influence, and education. We prove the existence of three possible equilibria, that without media influences are disease-free, bulimic-endemic, and endemic. Neglecting media and education effects we investigate the stability of such equilibria, and we prove that under the influence of media, only one of such equilibria persists and becomes a global attractor. Which of the three equilibria becomes global attractor depends on the other parameters.
Joint work with C. Ciarcia, A. Giacobbe, G. Mulone.
References
- Mulone G, Straughan: Modeling binge drinking, Int. J. Biomath., 5(1), 1250005 (2012).
- Mulone G, Straughan B: A note on heroin epidemics, Math. Biosci. 218, 118-141 (2009).
- Hethcote HW: The mathematics of infectious diseases, SIAM Rev. 42, 599-653 (2000).
- Gonzalez B et al.: Am I too fat? Bulimia as an epidemic, J. Math. Psych. 47, 515-526 (2003).
