A mathematical model of anorexia and bulimia

Abstract

a Communicated by E. VenturinoIn this paper, we propose a mathematical model to study the dynamics of anorexic and bulimic populations. 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.

E‐cigarette smoking with peer pressure

“…The approach of the fully non-linear solution to equilibrium is shown in Figure 1. To converge to actual equilibrium, it requires a longer time than shown since s(t) and e(t) wiggle for a long time before converging to the equilibrium solution (12). For all of the computations reported here, we have checked carefully to ensure convergence was achieved.…”

“…In particular, SIR models and ramifications thereof, such as those involving conformity bias (Walters, Walters and Kendal, and Bissell), incorporating external information (Buonomo et al and Giacobbe et al), and allowing for multi‐patch models (Wang and Mulone), have been employed in modelling alcohol studies (Mulone and Straughan,) Huo and Song, Huo and Wang, Giacobbe et al, and Walters, in drug models (Mushanyu, Nyabadza, Mulone and Straughan), in smoking (Sharomi and Gumel, Bissell, Caiado, and Bissell et al), in bulimia studies (Gonzalez et al and Ciarcia et al), in modelling possible eradication of polio (Pomeroy), in analysing rabies in dogs (Ruan), in childhood disease (Srivastava and Günerhan), in academic underachievement (Usaini et al), and many others.…”

“…Our objective here is to present and analyse an SIR or SI like ODE model for non-smokers, tobacco smokers, and those who smoke e-cigarettes, incorporating peer pressure in the switch from tobacco to e-cigarette smoking. We note that differential equation models have been used extensively in modelling social problems and related issues, including the spread of infections; see, eg, Bissell,7,8 Bissell et al, 9 Buonomo et al, 10 Caiado, 11 Ciarcia et al, 12 Giacobbe and Mulone, 13 Giacobbe et al, 14 Gonzalez et al, 15 Guo et al, 16 Hethcote et al, 17 Huo and Song, 18 Huo and Wang, 19 Jung et al, 20 Mulone and Straughan, 21,22 Mulone et al, 23 Mushanyu et al, 24 Nyabadza et al, 25 Pomeroy, 26 Sharomi and Gumel, 27 Srivastava and Günerhan, 28 Straughan, 29 Takeuchi et al, 30 Usaini et al, 31 Walters, 32 Walters and Kendal, 33 Wang, 34 Wang et al, 35 Wang and Mulone, 36 Wang and Zhao, 37,38 Wang and Zou, 39 and Zhou et al 40 In particular, SIR models and ramifications thereof, such as those involving conformity bias (Walters, 32 Walters and Kendal, 33 and Bissell 8 ), incorporating external information (Buonomo et al 10 and Giacobbe et al 14 ), and allowing for multi-patch models (Wang and Mulone 36 ), have been employed in...…”

“…Our objective here is to present and analyse an SIR or SI like ODE model for non‐smokers, tobacco smokers, and those who smoke e‐cigarettes, incorporating peer pressure in the switch from tobacco to e‐cigarette smoking. We note that differential equation models have been used extensively in modelling social problems and related issues, including the spread of infections; see, eg, Bissell, Bissell et al, Buonomo et al, Caiado, Ciarcia et al, Giacobbe and Mulone, Giacobbe et al, Gonzalez et al, Guo et al, Hethcote et al, Huo and Song, Huo and Wang, Jung et al, Mulone and Straughan, Mulone et al, Mushanyu et al, Nyabadza et al, Pomeroy, Sharomi and Gumel, Srivastava and Günerhan, Straughan, Takeuchi et al, Usaini et al, Walters, Walters and Kendal, Wang, Wang et al, Wang and Mulone, Wang and Zhao, Wang and Zou, and Zhou et al …”

SIR Models: Differential Equations that Support the Common Good

“…al. [3] study the effects of peers, media, and education on the dynamics of anorexic and bulimic populations.…”