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Binge drinking is a multi-factorial problem where peer influence in the immediate environment has a key role in the appearance of the first episode and the recurrence. However, information regarding the interaction of variables that mediate the influence among people is limited. Binge drinking pattern is generally derived from interrelationships with other drinking states in a manner analogous to the susceptible-infectious relationship. Nevertheless, the classic modelling approach is not appropriate because the periodicity of consumption is associated with specific social contexts where social drinkers adopt binge drinking. We analyse the temporal evolution of binge drinkers, formulating a discrete mathematical model that incorporates the effect of the size of the influence group, the incitement-to-use and the refractoriness to recurrence as parameters. Our results allow evaluating the potential impact of interventions according to the individual and social characteristics of the susceptible population. New horizons of epidemiological research are established to prevent alcoholism. [ABSTRACT FROM AUTHOR]

We study a predator-prey model with Holling type Ⅰ functional response, an alternative food source for the predator, and multiple Allee effects on the prey. We show that the model has at most two equilibrium points in the first quadrant, one is always a saddle point while the other can be a repeller or an attractor. Moreover, there is always a stable equilibrium point that corresponds to the persistence of the predator population and the extinction of the prey population. Additionally, we show that when the parameters are varied the model displays a wide range of different bifurcations, such as saddle-node bifurcations, Hopf bifurcations, Bogadonov-Takens bifurcations and homoclinic bifurcations. We use numerical simulations to illustrate the impact changing the predation rate, or the non-fertile prey population, and the proportion of alternative food source have on the basins of attraction of the stable equilibrium point in the first quadrant (when it exists). In particular, we also show that the basin of attraction of the stable positive equilibrium point in the first quadrant is bigger when we reduce the depensation in the model. [ABSTRACT FROM AUTHOR]