Human networks and toxic relationships

We devise a theoretical model to shed light on the dynamics leading to the so called toxic relationships. We want to investigate what policy interventions people could advocate to protect themselves and to reduce suffocant assuefaction so to escape to the trap of physical or psychological abuses either in family or at work. By assuming that the toxic partner's behavior is exogenous and that the main source of addiction is income or wealth, and solving a dynamical system of differential equations we find that an asympotically stable equilibrium with positive love is always possibile for enough high level of appealing unless subsides to reduces assuefaction are introduced. Also the existence of a third uncondicionally reciprocating part as a benckmark (which represents not only the real presence of another partner but also the support from family, friends and overall private organizations. These last may help victims of domestic abuses or private organizations by offering economic and psychological support as well as legal counseling to victims of bullying at workplace and placement offices which e ectively help to find soon another job)plays an important role in reducing the toxic partner's appealing. By solving our model we outline the condition for a best mixed policy where both monetary subsides and alternatives are at work