A simplified mathematical model of gender-based family violence in Mexico

Gender-based violence is a major global public health challenge that persists in many societies. This study aims to assess the problem of gender-based family violence in Mexico, addressing the social neglect surrounding this issue and proposing viable strategies for its reduction. To achieve this, we analyze public health data regarding individuals who required medical attention due to injuries from family violence in Mexico, examining trends and implications. To analyze the temporal evolution of these trends we propose a simplified mathematical model to assess the problem of gender-segregated violence. This model is compartmental and consists of a system of non-linear ordinary differential equations that describe the time evolution of a gender-segregated population susceptible to violence. We employed public health data to fit the model parameters related to family violence cases and develop plausible scenarios for the evolution of the model. To evaluate the model's performance, we also analyze data related to non-family violence and self-inflicted violence. Our initial findings reveal significant differences in parameter values and the projected evolution of the population based on gender. Notably, we observe a tendency for female victims to outnumber male victims by almost two orders of magnitude in cases of family violence in Mexico. Additionally, we explore theoretical recovery measures integrated into the model to reduce the number of female victims. Our results indicate that achieving equality in the number of male and female victims of family violence is only possible if both female victims and aggressors receive rehabilitation. Therefore, this dynamic modeling approach underscores the need for public strategies that not only assist female victims in escaping violent environments, but also promote awareness and recovery programs for those who commit acts of violence.