Mathematical modeling and optimal control of depression dynamics influenced by saboteurs

Depression disorder affects millions globally, characterized by symptoms such as profound sadness, loss of interest in activities, and disruptions in eating and sleeping patterns. Understanding depression within the context of chronic pain is essential for developing effective management and intervention strategies. This study utilizes mathematical modeling to analyze depression trends using empirical data from Spain spanning from 2011 to 2022. Our depression model incorporates distinct compartments for primary and secondary depressed populations, along with a category for individuals categorized as saboteurs, who may actively influence the depression prevalence. We calculated the basic reproduction number [Formula: see text] and identified four equilibrium points and evaluated their stability. Additionally, sensitivity analysis was conducted to assess the impact of [Formula: see text] on depression prevalence. Furthermore, optimal control strategies were explored for the model. These strategies aim to improve treatment adherence, encourage doctor consultations, promote self-medication practices, and enhance recovery rates, ultimately aiming to reduce spread of depressive disorders and associated mortality. Data fitting was conducted using Python, and simulations were carried out in MATLAB to ensure rigorous validation of the model.