Mathematical modeling of drug abuse, unemployment and mental stress on population dynamics of mental illness

Abstract

There has been a rise in the number of reported cases of mental illness in both High Income Countries (HICs) and Low and Middle Income Countries (LMICs). Non-communicable Diseases (NCDs) seldom make use of mathematical modeling. This research suggests eight first-order differential equations to form the basis of a mathematical model for psychiatric disorders. There are eight distinct categories created to reflect the public at large: the vulnerable, the working and jobless, drug addicts, the emotionally distraught, and the mentally ill. Theoretically, the well-possedness of the model equations is established by examining the positive, bounded, existing, unique solutions and the local and global stability. The eigenvalue approach was used to investigate local stability, and a Lyapunov function was created to analyze global behavior. In order to back up the analytical results, we performed a numerical investigation of the dynamical behavior of the model's equations using the fourth-order Runge-Kutta technique with the use of the MATLAB software package. To better understand the impact of environmental factors on mental disease, researchers have experimented with changing a number of variables related to mental stress, unemployment and drug addiction among certain groups. Based on visual representations, the prevalence of mental illness skyrocketed anytime variables related to psychological strain or substance (drug) addiction rose in severity. In conclusion, lowering the growing rates of mental illness may be accomplished through increasing options for employment, improving working conditions, and fostering a welcoming workplace.