Analyzing the Interplay of Seasonality and Relapse in the Mathematical Model Dynamics of Sex Workers, Drug Use and Rehabilitation

This paper presents a mathematical model that investigates the dynamics of subpopulation of humans engaged in prostitution and drug use, incorporating seasonality and relapse. The model features compartments representing susceptible individuals, individuals engaged in prostitution, drug users, individuals in both activities, and rehabilitated individuals. Nonlinear differential equations govern the system, solved using the Runge-Kutta fourth order method. Using relevant variable/parameters, results show cyclic patterns in prostitution and drug use, with susceptibility resurging after decline. Rehabilitation leads to declines in risky behaviors, but relapse occurs without consistent support. The findings underscore the importance of tailored interventions and sustained assistance for effective behavioral change and public health improvement.