Modeling the Effect of Inpatient Rehabilitation of Tobacco Smokers on Smoking Dynamics

Aims: Develop and analyze a mathematical model of the effect of inpatient rehabilitation of tobacco smokers on tobacco smoking using Kenya as a case study. Perform stability analysis on the smoking free equilibrium point and endemic equilibrium point of the model. Use numerical simulation to investigate the impact of inpatient rehabilitation of tobacco smokers on smoking. Place and Duration of Study: Department of Mathematics and Actuarial Science, School of Pure and Applied Sciences (SPAS), Kenyatta University, Kenya, between May 2019 and September 2020. Tobacco smoking is a serious burden in Kenya and the world at large. Smoking harms nearly every organ of the body and affects the overall health of a person. Despite the overwhelming facts about the consequences of tobacco smoking, it remains a bad wont which is socially accepted and widely spread. In this research we numerically analyze the dynamics of smoking incorporating the impact of inpatient rehabilitation to curb the smoking habit. We first present a three-compartment model incorporating inpatient rehabilitation, then develop the system of ordinary differential equations governing the smoking dynamics. The basic reproduction number is determined using next generation matrix method. The model equilibria were computed and the stability analysis carried out. The results of stability analysis indicate that the disease-free equilibrium (DFE) is both locally and globally asymptotically stable for RS < 1 while the endemic equilibrium is both locally and globally asymptotically stable for RS > 1. Numerical simulations of model carried out with the help of MATLAB shows that, when rehabilitation is implemented effectively, it helps in minimization of smoking in the community.