Modeling the Effect of Inpatient Rehabilitation of Tobacco Smokers on Smoking Dynamics
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Date
2021
Authors
Nyamai, Amos Mwendwa
Mutuku, Winifred N.
Journal Title
Journal ISSN
Volume Title
Publisher
Journal of Advances in Mathematics and Computer Science
Abstract
Aims:
1. Develop and analyze a mathematical model of the effect of inpatient rehabilitation of tobacco smokers
on tobacco smoking using Kenya as a case study.
2. Perform stability analysis on the smoking free equilibrium point and endemic equilibrium point of the
model.
3. 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
Description
An Article Published in Journal of Advances in Mathematics and Computer Science
Keywords
Tobacco smoking, Inpatient rehabilitation, Reproduction number, Numerical simulation
Citation
Nyamai, A. M., & Mutuku, W. N. (2021). Modeling the Effect of Inpatient Rehabilitation of Tobacco Smokers on Smoking Dynamics. Journal of Advances in Mathematics and Computer Science, 1-14.