Mathematical Modelling of the Dynamics of Tuberculosis and Tobacco Smoking

Abstract: Tuberculosis (TB) remains a major global public health challenge, particularly in low- and middle-income countries, with tobacco smoking worsening disease outcomes. This study developed a deterministic compartmental model to investigate the combined dynamics of TB transmission and tobacco smoking, incorporating vaccination, smoking behaviour, smoking cessation, waning immunity, recovery, and TB-induced mortality. The model stability and the existence of equilibrium points were determined. The basic reproduction number ( R0) was obtained using the next-generation matrix, while sensitivity analysis identified parameters with the greatest influence on TB transmission. Numerical simulations were conducted using MATLAB to investigate the effects of smoking, vaccination, vaccine efficacy, and smoking cessation on the dynamics of tuberculosis. Results indicate that the effective TB transmission rate and smoking modifying factor are key drivers of transmission, whereas vaccination and smoking cessation contribute to reducing the spread of TB. The model provided quantitative insights into the interaction between smoking and TB and offers a mathematical framework for evaluating combined behavioural and vaccination interventions for TB control. Keywords: Tuberculosis; Tobacco smoking; Mathematical modelling; Basic reproduction number; Vaccination; Smoking cessation. Title: Mathematical Modelling of the Dynamics of Tuberculosis and Tobacco Smoking Author: Maurice Oluoch Ojwang, Caroline Kanyiri, Brian Nyanaro International Journal of Novel Research in Physics Chemistry & Mathematics ISSN 2394-9651 Vol. 13, Issue 3, September 2026 - December 2026 Page No: 1-12 Novelty Journals Website: www.noveltyjournals.com Published Date: 22-September-2026 DOI: https://doi.org/10.5281/zenodo.22893870 Paper Download Link (Source) https://www.noveltyjournals.com/upload/paper/Mathematical%20Modelling%20of%20the%20Dynamics-22092026-4.pdf