Mathematical Modeling and Analysis on the Dynamics of Tobacco Smoking by Considering Occasional and Habitual Smokers

Abstract

This study investigate smoking tobacco considering occasional and habitual smokers using mathematical model. The study aims to understand how to decrease smoking habit. we clas sified the total population in to four compartments namely; susceptible, secondhand smokers, occasional smokers, habitual smokers and Recovered. Positivity of the solutions and bound edness of the model are discovered. Using Routh-Hurwitz criteria ,center manifold theory and Castillo Chavez Theorem, we assed equilibrium point of the model and investigate their sta bility. The basic reproduction number (R0) is computed using next generation matrix method. We have proved that the smoking free equilibrium is locally and globally asymptotically stable when R0 < 1 the smoking habit removed & unstable. Also smoking present equilibrium point is locally asymptotically stable,when R0 > 1 smoking habit persist. Additionally, our model in dicates that a forward bifurcation and sensitive analysis is performed. Using sensitivity analysis the rate of interaction of smokers with susceptible and rate of recruitment has positive impact on the spread of smoking habit and rate of death due to smoking and treatment rate has negative impact on the spread of smoking habit. Finally, we perform numerical simulations using MAT LAB software Ode 45 codes to support the analytical results are in agreement with numerical solutions