Abstract
In this paper we propose smoking epidemic model which analyzes the spread of smoking in a population. The model consists of five compartments corresponding to five population classes, namely, potential-moderate-heavy-temporarily recovered- permanently recovered class. The basic reproduction number R0 has been derived, and then the dynamical behaviors of both smoking free equilibrium and smoking persistent equilibrium are analyzed by the theory of differential equation, and Numerical simulation has been carried out and the results have confirmed the verification of analytical results. Sensitivity analysis of R0 identifies β1, the transmission coefficient from potential smokers to moderate smokers and β2, the transmission coefficient from potential smokers to heavy smokers, as the most useful parameters to target for the reduction of R0.
Highlights
Smoking is a practice in which a substance is burned and the resulting smoke breathed in to be tasted and absorbed into the bloodstream
We develop a new model based on the idea given in [6, 7 and 8] by considering, basically, the effect of both moderate and heavy smokers on the potential smokers, and the effect of heavy smokers on temporarily quit smokers
The results show that the smoking free equilibrium value of the system is asymptotically stable, which is as expected from our theoretical analysis as
Summary
Smoking is a practice in which a substance is burned and the resulting smoke breathed in to be tasted and absorbed into the bloodstream. We develop a new model based on the idea given in [6, 7 and 8] by considering, basically, the effect of both moderate and heavy smokers on the potential smokers, and the effect of heavy smokers on temporarily quit smokers. It assesses the impact of this peer pressure on the existence and stability of steady state solutions, and the Sintayehu Agegnehu Matintu: Smoking as Epidemic: Modeling and Simulation Study result is supported with numerical simulation
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