Abstract
In this paper, we are concerned with a mathematical model of secondhand smoker. The model is biologically meaningful and mathematically well posed. The reproductive number R_{0} is determined from the model, and it measures the average number of secondary cases generated by a single primary case in a fully susceptible population. If R_{0}<1, the smoking-free equilibrium point is stable, and if R_{0}>1, endemic equilibrium point is unstable. We also provide numerical simulation to show stability of equilibrium points. In addition, sensitivity analysis of parameters involving in the dynamic system of the proposed model has been included. The parameters involving in reproductive number measure the relative change in R_{0} when the value of the parameter changes.
Highlights
Secondhand smoke is defined as “the combination of smoke emitted from the burning end of a cigarette or other tobacco products and smoke exhaled by the smoker” [1]
Secondhand smoke exposure consists of an unintentional inhalation of smoke that occurs close to people smoking and/or in indoor environments where tobacco was recently used
Subjects may be exposed to secondhand smoke in multiple sites, such as the home [2], public places, cars, homes of relatives [3], and the workplace [4]
Summary
Secondhand smoke is defined as “the combination of smoke emitted from the burning end of a cigarette or other tobacco products and smoke exhaled by the smoker” [1]. Secondhand smoke exposure consists of an unintentional inhalation of smoke that occurs close to people smoking and/or in indoor environments where tobacco was recently used. Just 30 min of exposure to secondhand smoke can cause heart damage similar to that of habitual smokers [9]. Secondhand smoke exposure is a topic of great concern for us because of its well-known adverse effects on human health [10]. Different scholars discussed about secondhand smoke in relation to health problem. All studies mentioned above showed secondhand smoke is a big problem in the world as the result of leading peoples to diseases and death. There are a number of studies on mathematical model of smoking by taking different assumption. Model assumption We have the following assumptions in preparing the model
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