Stability analysis of mathematical model of smoking behavior with non-monotone incidence rate

Cigarettes, processed tobacco products, are produced from Nicotiana tabacum, Nicotiana rustica that are containing nicotine and tar. Smoking behavior is a health-related problem because it can cause various diseases and death for smokers and people around it. A mathematical model approach on the spread of smoking behavior is needed to predict the spread of smoking behavior in the future. In this paper, we propose a mathematical model of smoking behavior with non-monotone incidence rate. The model has two equilibriums, namely the free equilibrium point of smoking behavior (non-endemic) and equilibrium point of smoking behavior (endemic). The existence of the endemic equilibrium and its stability depend on the basic reproduction number (R0). The non-endemic equilibrium is locally asymptotically stable if R0 < 1, while the endemic equilibrium will tend to be locally asymptotically stable if R0 > 1. Furthermore, we also perform a sensitivity analysis to determine the most influential parameter in the model on the basic reproduction number. Based on the results of sensitivity analysis obtained, it is known that the most influential parameters on the model are the rate of movement from the population of potential smokers to heavy smokers and the rate of light smokers affected diseases due to smoking. Based on the numerical simulation, it supports the result of analytical study the dynamics behavior of smoking.