Abstract: This paper studies the impact of human behavior on quitting smoking dynamics by a PLSQ mathematical model. We start with a quitting smoking ordinary differential equation (ODE) model with nonlinear incidence and human behavior impacts. The basic reproduction number of the model is obtained by establishing the basic reproduction matrix. Using the Routh-Hurwitz criterion and Lyapunov functionals and LaSalle's invariant principle and the second additive compound matrix, local and global dynamics of the model are analysed. Based on the partial rank correlation coefficients (PRCCs), the influence of various parameters in the basic reproduction number on the transmission of smokers is analysed. Particularly, the influence of human behavior on the transmission of smokers is obtained through theoretical deduction. Finally, the theoretical derivation is verified by numerical simulation. Our results show that human behavior can reduce the number of smokers.

Key words: nonlinear incidence, quitting smoking model, human behavior, local stability, global stability