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Analysis of a Kind of Quitting Smoking Modelwith Beddington-DeAngelis Function
  
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KeyWord:Stochastic Beddington-DeAngelis predator-prey model; Distributed delay; Stationary distribution; Extinction
Author NameAffiliation
Zhimin Li School of Science, Chang’an University, Xi’an, Shaanxi 710064, China 
Tailei Zhang School of Science, Chang’an University, Xi’an, Shaanxi 710064, China 
Jianzhong Gao School of Ecological Environment, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, China 
Shu Fang School of Science, Chang’an University, Xi’an, Shaanxi 710064, China 
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Abstract:
      In this paper, we discuss the dynamics of quitting smoking with Beddington-Deangelis function. Firstly, the basic reproduction number of the model is obtained by establishing the basic reproduction matrix. Then, by 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 analyzed. Based on the partial rank correlation coefficients (PRCCs), we discuss some biological implications and focus on the impact of some key model parameters. Finally, the numerical simulations show the theoretical analysis more intuitively, and we give some strategies to control the spread of smokers.