Global Aspects of Age-Structured Cigarette Smoking Model

Stability and Hopf bifurcation analysis of a delayed tobacco smoking model containing snuffing class

“…However, once the value of delay is above τ 0 , populations in system (2) may coexist in an oscillatory mode under some conditions. Therefore, we should control and postpone the occurrence of Hopf bifurcation in system (2). From this point of view, we can conclude that people who would like to quit smoking should quit it as soon as possible.…”

“…Author details 1 School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu, 233030, China. 2 Department of Mathematics & Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, India. 3 Department of Mathematics, Alagappa University Alagappapuram, Karaikudi, 630 004, India.…”

“…Since the advent of tobacco in 6000 BC, smoking has contributed heavily not only to problems leading to serious illness or even death, but it has also done harm to the whole society [1][2][3]. According to the third edition of cancer atlas jointly released by International Agency for Research on Cancer (IARC), American Cancer Society (ACS), and Union for International Cancer Control (UICC) on October 16, 2019, smoking causes more preventable cancer deaths than any other risk factor, and in 2017 alone, 2.3 million people worldwide died from smoking, which accounts for 24% of all cancer deaths.…”

“…Thus, in recent years, scholars at home and abroad have formulated different forms of smoking models with linear incidence rate [6][7][8][9], saturated incidence rate [10,11], square root type incidence rate [12][13][14], and harmonic mean type incidence rate [15]. Several others presented fractional smoking models [16][17][18][19][20] and age-structured smoking models [2,21]. It is worth noting that all the smoking models above neglect the fact that the use of tobacco also occurs in the form of snuffing.…”

Non-standard finite difference scheme and analysis of smoking model with reversion class

“…Then, square root dynamics of smoking model were presented by Zeb et al [12] for the purpose that the model go to extinction in finite time. Many researchers tried on different aspects to developed smoking models and control on the epidemic models [8] , [7] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] . In this work, first we frame a mathematical model contains the reversion class then study the equilibrium points that are free smoking and positive smoking equilibrium points.…”