Backward bifurcation in a smoking cessation model with media campaigns

Abstract

a b s t r a c tNowadays, most of the public policies to manage the social issues are focusing on motivating people via media campaigns. In view of this, we propose and analyze a nonlinear mathematical model to study the effect of media campaigns on smoking cessation. The equilibria of the model have been obtained and their stability discussed. Using center manifold reduction theory, we reduce the proposed model to a system of lower dimension. The reduced system contains all the necessary information regarding the asymptotic behavior of small solutions of the original system. The analysis shows that on changing one parameter of the system (reproduction number, R, which depends on various other parameters), two different manifolds of fixed points cross each other and transcritical bifurcation occurs. Further, for large value of relapse rate the bifurcation is subcritical (backward). This shows that requirement R < 1 is only necessary, but not sufficient, for smoking cessation. Numerical simulation also supports the analytically obtained results.

Dynamics of Duopoly Models with Undecided Clients under Decentralized Affine Feedback Advertising Policies

“…Assuming that the total population size is constant and normalized to unity [5], i.e., x 1 + x 2 + x 3 � 1, model (7) can also be expressed as follows:…”

“…On the contrary, the consumer buying process is strongly in uenced by cultural, social, personal, and psychological factors [4]. In order to in uence the buying behavior of people [5], rms use advertising to promote the sale of their products [6]. Advertising can be understood as a form of communication used to induce consumers to take a particular action with respect to products or services [7].…”

Dynamical analysis of a giving up smoking model with time delay

“…They examined the stability and attractivity of the proposed model. For the analytical study of stochastic giving up smoking models or some other giving up smoking models, we can refer to [16][17][18][19][20].…”

Qualitative and Sensitivity Analysis of the Effect of Electronic Cigarettes on Smoking Cessation

“…On the one hand, from the mathematical modelling point of view, the smoking cessation models have been studied by using mathematical modelling [ 8 – 11 ]. For instance, Sharma and Misra have studied a mathematical model of smoking cessation with media campaigns and bifurcation analysis [ 12 ]. Furthermore, Pang et al have proposed a mathematical model with a saturated incidence rate to explore the effect of controlling smoking [ 13 ].…”