Modelling the Dynamics of Smoking Epidemic

Abstract

Our study is made up two sections: Non-smokers, problem- smokers, smokers-in-treatment and counselling, and removed-smokers (SPTcR) mathematical model that explains the dynamics of smoking epidemic without considering the recovery class to susceptible class transferring followed by modelling smoking epidemic where the recovery class is considered to revert to susceptible class to become problem smokers again after treatment and recovery respectively. We discussed the existence and stability of the smoking-free and endemic equilibria of both models. Our mathematical analysis of both models establish that the global dynamics of smoking epidemic transmission can be determined by the basic reproductive number. The smoking-free equilibrium was locally asymptotically stable if R0 < 1 and unstable if R0 > 1 in both models. Global stability of smoking-free and endemic equilibria was also discussed in our first model, using Lassalle’s invariance principle of Lyapunov functions. Numerical simulations were conducted using Matlab software to confirm our analytic results in both models. Our findings were that reducing the contact rate between the non-smokers and problem smokers, increasing the number of smokers that go into treatment and educating smokers to refrain from smoking can be useful in combating the smoking epidemic.