Backward bifurcation arises from the smoking transmission model considering media campaign

In this paper, we present and analyze a smoking cessation model with intervention from media campaigns. In our model, we consider potential smokers choosing not to smoke because of media campaign interventions. From the mathematical analysis, we obtain a threshold value of the model, called the basic reproduction number, which is the threshold condition for the smoking-free and endemic equilibrium stability. Next, it is shown that two endemic equilibrium may exist when the threshold basic reproduction number less than unity, and a unique endemic equilibrium exists if the threshold basic reproduction number exceeds unity. Using the center-manifold theory, we show that a backward bifurcation may occur when the value of the basic reproduction number equal to unity. This result implies that the classical epidemiological requirement of making basic reproduction number less than unity is no longer sufficient, although necessary, for effectively controlling the spread of smoking in a population. The numerical simulation was conducted for several scenarios to support and visualize our analytical results.