We derive and analyze a mathematical model of smoking in which the population is divided into four classes: potential smokers, smokers, temporary quitters, and permanent quitters. In this model we study the effect of smokers on temporary quitters. Two equilibria of the model are found: one of them is the smoking-free equilibrium and the other corresponds to the presence of smoking. We examine the local and global stability of both equilibria and we support our results by using numerical simulations.

We present a non-linear mathematical model which analyzes the spread of smoking in a population. In this paper, the population is divided into …ve classes: potential smokers, occasional smokers, heavy smokers, temporary quitters and permanent quitters. We study the e¤ect of considering the class of occasional smokers and the impact of adding this class to the smoking model in [1] on the stability of its equilibria. Numerical results are also given to support our results.Mathematics Subject Classi…cation: 34D23, 91D10

Virotherapy is a therapeutic treatment for cancer. It uses genetically engineered viruses to selectively infect, replicate in, and destroy cancer cells without damaging normal cells. In this paper, we present a modified model to include, within the dynamics of virotherapy, the interaction between uninfected tumor cells and immune response. The model is analyzed qualitatively to produce five equilibrium points. One of these equilibriums demonstrates the effect observed in virotherapy, where the immune system demolishes infected cells as well as viruses. Moreover, the existence and stability of the equilibrium points are established under certain criteria. Numerical simulations are performed to display the agreement with the analytical results. Finally, parameter analysis is carried out to illustrate which parameters in the model affect the outcome of virotherapy.

In this paper, we propose a rumor transmission model with incubation period considering the fact that incubators may move to stifler class and susceptibles may move to spreader class. The model is formulated with constant recruitment and varying total population. The full system of the model is studied qualitatively producing rumor-free and rumor-existence equilibriums. The existence conditions of the equilibriums are investigated. Moreover, the local and global stability analysis of both equilibriums is examined. Furthermore, numerical simulations are used to support the qualitative analysis. Finally, the impact of different management strategies on the dissipation of rumors is analyzed numerically by varying key parameters in the model.

In this paper we present and analyze a generalization of the giving up smoking model that was introduced by Sharomi and Gumel [4], in which quitting smoking can be temporary or permanent. In our model, we study a population with peer pressure effect on temporary quitters and we consider also the possibility of temporary quitters becoming permanent quitters and the impact of this transformation on the existence and stability of equilibrium points. Numerical results are given to support the results.