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.

Virotherapy is a novel treatment for cancer, which may be delivered as a single agent or in combination with other therapies. Research studies indicated that the combination of viral therapy and radiation therapy has synergistic antitumor effects in in vitro and in vivo. In this paper, we proposed two models in the form of partial differential equations to investigate the spatiotemporal dynamics of tumor cells under virotherapy and radiovirotherapy. We first presented a virotherapy model and solved it numerically for different values of the parameters related to the oncolytic virus, which is administered continuously. The results showed that virotherapy alone cannot eradicate cancer, and thus, we extended the model to include the effect of radiotherapy in combination with virotherapy. Numerical investigations were carried out for three modes of radiation delivery which are constant, decaying, and periodic. The numerical results showed that radiovirotherapy leads to complete eradication of the tumor provided that the delivery of radiation is constant. Moreover, there is an optimal timing for administering radiation, as well as an ideal dose that improves the results of the treatment. The virotherapy in our model is given continuously over a certain period of time, and bolus treatment (where virotherapy is given in cycles) could be considered and compared with our results.

License, which perm its unrestricted use, distribution, and reproduction in any m edium , provided the original work is prop erly cited. AbstractResearchers have applied epidemiological models to study the dynamics of social and behavioral processes, based on the fact that both biological diseases and social behavioral are a result from interactions between individuals. The main feature of the paper is to understand the dynamics of spreading a meme on a large scale in a short time through a chain of communications. In this paper we study a meme transmission model, which is an extension of the deterministic Daley-Kendall model and we analyze it by using stability theory of nonlinear differential equations. The model is based on dividing the population into three disjoint classes of individuals according to their reaction to the meme. We examine the existence of equilibria of the model and investigate their stability using linearization methods, Lyapunov method and Hopf bifurcation analysis. One of the significant results in this paper is finding conditions that will lead to persistent of memes. Also numerical simulations are used to support the results.

This paper intends to investigate the impact of external computers and removable devices on virus spread in a network with heterogeneous immunity. For that purpose, a new dynamical model is presented and discussed. Theoretical analysis reveals the existence of a unique viral equilibrium that is locally and globally asymptotically stable with no criteria. This result implies that efforts to eliminate viruses are not possible. Therefore, sensitivity analysis is performed to have more insight into parameters’ impact on virus prevalence. As a result, strategies are suggested to contain virus spread to an acceptable level. Finally, to rationalize the analytical results, we execute some numerical simulations.