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.
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.
Introduction: Middle East respiratory syndrome coronavirus (MERS-CoV) is an emerging zoonotic viral pathogen and a serious public health concern. The virus was first reported in Saudi Arabia in 2012 and continues to be endemic in the region. Most of the initial MERS-CoV cases in 2012 and early 2013 were sporadic, and it remains unclear whether MERS-CoV was circulating before 2012 or not. Therefore, we tried here to find any molecular evidence of MERS-CoV circulation in humans before or during 2012 in the city of Jeddah, Saudi Arabia. Methodology: We examined 349 archived respiratory samples collected between January 2010 and December 2012 from patients with acute respiratory illnesses from the city of Jeddah in Western Saudi Arabia. All samples were screened for MERS-CoV by real-time RT-PCR targeting the upstream E-gene (UpE) and the open reading frame 1 a (ORF1a). Results: All tested samples which were originally found negative for influenza A H1N1 virus were also found to be negative for MERS-CoV. Conclusions: These results suggest that circulation of MERS-CoV was uncommon among patients with acute respiratory symptoms in Western Saudi Arabia between 2010 and 2012.
Memes propagation is a usual form of social interaction. Understanding the dynamics of memes transmission enables one to find the conditions that leads to persistence or disappearance of memes. In this paper we analyze qualitatively a mathematical model of variable meme transmission. Two equilibrium points of the model are examined: meme free equilibrium and meme existence equilibrium. The reproduction number R 0 that generates new memes is found. Local and global stability of the equilibrium points are explored. Finally, we support our results using numerical simulations.
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