The 2015 epidemic of Middle East respiratory syndrome (MERS) in the Republic Korea has been largest outbreak outside East. This had caused 185 laboratory-confirmed cases and 36 deaths until September 2, 2015, which attracted public's attention. Based on detailed data patients released by World Health Organization (WHO) actual propagation epidemic, we construct two dynamical models to simulate processes from May 20 June 8 9 July 10, respectively find that basic reproduction number R0 reaches...

In this paper, we study a kind of the delayed SEIQR infectious disease model with quarantine and latent, get threshold value which determines global dynamics outcome disease. The has disease-free equilibrium is unstable when basic reproduction number greater than unity. At same time, it unique endemic According to mathematical analysis, show that are locally asymptotically stable by using Hurwitz criterion they globally suitable Lyapunov functions for any Besides, nonlinear incidence rate...

In this paper we present a highly pathogenic Avian influenza epidemic model with saturated contact rate. According to study of the dynamics, calculated basic reproduction number model. Through analysis model, have following conclusion: if R0 ≤ 1, there is only one disease-free equilibrium which globally stable, disease will die; > endemic be popular.

The rogue waves of the nonlinear Schrödinger equation with time-dependent linear potential function are investigated by using similarity transformation in this paper. first-order and second-order solutions obtained dynamic behaviors these discussed detail. In addition, amplitudes under effect gravity field external magnetic changing time analyzed numerical simulation. results can be used to study matter Bose-Einstein condensates other fields science.

In this paper, we investigate the emergence of a predator-prey model with Beddington-DeAngelis-type functional response and reaction-diffusion. We derive conditions for Hopf Turing bifurcation on spatial domain. Based stability analysis, give pattern formation via numerical simulation, i.e., evolution process near coexistence equilibrium point. find that consider, pure instability gives birth to spotted pattern, spiral wave both stripe-like pattern. Our results show reaction-diffusion is an...

In this paper, we focus on a spatial Holling-type IV predator-prey model which contains some important factors, such as diffusion, noise (random fluctuations) and external periodic forcing. By brief stability bifurcation analysis, arrive at the Hopf Turing surface derive symbolic conditions for in domain. Based obtain spiral pattern formation via numerical simulation. Additionally, study with colored From results, know that or forcing can induce instability enhance oscillation of species,...

Worms spreading through Web-based scanning and removable devices pose a serious threat to Internet security. This paper is devoted solving the problems of computer worms. A nonlinear mathematical model problem established, characteristics mechanisms worm propagation are analyzed by means stability theory differential equations, optimal control simulation. The results provide some new insights security, which predict tendency endemic equilibrium, identify epidemic strategies disease-free...

The rogue wave solutions are discussed for an inhomogeneous fifth-order nonlinear Schrödinger equation, which describes the dynamics of a site-dependent Heisenberg ferromagnetic spin chain. Using Darboux matrix, generalized transformation is constructed and recursive formula derived. Based on transformation, first-order to third-order obtained. Then, waves studied basis some free parameters. Several new structures found using numerical simulation. conclusions will be supportive tool study better.

In order to prevent the propagation of computer worms effectively, based on latent character worms, exposed compartments and USB device are introduced respectively, a series worm models with saturation incidence rate proposed. The qualitative behavior proposed model is studied. Firstly, threshold R 0 derived by using next-generation matrix method, which completely characterized stability disease free equilibrium endemic equilibrium. If < 1, asymptotically stable, implying that dies...

An SIR epidemic model with pulse birth and standard incidence is presented. The dynamics of the analyzed. basic reproductive number R ∗ defined. It proved that infection‐free periodic solution global asymptotically stable if < 1. unstable disease uniform persistent > Our theoretical results are confirmed by numerical simulations.

This paper proposes an evaluation system of graduate education quality by using gray theory, the use models to assess basic steps, based on AHP's assessment model, final overall design system.

In this paper, we introduce an improved hepatitis B virus(HBV) model to discuss the impact of vaccination.The basic reproductive number 0 R determine extinction and persistence virus infection.When is less than one,the disease- free equilibrium globally-asymptotically stable infection becomes extinct eventually;When greater unique endemic exists locally asymptotically.The results indicate that vaccination plays importment role in preventing controlling spread HBV.

In this paper, a new SEIR model incorporating the effects of awareness programs on epidemic spreading is analyzed. Two types equilibria and basic reproduction number are given, an algebraic approach used to prove global stability equilibria. Then sensitivity analysis endemic equilibrium performed. Moreover, media parameters system dynamics Finally, we conduct numerical simulation verify analytical results.