流行性病毒传播生态动力学系统

利用近代数学物理的渐近理论,研究了一类流行性传染病传播非线性动力学系统.首先,提出了流行性传染病传播微分动力学模型.其次,引入一组泛函分析同伦映射,将动力学系统的解展为由一个人工参数的幂级数.然后,逐次地求出该动力学系统的各次渐近解析解.最后,阐述了动力学模型解的意义.

Dynamical analysis for a malware propagation model in wireless sensor network

The threat of malware in wireless sensor network has stimulated some activities to model and analyze the malware prevalence.To understand the dynamics of malware propagation in wireless sensor network,we propose a novel epidemic model named as e-SEIR(susceptible-exposed-infectious-recovered)model,which is a set of delayed differential equations,in this paper.The model has taken into account the following two factors:1 Multi-state antivirus measures;2 Temporary immune period.Then,the stability and Hopf bifurcation at the equilibria of linearized model are carefully analyzed by considering the distribution of eigenvalues of characteristic equations.Both mathematical analysis and numerical simulations show that the dynamical features of the proposed model rely on the basic reproduction number R0 and time delayτ.This novel model can help us to better understand and predict the propagation behaviors of malware in wireless sensor networks.

Analysis of an Epidemic Model with Age of Vaccination

A simple SI epidemic model with age of vaccination is discussed in this paper.Both vexing birth rate, the mortality rate caused by disease and vaccine waning rate areconsidered in this model. We prove that the global dynamics is completely determined bythe basic reproductive number R（ψ）（ψ denotes per capita vaccination rate）. If R（0） 〈 1,the disease-free equilibrium is a global attractor; If R（ψ） 〈： 1, the disease-free equilibriumis locally asymptotically stable; If R（ψ） ：〉 1, an unique endemic equilibrium exists and islocally asymptotically stable under certain condition.

Existence for positive steady states of an eco-epidemiological model

An eco-epidemiological model with an epidemic in the predator and with a Holling type Ⅱ function is considered.A system with diffusion under the homogeneous Neumann boundary condition is studied.The existence for a positive solution of the corresponding steady state problem is mainly discussed.First,a prior estimates（positive upper and lower bounds） of the positive steady states of the reaction-diffusion system is given by the maximum principle and the Harnack inequation.Then,the non-existence of non-constant positive steady states by using the energy method is given.Finally,the existence of non-constant positive steady states is obtained by using the topological degree.

一类非线性传染病生态系统的泛函渐近解

讨论了一类非线性传染病传播群体的模型,利用泛函同伦映射的方法来探求传染病的传播规律,构造一对泛函同伦映照,讨论模型相应的线性系统。在一定的情况下,在零点处是一个稳定的结点,即原流行性传染病传播系统在零点处为稳定结点。因此,系统模型的时间当变量t趋于无穷时而趋于零点(解)。对于这种流行传染病传播模式,就能采取较好的措施,使传染病将得到控制。最后通过一个例子,说明了所用的方法的正确性,泛函同伦映照方法可采取对应的措施来控制它,解的表示式还能进一步进行解析运算。因此,它能够继续其它相关物理量的各种性态更深入的讨论。

Model prediction of the operating behavior of a circulating fluidized bed boiler

An improved mathematical model for a circulating fluidized bed (CFB) boiler based on the model developed earlier by the authors was applied to simulate the operation of a 12 MW CFB boiler. The influences of the excess air ratio, primary air ratio, coal particle size distribution, coal properties (ash content and volatile content) and Ca/S ratio on the boiler operation were analyzed. The results showed that the model simulation may be applied to the optimum design and economic operation of the CFB boiler.

Comparison and Evaluation of Three Animal Models for Studyingthe Pathogenicity of Staphylococcus epidermidis

In order to compare and evaluate three animal models for studying the pathogenicity of Staphylococcus epidermidis strains, three experimental animal models, namely, murine intra-venous LD 50, mouse foreign body infection and rat central venous catheter (CVC) infection models were used to assess the relative virulence of two S. epidermidis strains, ATCC 12228 and 97-337. The results from three animal models were comparable, indicating S.epidermidis 97-337 was more virulent than strain ATCC 12228. The rat CVC infection model best mimicked the conditions of clinical patients with intra-venous catheters, and more information could be obtained from this model. We conclude that different in vivo models serve for different purposes, and the rat CVC infection model is most suitable for studying specific characteristics of catheter related infections caused by S. epidermidis strains.

Epidemiological modeling of passive worm propagation on the P2P file-sharing network

The peer-to-peer（P2P） file-sharing network as a vehicle of disseminating files has become very popular. The appearance of dozens of kinds of passive worms on this network has, however, made it unsecured. This problem has been paid attention and a few of models for passive worm propagation has been presented. Unfortunately, the dynamic properties of this network are ignored in these models. Given the fact, the characteristics of both this network and the passive worm are identified, and on this basis a new mathematical model of passive worm propagation on the P2P network is presented in applying epidemiology in this paper. Note that the dynamic properties of this network are considered in the presented model. The model has been validated by large scale simulation experiments, which demonstrates that the presented model may be used for analyzing the behaviors of passive worms and predicting the trend of their propagation.

GLOBAL ASYMPTOTIC STABLE ERADICATION FOR THE SIV EPIDEMIC MODEL WITH IMPULSIVE VACCINATION AND INFECTION-AGE

We study the application of a pulse vaccination strategy to eradicate the slowly progressing diseases that have infectiousness in latent period. We derive the condition in which eradication solution is a global attractor, this condition depends on pulse vaccination proportion p. We also obtain the condition of the global asymptotic stability of the solution. The condition shows that large enough pulse vaccination proportion and relatively small interpulse time lead to the eradication of the diseases. Moreover the results of the theoretical study might be instructive to the epidemiology of HIV.

Simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model

Fresh cement mortar is a type of workable paste, which can be well approximated as a Bingham plastic and whose flow behavior is of major concern in engineering. In this paper, Papanastasiou＇s model for Bingham fluids is solved by using the multiple- relaxation-time lattice Boltzmann model （MRT-LB）. Analysis of the stress growth exponent m in Bingham fluid flow simulations shows that Papanastasiou＇s model provides a good approximation of realistic Bingham plastics for values of m 〉 108. For lower values of m, Papanastasiou＇s model is valid for fluids between Bingham and Newtonian fluids. The MRT-LB model is validated by two benchmark problems： 2D steady Poiseuille flows and lid-driven cavity flows. Comparing the numerical results of the velocity distributions with corresponding analytical solutions shows that the MRT-LB model is appropriate for studying Bingham fluids while also providing better numerical stability. We further apply the MRT-LB model to simulate flow through a sudden expansion channel and the flow surrounding a round particle. Besides the rich flow structures obtained in this work, the dynamics fhi d force on the round particle is calculated. Results show that both the Reynolds number Re and the Bingham number Bn affect the drag coefficients Co, and a drag coefficient with Re and Bn being taken into account is proposed. The relationship of Bn and the ratio of unyielded zone thickness to particle diameter is also analyzed. Finally, the Bingham fluid flowing around a set of randomly dispersed particles is simulated to obtain the apparent viscosity and velocity fields. These results help simulation of fresh concrete flowing in porous media.

Zero-Hopf bifurcation for an infection-age structured epidemic model with a nonlinear incidence rate

An infection-age structured epidemic model with a nonlinear incidence rate is investigated.We formulate the model as an abstract non-densely defined Cauchy problem and derive the condition which guarantees the existence and uniqueness for positive age-dependent equilibrium of the model.By analyzing the associated characteristic transcendental equation and applying the normal form theory presented recently for non-densely defined semilinear equations,we show that the SIR(susceptible-infected-recovered)epidemic model undergoes Zero-Hopf bifurcation at the positive equilibrium which is the main result of this paper.

Global stability and vaccination of an SEIVR epidemic model with saturated incidence rate

This study considers SEIVR epidemic model with generalized nonlinear saturated inci- dence rate in the host population horizontally to estimate local and global equilibriums. By using the Rout^Hurwitz criteria, it is shown that if the basic reproduction number R0 〈 1, the disease-free equilibrium is locally asymptotically stable. When the basic reproduction number exceeds the unity, then the endemic equilibrium exists and is stable locally asymptotically. The system is globally asymptotically stable about the disease-free equilibrium if R0 〈 1. The geometric approach is used to present the global stability of the endemic equilibrium. For R0〉 1, the endemic equilibrium is stable globally asymptotically. Finally, the numerical results are presented to justify the mathematical results.

STOCHASTIC DISCRETE-TIME AGE-OF-INFECTION EPIDEMIC MODELS

We present an epidemic model which can incorporate essential biological detail as well as the intrinsic demographic stochastieity of the epidemic process, yet is very simple, enabling rapid generation of a large number of simulations, A deterministic version of the model is also derived, in the limit of infinitely large populations, and a final-size formula for the deterministic model is proved. A key advantage of the model proposed is that it is possible to write down an explicit likelihood functions for it, which enables a systematic procedure for fitting parameters to real incidence data, using maximum likelihood.

GLOBAL STABILITY OF AN EPIDEMIC MODEL FOR VECTOR-BORNE DISEASE

This paper considers an epidemic model of a vector-borne disease which has the vectormediated transmission only. The incidence term is of the bilinear mass-action form. It is shown that the global dynamics is completely determined by the basic reproduction number Ro. If Ro ≤ 1, the diseasefree equilibrium is globally stable and the disease dies out. If Ro 〉 1, a unique endemic equilibrium is globally stable in the interior of the feasible region and the disease persists at the endemic equilibrium. Numerical simulations are presented to illustrate the results.

Bounding the Inefficiency of the C-Logit Stochastic User Equilibrium Assignment

Compared with standard logit-based stochastic user equilibrium assignment model,the C-logit model describes route choice behavior in a more realistic way by considering the overlapping effect between routes.This paper investigates the inefficiency upper bounds of this model against the deterministic system optimum and the C-logit stochastic system optimum in terms of the total network travel time.It is found that the commonality factor of overlapping routes significantly affects the inefficiency bound,besides link congestion degree,total demand and the number of feasible routes.If the commonality factor is not considered,the efficiency loss resulting from selfishly stochastic travel behavior will be to large extent underestimated.

Global stability of an SEIQV epidemic model with general incidence rate

In this paper, a class of SEIQV epidemic model with general nonlinear incidence rate is investigated. By constructing Lyapunov function, it is shown that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number R0 ≤ 1. If R0 〉 1, we show that the endemic equilibrium is globally asymptotically stable by applying Li and Muldowney geometric approach.

Global stability for a multi-group SVIR model with age of vaccination

In this paper, a multi-group SVIR epidemic model with age of vaccination is considered. The model allows the vaccinated individuals to become susceptible after the vaccine loses its protective properties, and the vaccination classes satisfy first-order the partial differential equations structured by vaccination age. Combining the Lyapunov functional method with a graph-theoretic approach, we show that the global stability of endemic equilibrium for the strongly connected system is determined by the basic reproduction number. In addition, the dynamics for non-strongly connected model are also investi- gated, depending on the basic reproduction numbers corresponding to each strongly connected component. Numerical simulations are carried out to support the theoretical conclusions.

Global asymptotic stability for a SEI reaction-diffusion model of infectious diseases with immigration

This paper studies the local and global stability of solutions for a spatially spread SEI epidemic model with immigration of individuals using a Lyapunov functional. It is shown that in the presence of diffusion, the unique steady state remains globally stable. Numerical results obtained through Matlab simulations are presented to confirm the findings of this study.

Global stability of an SEIR epidemic model with vaccination

In this paper, an SEIR epidemic model with vaccination is formulated. The results of our mathematical analysis indicate that the basic reproduction number plays an important role in studying the dynamics of the system. If the basic reproduction number is less than unity, it is shown that the disease-free equilibrium is globally asymptotically stable by comparison arguments. If it is greater than unity, the system is permanent and there is a unique endemic equilibrium. In this case, sufficient conditions are established to guarantee the global stability of the endemic equilibrium by the theory of the compound matrices. Numerical simulations are presented to illustrate the main results.

Nonlinear stability of traveling waves for a multi-type SIS epidemic model

The nonlinear stability of traveling waves for a multi-type SIS epidemic model is inves- tigated in this paper. By using the comparison principle together with the weighted energy function, we obtain the exponential stability of traveling wavefront with large wave speed. The initial perturbation around the traveling wavefront decays exponen- tially as x → -∞, but it can be arbitrarily large in other locations.