Stability analysis of VEISV propagation modeling for network worm attack

In this paper, we propose VEISV (vulnerable – exposed – infectious – secured – vulnerable) network worm attack model, which is appropriate for measuring the effects of security countermeasures on worm propagation. Contrary to existing models, our model takes into consideration accurate positions for dysfunctional hosts and their replacements in state transition. Using the reproduction rate, we derive global stability of a worm-free state and local stability of a unique worm-epidemic state. Furthermore, simulation results show the positive impact of increasing security countermeasures in the vulnerable state on worm-exposed and infectious propagation waves. Finally, equilibrium points are confirmed by phase plots.     

Dynamic model of worms with vertical transmission in computer network

An e-epidemic SEIRS model for the transmission of worms in computer network through vertical transmission is formulated. It has been observed that if the basic reproduction number is less than or equal to one, the infected part of the nodes disappear and the worm dies out, but if the basic reproduction number is greater than one, the infected nodes exists and the worms persist at an endemic equilibrium state. Numerical methods are employed to solve and simulate the system of equations developed. We have analyzed the behavior of the susceptible, exposed, infected and recovered nodes in the computer network with real parametric values.     

考虑蠕虫传播风险的信任度更新模型

基于网络节点信任度的评估机制是一种有效防御蠕虫传播的方法。针对现有节点信任度计算模型对蠕虫攻击行为不敏感,对恶意节点识别不全面的问题,本文提出了一种考虑蠕虫传播风险的信任度更新模型。通过蠕虫传播模型中STIDR状态定义,对节点信任度和传播概率的关系进行了定量刻画;建立了直接风险、间接风险和传播性风险三种条件下的信任度更新模型。仿真结果表明,与基本信任模型相比,本文考虑蠕虫传播风险的信任度更新模型使网络中感染状态节点的信任度更低,感染状态节点数目更少,隔离状态节点数目更多,表明信任度的更新使节点对感染状态节点的识别更加有效,在一定程度上达到了抵御蠕虫攻击,抑制蠕虫在网络中传播的目的。     

SEIQRS model for the transmission of malicious objects in computer network

Susceptible (S) – exposed (E) – infectious (I) – quarantined (Q) – recovered (R) model for the transmission of malicious objects in computer network is formulated. Thresholds, equilibria, and their stability are also found with cyber mass action incidence. Threshold R_cq determines the outcome of the disease. If R_cq ? 1, the infected fraction of the nodes disappear so the disease die out, while if R_cq > 1, the infected fraction persists and the feasible region is an asymptotic stability region for the endemic equilibrium state. Numerical methods are employed to solve and simulate the system of equations developed. The effect of quarantine on recovered nodes is analyzed. We have also analyzed the behavior of the susceptible, exposed, infected, quarantine, and recovered nodes in the computer network.     

Vaccination strategies based on feedback control techniques for a general SEIR-epidemic model

This paper presents several simple linear vaccination-based control strategies for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes more difficult contacts among susceptible and infected. The vaccination control objective is the asymptotically tracking of the removed-by-immunity population to the total population while achieving simultaneously that the remaining populations (i.e. susceptible plus infected plus infectious) tend asymptotically to zero.     

一类具有二次感染和接种的两病株流行病模型

本文考虑了一类具有二次感染和接种的两病株流行病模型，通过定义每一病株的基本再生数和侵入再生数，我们分析了非负平衡态的稳定性并获得了这样结论：对于较低的接种水平，病株一感染者处于支配地位而病株二感染者将从易感人群中消失，对于非常高的接种水平，疾病将均被消除。     

Fuzzy epidemic model for the transmission of worms in computer network

An e-epidemic SIRS (susceptible–infectious–recovered–susceptible) model for the fuzzy transmission of worms in computer network is formulated. We have analyzed the comparison between classical basic reproduction number and fuzzy basic reproduction number, that is, when both coincide and when both differ. The three cases of epidemic control strategies of worms in the computer network–low, medium, and, high–are analyzed, which may help us to understand the attacking behavior and also may lead to control of worms. Numerical methods are employed to solve and simulate the system of equations developed.     

Dynamic model of worm propagation in computer network

In this paper, an attempt has been made to mathematically formulate a compartmental susceptible – exposed – infectious – susceptible with vaccination (that is, anti-virus treatment) (SEIS-V) epidemic transmission model of worms in a computer network with natural death rate (which depends on the total number of nodes). The stability of the result is stated in terms of modified reproductive number R_v. We have derived an explicit formula for the modified reproductive number R_v, and have shown that the worm-free equilibrium, whose component of infective is zero, is globally asymptotically stable if R_v < 1, and unstable if R_v > 1. The contribution of vertical transmission to the modified reproductive number is also analyzed. Numerical methods are employed to solve and simulate the system of equations developed and interpretation of the model yields interesting revelations. Analysis of efficient antivirus software is also performed.     

Global analysis of a periodic epidemic model on cholera in presence of bacteriophage

We propose and analyze a recurrent epidemic model of cholera in the presence of bacteriophage. The model is extended by general periodic incidence functions for low‐infectious bacterium and high‐infectious bacterium, respectively. A general periodic shedding function for two infected class (phage‐positive and phage‐negative) and a generalized contact and intrinsic growth function for susceptible class are also considered. Under certain biological assumptions, we derive the basic reproduction number (R₀) in a periodic environment for the proposed model. We also observe the global stability of the disease‐free equilibrium, existence, permanence, and global stability of the positive endemic periodic solution of our proposed model. Finally, we verify our results with specific functional form. Copyright © 2016 John Wiley & Sons, Ltd.     

一类带有感染年龄SIR模型最优化免疫策略的存在性

对于一个免疫策略来讲,付出(单位时间内接种疫苗的数量)和效果(再生数的大小)是两个重要概念.在给定的费用下找到带有最小再生数的策略和在给定的再生数下找到最小费用的策略是两个最优问题.对一个确定的免疫策略来说,人群中的易感群体和染病群体会趋于相对稳定的状态.当一种疾病侵袭已免疫人群时,用带有感染年龄的SIR模型去描述这类疾病的传播更为准确.因此,本文研究了一类带有感染年龄的SIR模型,得到了最优化策略的存在性.     

Two time-delay dynamic model on the transmission of malicious signals in wireless sensor network

Deployed in a hostile environment, motes of a Wireless sensor network (WSN) could be easily compromised by the attackers because of several constraints such as limited processing capabilities, memory space, and limited battery life time etc. While transmitting the data to their neighbour motes within the network, motes are easily compromised due to resource constraints. Here time delay can play an efficient role to reduce the adversary effect on motes. In this paper, we propose an epidemic model SEIR (Susceptible–Exposed–Infectious–Recovered) with two time delays to describe the transmission dynamics of malicious signals in wireless sensor network. The first delay accounts for an exposed (latent) period while the second delay is for the temporary immunity period due to multiple worm outbreaks. The dynamical behaviour of worm-free equilibrium and endemic equilibrium is shown from the point of stability which switches under some threshold condition specified by the basic reproduction number. Our results show that the global properties of equilibria also depends on the threshold condition and that latent and temporary immunity period in a mote does not affect the stability, but they play a positive role to control malicious attack. Moreover, numerical simulations are given to support the theoretical analysis.     

Conficker蠕虫传播模型

"飞客"(conficker)蠕虫病毒是近期在全球爆发的以微软的windows操作系统为攻击目标的计算机蠕虫病毒,从爆发至今,感染数量巨大,形成了巨大规模的僵尸网络,对互联网安全形成了巨大的威胁.采用域名重定向技术监测conficker蠕虫的扩散传播,针对其查杀率低,传播周期长的特点,考虑地域、连通性等因素所导致的感染主机传播能力的差异,建立conficker蠕虫传播模型,最后通过真实的conficker蠕虫监测数据验证了模型的有效性.     

Pulse and constant control schemes for epidemic models with seasonality

Control schemes for infectious disease models with time-varying contact rate are analyzed. First, time-constant control schemes are introduced and studied. Specifically, a constant treatment scheme for the infected is applied to a SIR model with time-varying contact rate, which is modelled by a switching parameter. Two variations of this model are considered: one with waning immunity and one with progressive immunity. Easily verifiable conditions on the basic reproduction number of the infectious disease are established which ensure disease eradication under these constant control strategies. Pulse control schemes for epidemic models with time-varying contact rates are also studied in detail. Both pulse vaccination and pulse treatment models are applied to a SIR model with time-varying contact rate. Further, a vaccine failure model as well as a model with a reduced infective class are considered with pulse control schemes. Again, easily verifiable conditions on the basic reproduction number are developed which guarantee disease eradication. Some simulations are given to illustrate the threshold theorems developed.     

A propagation model with defensive measures for PLC-PC worms in industrial networks

Programmable logic controllers (PLCs) are important components of industrial control systems (ICSs), which are digital electronic devices with microprocessors and lack network security considerations. With the explosion of cyber-attacks on the ICS network, the concept of the worm known as PLC-PC worm that can spread between the Internet and ICS network has attracted a great deal of attention. In this paper, for the first time, we propose a propagation model to explore the spread behavior of PLC-PC worms across the PLC-PC coupled network. Theoretical analysis of the model shows the disease-free and endemic equilibriums of the network with defensive measures. And the stability of the model is examined by an epidemic threshold value. Several numerical and simulation experiments are presented to illustrate the analysis. Based on the results, some ideas for restraining the spread of PLC-PC worms or reducing the security threats of the ICS network are suggested.     

Analysis of an SVIC model with age-dependent infection and asymptomatic carriers

In this paper,we formulated an age-dependent model for the transmission dynamics of HBV with vaccination. The class of acutely infectious individuals,asymptomatic carrier of host population is stratified by age. Mathematically, we established that basic reproduction number can govern the global stability of equilibria. Biologically, we verify the impacts of the asymptomatic carriers and the effectiveness of vaccination on the disease transmission through numerical simulation. Our results indicated that the more number of infectious individuals specific to frequently progressed to asymptomatic carriers, the more likely the disease can be eradicated by continuous vaccination strategies.     

一类带有非线性传染率的SEIR传染病模型的全局分析

通过假设被传染的易感者一部分经过一段潜伏期后才具有传染性,而另一部分被感染的易感者直接成为传染者,建立了一类带有非线性传染率的SEIR传染病模型,得到了确定疾病是否成为地方病的基本再生数以及无病平衡点和地方病平衡点的全局稳定性.     

Cooperative differential game model based on trade-off between energy and delay for wireless sensor networks

A wireless sensor network (WSN) consists of a large number of unattended sensors with limited storage, battery power, computation, and communication capabilities, where battery power (or energy) is the most crucial resource for sensor nodes. The information sensed by sensors needs to be transmitted to sink quickly especially for the applications with delay restriction. However, it is difficult to achieve optimal energy efficiency and source-to-sink delay simultaneously. So it is very necessary to find a power control solution based tradeoff between energy and delay. In this paper, a cooperative differential game model is proposed, and a power solution is obtained which determines a fair distribution of the total cooperative cost among sources.     

On vaccination controls for the SEIR epidemic model

This paper presents a simple continuous-time linear vaccination-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) disease propagation model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes more difficult contacts among susceptible and infected. The control objective is the asymptotically tracking of the removed-by-immunity population to the total population while achieving simultaneously the remaining population (i.e. susceptible plus infected plus infectious) to asymptotically tend to zero.     

Impacts of TV and radio advertisements on the dynamics of an infectious disease: A modeling study

TV and radio advertisements are widely acknowledged as important interventions in raising issues of public health care and play promising role to control the infection through propagating awareness among the individuals. In this paper, a nonlinear susceptible‐infected‐susceptible (SIS) model is proposed and analyzed to see the impacts of TV and radio advertisements on the spread of influenza epidemic. In the model formulation, it is assumed that the susceptible individuals contract infection through the direct contact with infected individuals. The information regarding the protection against the disease is propagated via TV and radio advertisements, and their growth rates are assumed to be proportional to the fraction of infected individuals. However, the growth rate of TV advertisements decreases with the increase in number of aware individuals. The information broadcasted through TV and radio advertisements induces behavioral changes among the susceptible individuals, and they form an isolated aware class. The epidemiological feasible equilibria, their stability properties, and direction of bifurcation are discussed. The expression for modified basic reproduction number is obtained. The model analysis shows that the dissemination rate of awareness among susceptible individuals due to TV and radio advertisements and baseline number of TV and radio advertisements have potential to reduce the epidemic peak and, thus, control the spread of infection. Further, the analytical findings are well supported through numerical simulation.     

两类网络蠕虫的模型建立及动力学性态分析

网络蠕虫之间存在着复杂的关系,它们对蠕虫的传播和演化等动力学行为有着重要的影响,刻画这些关系有助于找到更好的控制和预防策略.本文建立了两类蠕虫(蠕虫I、蠕虫II)传播的数学模型,通过分析得到两个阈值条件R_1和R_2,当R_11和R_21,无病平衡点全局渐近稳定,意味着两类蠕虫最终均被清除;当R_21R1边界平衡点Q_1全局渐近稳定,也即蠕虫II灭绝,蠕虫I将持续存在;当R_11R2边界平衡点Q2全局渐近稳定,也即蠕虫I灭绝,蠕虫II将持续存在;当R_11和R21时,存在惟一正平衡点且全局渐近稳定,即两类蠕虫(蠕虫I与蠕虫II)同时持续存在.通过理论分析可以得到要控制蠕虫病毒可以通过控制参数来实现,进一步给出控制蠕虫病毒相对应的措施.最后通过数值模拟验证了理论分析结果.