Hopf Bifurcation of Nonresident Computer Virus Model with Age Structure and Two Delays Effects

This paper constructed and studied a nonresident computer virus model with age structure and two delays effects. The non-negativity and boundedness of the solution of the model have been discussed, and then gave the basic regeneration number, and obtained the conditions for the existence and the stability of the virus-free equilibrium and the computer virus equilibrium. Theoretical analysis shows the conditions under which the model undergoes Hopf bifurcation in three different cases. The numerical examples are provided to demonstrate the theoretical results.

ON GLOBAL STABILITY OF A NONRESIDENT COMPUTER VIRUS MODEL

In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent literature.

A Stochastic Numerical Analysis for Computer Virus Model with Vertical Transmission Over the Internet

We are presenting the numerical analysis for stochastic SLBR model of computer virus over the internet in this manuscript.We are going to present the results of stochastic and deterministic computer virus model.Outcomes of the threshold number C∗hold in stochastic computer virus model.If C∗<1 then in such a condition virus controlled in the computer population while C∗>1 shows virus spread in the computer population.Unfortunately,stochastic numerical techniques fail to cope with large step sizes of time.The suggested structure of the stochastic non-standard finite difference scheme(SNSFD)maintains all diverse characteristics such as dynamical consistency,bounded-ness and positivity as well-defined by Mickens.On this basis,we can suggest a collection of plans for eradicating viruses spreading across the internet effectively.

Spatio-Temporal Dynamics and Structure Preserving Algorithm for Computer Virus Model

The present work is related to the numerical investigation of the spatio-temporal susceptible-latent-breaking out-recovered(SLBR)epidemic model.It describes the computer virus dynamics with vertical transmission via the internet.In these types of dynamics models,the absolute values of the state variables are the fundamental requirement that must be fulfilled by the numerical design.By taking into account this key property,the positivity preserving algorithm is designed to solve the underlying SLBR system.Since,the state variables associated with the phenomenon,represent the computer nodes,so they must take in absolute.Moreover,the continuous system(SLBR)acquires two steady states i.e.,the virus-free state and the virus existence state.The stability of the numerical design,at the equilibrium points,portrays an exceptional aspect about the propagation of the virus.The designed discretization algorithm sustains the stability of both the steady states.The computer simulations also endorse that the proposed discretization algorithm retains all the traits of the continuous SLBR model with spatial content.The stability and consistency of the proposed algorithm are verified,mathematically.All the facts are also ascertained by numerical simulations.

Dynamical study of varicella-zoster virus model in sense of Mittag-Leffler kernel

The primary varicella-zoster virus(VzV)infection that causes chickenpox(also known as varicella),spreads quickly among people and,in severe circumstances,can cause to fever and encephalitis.In this paper,the Mittag-Leffler fractional operator is used to examine the mathematical representation of the vzV.Five fractional-order differential equations are created in terms of the disease's dynamical analysis such as S:Susceptible,V:Vaccinated,E:Exposed,I:Infectious and R:Recovered.We derive the existence criterion,positive solution,Hyers-Ulam stability,and boundedness of results in order to examine the suggested fractional-order model's wellposedness.Finally,some numerical examples for the VzV model of various fractional orders are shown with the aid of the generalized Adams-Bashforth-Moulton approach to show the viability of the obtained results.

Global asymptotic stability in a pseudorabies virus model with age structure

Pseudorabies is a highly contagious disease caused by pseudorabies virus(PRV)or suid herpesvirus 1(SuHV1),causing significant economic losses to the swine industry in countries where the disease exists.In this paper,we formulate an age structure model of pseudorabies virus that takes into account disease-related mortality and vertical trans-mission.We find a threshold to determine the stability and existence of the disease.We show that there is always a globally asymptotically stable boundary equilibrium if and only if R_(02)<1+q,which means that the disease always exists in piglets and will die out in adult pigs.When R_(02)>1+q,the boundary equilibrium is unstable and there exists a unique disease-endemic equilibrium,which is globally asymptotically stable.We give detailed proofs of our theoretical results and numerical examples.Brief concluding re-marks are also provided.

DUCK HEPATITIS B VIRUS MODEL FOR SCREENING OF ANTIVIRAL AGENTS FROM MEDICINAL HERBS

The effects of the extracts of 20 Chinese medicinal herbs and an antiviral drug foscarnet on duck hepatitis B virus (DHBV) endogenous DNA polymerase (DNAp) activity were compared. The extracts of P. urinaria showed a dose-dependent inhibition on DHBV DNAp. And those of other herbs showed little inhibition effect. Primary duck hepatocyte (PDH) cultures were used for evaluating effects of the extract of P. urinaria, foscarnet and acyclovir (ACV) on DHBV, and all the drugs or the extracts showed inhibition of DHBV DNA replication. Furthermore, in vivo trials were carried out. Peking ducks infected with LJ-76 strain of DHBV were treated with the extract of P. urinaria or ACV and compared with placebo treated control ducks. The treatment results in the loss or reduction of circulating viral DHBV DNA and DHBsAg.

Numerical Simulations for Stochastic Computer Virus Propagation Model

We are presenting the numerical simulations for the stochastic computer virus propagation model in this manuscript.We are comparing the solutions of stochastic and deterministic computer virus models.Outcomes of a threshold number R0 hold in stochastic computer virus model.If R_(0)<1 then in such a condition virus controlled in the computer population while R_(0)>1 shows virus rapidly spread in the computer population.Unfortunately,stochastic numerical techniques fail to cope with large step sizes of time.The suggested structure of the stochastic non-standard finite difference technique can never violate the dynamical properties.On this basis,we can suggest a collection of strategies for removing virus’s propagation in the computer population.

System Recovery-Aware Virus Propagation Model and Its Steady-State Analysis

Network structures and human behaviors are considered as two important factors in virus defense currently. However, due to ignorance of network security, normal users usually take simple activities, such as reinstalling computer system, or using the computer recovery system to clear virus. How system recovery influences virus spreading is not taken into consideration currently. In this paper, a new virus propagation model considering the system recovery is proposed first, and then in its steady-state analysis, the virus propagation steady time and steady states are deduced. Experiment results show that models considering system recovery can effectively restrain virus propagation. Furthermore, algorithm with system recovery in BA scale-free network is proposed. Simulation result turns out that target immunization strategy with system recovery works better than traditional ones in BA network.

A Theoretical Investigation of the SARS-CoV-2Model via Fractional Order Epidemiological Model

We propose a theoretical study investigating the spread of the novel coronavirus(COVID-19)reported inWuhan City of China in 2019.We develop a mathematical model based on the novel corona virus’s characteristics and then use fractional calculus to fractionalize it.Various fractional order epidemicmodels have been formulated and analyzed using a number of iterative and numerical approacheswhile the complications arise due to singular kernel.We use the well-known Caputo-Fabrizio operator for the purposes of fictionalization because this operator is based on the non-singular kernel.Moreover,to analyze the existence and uniqueness,we will use the well-known fixed point theory.We also prove that the considered model has positive and bounded solutions.We also draw some numerical simulations to verify the theoretical work via graphical representations.We believe that the proposed epidemic model will be helpful for health officials to take some positive steps to control contagious diseases.

计算机网络病毒传播模型

根据生物流行病毒的数学模型,对计算机网络病毒的传播模型进行了研究。根据计算机蠕虫病毒最常见的传播特征,把经典的传染病模型划分为三部分。最后采用仿真试验的方法,验证了模型的基本合理性。

邮件病毒传播的迭代模型

邮件病毒的传播不同于流行病的传播,如不同的邮件用户的杀毒率、打开附件的概率以及发送邮件的频率是不同的。为群组定义了一个通信频率邻接矩阵,并借助该矩阵建立了一个可以递推的离散模型。从理论上证明了邮件病毒在群组中消亡的充要条件为群组的谱半径小于1,为实际工作中降低邮件病毒的感染率提供了理论依据。对模型进行了模拟实验,实验数据证明了模型的有效性。

柯萨奇病毒B_3致病模型的建立

目的 :建立柯萨奇病毒 (CV)B3 的实验动物模型 ,以期为抗病毒药物筛选提供工具。方法 :雄性BALB/C鼠腹腔注射CVB3 后 ,观察小鼠发病症状 ,并在不同时间处死小鼠 ,取小鼠心、脾、肝、肾等组织进行病毒分离、病毒核酸检测、心肌组织病理检查。结果 :感染后第 3d小鼠即出现症状 ,第 5d在小鼠的心脏、脾脏、肾脏均可分离出感染性病毒 ,其滴度分别为 :10 4 .7,10 3.3 ,10 3.2 TCID50 / 0 .1ml,同时小鼠心、脾、肾、等组织及血清中CVB RNA检测为阳性 ,心肌组织出现典型炎性改变。结论 :雄性BALB/C鼠感染CVB3

一种新的计算机病毒模型的稳定性分析

目前,网络中计算机病毒的威胁引起了对计算机病毒传播建模和分析的研究热潮.为了更好地反映实际情况,该文基于现有的SIR模式,提出一个新的计算机病毒传播模型.该模型主要考虑了多种状态下的预先免疫措施.同时,利用特征方程的特征值分布和线性微分系统对该模型在平衡点处的稳定性进行了讨论.理论分析和数值模拟表明,这一模型的动力学行为依赖于基本再生数,该模型可以帮助我们更好地了解和预测计算机病毒在网络中的传播行为.

P2P文件共享网中病毒传播建模

鉴于病毒在P2P文件共享网中的巨大危害性,对P2P文件共享网和P2P病毒的传播特点进行了深入的分析,并在此基础上提出了P2P病毒的传播模型。为了考查模型中各参数对病毒传播的影响,使用了专门的数字分析软件进行了大规模仿真实验。不同参数对病毒传播有着不同影响这一仿真实验结果表明,可以通过控制那些影响大的参数来抑制病毒传播。

一类具有病毒变异的SEIR传染病模型的稳定性

考虑疾病在传播过程中病毒产生变异的影响,建立了具有病毒变异情况的SEIR传染病模型,借助Liapunov函数,分析了无病平衡点和地方病平衡点的全局稳定性.并通过数值模拟分析了模型中的参数对疾病传播的影响.

网络病毒传播模型中的两个问题

现有的网络病毒分析模型大都依据流行病模型建立,这些模型并不能反映现代网络环境下病毒的传播规律,故有一些问题不能得到很好的解决。文章在新模型的基础上重点讨论其中的两个最为突出的问题:网络病毒的门限值问题和单节点在病毒传播中的不同作用。通过对新模型解的分析得出结论:如果病毒的传播紧密地依赖网络的连接率,而它们的治愈率又相对较小,那么这类病毒的门限值是不存在的。基于该结论文章对长期以来困扰网络病毒传播模型的两个公开的问题给出了合理的解释。文章将电脑的连接率作为节点的一个最基本的特征,从而指出具有不同连接率的节点,它们在病毒传播中的作用也不相同,文章还首次给出了它们的估算公式,从而也为刚刚起步的网络免疫系统中节点的选择提供了有力的理论支持。文章最后进行了模拟实验,实验的结果基本验证了分析结论。

具有分级感染率的4仓室计算机病毒传播模型

根据计算机病毒的性质,针对常驻病毒所经历2个重要阶段的特点:在潜伏阶段病毒因未加载入内存而不具有感染力;在活跃阶段,病毒驻留于内存并伺机感染目标文件,划分了2个新的具有不同感染率的计算机仓室,建立了一种新的具有分级感染率的常驻病毒传播模型,并应用稳定性理论和仿真实验研究了该模型的动力性质,研究结果表明所提模型的动力行为完全由基本再生率决定,如果基本再生率小于等于一则无毒平衡点的全局稳定,如果基本再生率大于一则有毒平衡点局部稳定,并根据仿真实验猜测其全局稳定,通过对基本再生率进行系统参数敏感性分析,提出了有效阻止病毒网络传播的控制策略。

移动P2P网络中的病毒传播建模

对移动P2P网络的体系结构和关键协议进行了深入研究分析;在此基础上,根据病毒传播特点并利用流行病学理论,提出了移动P2P网络中病毒的传播数学模型。基于提出的病毒传播模型,使用专门的数字分析软件进行了大量仿真实验,实验主要考查了各P2P参数对病毒传播的影响。实验分析表明,通过控制固定节点的下载率和恢复率这两个影响病毒传播最关键的参数能有效遏制移动P2P病毒传播。