Modeling of Computer Virus Propagation with Fuzzy Parameters

Typically,a computer has infectivity as soon as it is infected.It is a reality that no antivirus programming can identify and eliminate all kinds of viruses,suggesting that infections would persevere on the Internet.To understand the dynamics of the virus propagation in a better way,a computer virus spread model with fuzzy parameters is presented in this work.It is assumed that all infected computers do not have the same contribution to the virus transmission process and each computer has a different degree of infectivity,which depends on the quantity of virus.Considering this,the parametersβandγbeing functions of the computer virus load,are considered fuzzy numbers.Using fuzzy theory helps us understand the spread of computer viruses more realistically as these parameters have fixed values in classical models.The essential features of the model,like reproduction number and equilibrium analysis,are discussed in fuzzy senses.Moreover,with fuzziness,two numerical methods,the forward Euler technique,and a nonstandard finite difference(NSFD)scheme,respectively,are developed and analyzed.In the evidence of the numerical simulations,the proposed NSFD method preserves the main features of the dynamic system.It can be considered a reliable tool to predict such types of solutions.

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.

Animal models for the study of hepatitis B virus infection

Even with an effective vaccine, an estimated 240 million people are chronically infected with hepatitis B virus （HBV） worldwide. Current antiviral therapies, including interferon and nucleot（s）ide analogues, rarely cure chronic hepatitis B. Animal models are very crucial for understanding the pathogenesis of chronic hepatitis B and developing new therapeutic drugs or strategies. HBV can only infect humans and chimpanzees, with the use of chimpanzees in HBV research strongly restricted. Thus, most advances in HBV research have been gained using mouse models with HBV replication or infection or models with HBV-related hepadnaviral infection. This review summarizes the animal models currently available for the study of HBV infection.

Prognostic values of the integrated model incorporating the volume of metastatic regional cervical lymph node and pretreatment serum Epstein-Barr virus DNA copy number in predicting distant metastasis in patients with N1 nasopharyngeal carcinoma

Background: According to the 7 th edition of the American Joint Committee on Cancer(AJCC) staging system, over50% of patients with nasopharyngeal carcinoma(NPC) have N1 disease at initial diagnosis. However, patients with N1 NPC are relatively under-researched, and the metastasis risk of this group is not well-stratified. This study aimed to evaluate the prognostic values of gross tumor volume of metastatic regional lymph node(GTVnd) and pretreatment serum copy number of Epstein-Barr virus(EBV) DNA in predicting distant metastasis of patients with N1 NPC, and to develop an integrated prognostic model that incorporates GTVnd and EBV DNA copy number for this group of patients.Methods: The medical records of 787 newly diagnosed patients with nonmetastatic, histologically proven N1 NPC who were treated at Sun Yat-sen University Cancer Center between November 2009 and February 2012 were analyzed. Computed tomography-derived GTVnd was measured using the summation-of-area technique. Blood samples were collected before treatment to quantify plasma EBV DNA. The receiver operating characteristic(ROC) curve analysis was used to evaluate the cut-off point for GTVnd, and the area under the ROC curve was used to assess the predicted validity of GTVnd. The survival rates were assessed by Kaplan-Meier analysis, and the survival curves were compared using a log-rank test. Multivariate analysis was conducted using the Cox proportional hazard regression model.Results: The 5-year distant metastasis-free survival(DMFS) rates for patients with GTVnd > 18.9 vs.≤ 18.9 mL were82.2% vs. 93.2%(P < 0.001), and for patients with EBV DNA copy number > 4000 vs. < 4000 copies/mL were 83.5% vs.93.9%(P < 0.001). After adjusting for GTVnd, EBV DNA copy number, and T category in the Cox regression model, both GTVnd > 18.9 mL and EBV DNA copy number > 4000 copies/mL were significantly associated with poor prognosis(both P < 0.05). According to combination of GTVnd and EBV DNA copy number, all patients were divided into low-,moderate-, and high-risk groups, with the 5-year DMFS rates of 96.1,87.4, and 73.8%, respectively(P < 0.001). Multivariate analysis confirmed the prognostic value of this model for distant metastatic risk stratification(hazard ratio [HR],4.17; 95% confidence interval [CI] 2.34-7.59; P < 0.001).Conclusions: GTVnd and serum EBV DNA copy number are independent prognostic factors for predicting distant metastasis in NPC patients with N1 disease. The prognostic model incorporating GTVnd and EBV DNA copy number may improve metastatic risk stratification for this group of patients.

Modified model for end-stage liver disease improves shortterm prognosis of hepatitis B virus-related acute-on-chronic liver failure

AIM To investigate whether the short-term prognosis of hepatitis B virus(HBV)-related acute-on-chronic liver failure(ACLF) could be improved by using a modified model for end-stage liver disease(MELD) including serum lactate.METHODS This clinical study was conducted at the First Affiliated Hospital, Fujian Medicine University, China. From 2009 to 2015, 236 patients diagnosed with HBV-related ACLF at our center were recruited for this 3-month followup study. Demographic data and serum lactate levels were collected from the patients. The MELD scores with or without serum lactate levels from survival and nonsurvival groups were recorded and compared.RESULTS Two hundred and thirty-six patients with HBV-ACLF were divided into two groups: survival group(S) andnon-survival group(NS). Compared with the NS group, the patients in survival the S group had a significantly lower level of serum lactate(3.11 ± 1.98 vs 4.67 ± 2.43, t = 5.43, P < 0.001) and MELD score(23.33 ± 5.42 vs 30.37 ± 6.58, t = 9.01, P = 0.023). Furthermore, serum lactate level was positively correlated with MELD score(r = 0.315, P < 0.001). Therefore, a modified MELD including serum lactate was developed by logistic regression analysis(0.314 × lactate + 0.172 × MELD-5.923). In predicting 3-month mortality using the MELD-LAC model, the patients from the S group had significantly lower baseline scores(-0.930 ± 1.34) when compared with those from the NS group(0.771 ± 1.32, t = 9.735, P < 0.001). The area under the receiver operating characteristic curve(AUROC) was 0.859 calculated by using the MELD-LAC model, which was significantly higher than that calculated by using the lactate level(0.790) or MELD alone(0.818). When the cutoff value was set at-0.4741, the sensitivity, specificity, positive predictive value and negative predictive value for predicting short-term mortality were 91.5%, 80.10%, 94.34% and 74.62%, respectively. When the MELD-LAC scores at baseline level were set at-0.5561 and 0.6879, the corresponding mortality rates within three months were 75% and 90%, respectively.CONCLUSION The short-term prognosis of HBV-related ACLF was improved by using a modified MELD including serum lactate from the present 6-year clinical study.

HBsAg/HBsAb Double Positive Hepatitis B Virus Infection Model in vitro and in vivo

The pathogenesis of HBsAg （＋）/HBsAb （＋） double positive hepatitis B virus infection was investigated by simulating HBsAg/HBsAb coexistence in vitro and establishing HBsAg/HBsAb double positive model in vivo. Eukaryotic expression plasmids PCI-SY, PCI-adw, PCI-adr, PCI-ayw, which expressed S gene product of different serotypes, were constructed and transfected into HepG2 cells. Recombinant proteins were purified from the transfected cells. At the same time, HBsAg mouse antiserum was obtained by immunizing mice with PCI-SY plasmid. HBsAg/HBsAb coexistence was simulated using these antigens and antiserum. Furthermore, the expression plasmids expressing different serotypes of S gene product including PCI-adw, PCI-adr, and PCI-ayw were injected into mice via tail vein. HBsAg and HBsAb in mice sera were tested at the first and 7th day respectively after antigen plasmids injection. Both in vitro simulation and in vivo animal models demonstrated that HBsAg antigen and HBsAb of the same serotypes Could not coexist, but HBsAg antigen and HBsAb of different serotype could coexist. HBsAg/HBsAb double positive hepatitis B virus infection could be due to infection of viruses of different serotypes.

Establishment and primary application of a mouse model with hepatitis B virus replication

AIM： To establish a rapid and convenient animal model with hepatitis B virus （HBV） replication.METHODS： A naked DNA solution of HBV-replicationcompetent plasmid was transferred to BALB/C mice via the tail vein, using a hydrodynamic in vivo transfection procedure. After injection, these mice were sacrificed on d 1, 3, 4, 5, 7 and 10. HBV DNA replication intermediates in the liver were analyzed by Southern blot hybridization. The expression of hepatitis B core antigen （HBcAg） and hepatitis B surface antigen （HBsAg） in the liver was checked by immunohistochemistry. Serum HBsAg and hepatitis B e antigen （HBeAg） was detected by enzyme- linked immunosorbent assay （ELISA）. Inhibition of HBV replication was compared in HBV replication model mice treated intraperitoneally with polyinosinic-polytidylin acid （polyIC） or phosphate-buffered saline （PBS）.RESULTS： After hydrodynamic in vivo transfection, HBV DNA replication intermediates in the mouse liver were detectable on d 1 and abundant on d 3 and 4, the levels were slightly decreased and remained relatively stable between d 5 and 7, and were almost undetectable on d 10. The expression patterns of HBcAg and HBsAg were similar to that of HBV replication intermediate DNA, except that they reached a peak on d 1 after injection. No obvious differences in HBV DNA replication intermediates were observed in the left, right and middle lobes of the liver. After treatment with polyIC, the level of HBV intermediate DNA in the liver was lower than that in the control mice injected with PBS.CONCLUSION： A rapid and convenient mouse model with a high level of HBV replication was developed and used to investigate the inhibitory effect of polyIC on HBV replication, which provides a useful tool for future functional studies of the HBV genome.

Hepatocellular carcinoma mouse models:Hepatitis B virusassociatedhepatocarcinogenesis and haploinsufficienttumor suppressor genes

The multifactorial and multistage pathogenesis of hepatocellular carcinoma(HCC)has fascinated a wide spectrum of scientists for decades.While a number of major risk factors have been identified,their mechanistic roles in hepatocarcinogenesis still need to be elucidated.Many tumor suppressor genes(TSGs)have been identified as being involved in HCC.These TSGs can be classified into two groups depending on the situation with respect to allelic mutation/loss in the tumors:the recessive TSGs with two required mutated alleles and the haploinsufficient TSGs with one required mutated allele.Hepatitis B virus(HBV)is one of the most important risk factors associated with HCC.Although mice cannot be infected with HBV due to the narrow host range of HBV and the lack of a proper receptor,one advantage of mouse models for HBV/HCC research is the numerous and powerfulgenetic tools that help investigate the phenotypic effects of viral proteins and allow the dissection of the dose-dependent action of TSGs.Here,we mainly focus on the application of mouse models in relation to HBV-associated HCC and on TSGs that act either in a recessive or in a haploinsufficient manner.Discoveries obtained using mouse models will have a great impact on HCC translational medicine.

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.

Globulin-platelet model predicts minimal fibrosis and cirrhosis in chronic hepatitis B virus infected patients

AIM： To establish a simple model consisting of the rou- tine laboratory variables to predict both minimal fibrosis and cirrhosis in chronic hepatitis B virus （HBV）-infected patients. METHODS： We retrospectively investigated 114 chron- ic HBV-infected patients who underwent liver biopsy in two different hospitals. Thirteen parameters were analyzed by step-wise regression analysis and correla- tion analysis. A new fibrosis index [globulin/platelet （GP） model] was developed, including globulin （GLOB） and platelet count （PLT）. GP model = GLOB （g/mL） x 100/PLT （x 109/L）. We evaluated the receiver operating characteristics analysis used to predict minimal fibrosis and compared six other available models. RESULTS： Thirteen clinical biochemical and hemato- logical variables [sex, age, PLT, alanine aminotransfer- ase, aspartate aminotransferase （AST）, albumin, GLOB, total bilirubin （T.bil）, direct bilirubin （D.bil）, glutamyl-transferase, alkaline phosphatase, HBV DNA and pro- thrombin time （PT）] were analyzed according to three stages of liver fibrosis （F0-F1, F2-F3 and F4）. Bivariate Spearman＇s rank correlation analysis showed that six variables, including age, PLT, T.bil, D.bil, GLOB and PT, were correlated with the three fibrosis stages （FS）. Cor- relation coefficients were 0.23, -0.412, 0.208, 0.220, 0.314 and 0.212; and P value was 0.014, 〈 0.001, 0.026, 0.018, 0.001 and 0.024, respectively. Univariate analysis revealed that only PLT and GLOB were signifi- cantly different in the three FS （PLT： F = 11.772, P 〈 0.001; GLOB： F = 6.612, P = 0.002）. Step-wise multiple regression analysis showed that PLT and GLOB were also independently correlated with FS （R2 = 0.237）. By Spearman＇s rank correlation analysis, GP model was significantly correlated with the three FS （r = 0.466, P 〈 0.001）. The median values in F0-F1, F2-F3 and F4 were 1.461, 1.720 and 2.634. Compared with the six available models （fibrosis index, AST-platelet ratio, FIB-4, fibrosis-cirrhosis index and age-AST model and age-PLT ratio）, GP model showed a highest correlation coefficient. The sensitivity and positive predictive value at a cutoff value 〈 1.68 for predicting minimal fibrosis F0-F1 were 72.4% and 71.2%, respectively. The speci- ficity and negative predictive value at a cutoff value 〈 2.53 for the prediction of cirrhosis were 84.5% and 96.7%. The area under the curve （AUC） of GP model for predicting minimal fibrosis and cirrhosis was 0.762 [95% confidence interval （CI）： 0.676-0.848] and 0.781 （95% CI： 0.638-0.924）. Although the differences were not statistically significant between GP model and the other models （P all 〉 0.05）, the AUC of GP model was the largest among the seven models. CONCLUSION： By establishing a simple model using available laboratory variables, chronic HBV-infected patients with minimal fibrosis and cirrhosis can be di- agnosed accurately, and the clinical application of this model may reduce the need for liver biopsy in HBV- infected patients.

Diagnostic non-invasive model of large risky esophageal varices in cirrhotic hepatitis C virus patients

AIM To build a diagnostic non-invasive model for screening of large varices in cirrhotic hepatitis C virus(HCV) patients. METHODS This study was conducted on 124 post-HCV cirrhotic patients presenting to the clinics of the Endemic Medicine Department at Mansoura University Hospital for evaluation before HCV antiviral therapy: 78 were Child A and 46 were Child B(score ≤ 8). Inclusion criteria for patients enrolled in this study was presence of cirrhotic HCV(diagnosed by either biopsy or fulfillment of clinical basis). Exclusion criteria consisted of patients with other etiologies of liver cirrhosis, e.g., hepatitis B virus and patients with high MELD score on transplant list. All patients were subjected to full medical record, full basic investigations, endoscopy, and computed tomography(CT), and then divided into groups with no varices, small varices, or large risky varices. In addition, values of Fibrosis-4 score(FIB-4), aminotransferase-to-platelet ratio index(APRI), and platelet count/splenic diameter ratio(PC/SD) were also calculated.RESULTS Detection of large varies is a multi-factorial process, affected by many variables. Choosing binary logistic regression, dependent factors were either large or small varices while independent factors included CT variables such coronary vein diameter, portal vein(PV) diameter, lieno-renal shunt and other laboratory noninvasive variables namely FIB-4, APRI, and platelet count/splenic diameter. Receiver operating characteristic(ROC) curve was plotted to determine the accuracy of non-invasive parameters for predicting the presence of large esophageal varices and the area under the ROC curve for each one of these parameters was obtained. A model was established and the best model for prediction of large risky esophageal varices used both PC/SD and PV diameter(75% accuracy), while the logistic model equation was shown to be(PV diameter ×-0.256) plus(PC/SD ×-0.006) plus(8.155). Values nearing 2 or more denote large varices.CONCLUSION This model equation has 86.9% sensitivity and 57.1% specificity, and would be of clinical applicability with 75% accuracy.

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.

THE PERIODIC SOLUTIONS FOR TIME DEPENDENT AGE-STRUCTURED POPULATION MODELS

In this paper, the existence of periodic solutions for a time dependent age-structured population model is studied. The averaged net reproductive number is introduced as the main parameter to determine the dynamical behaviors of the model. The existence of a global parameterized branch of periodic solutions of the model is obtained by using the contracting mapping theorem in a periodic and continuous function space. The global stability of the trivial equilibrium is studied and a very practical stability criteria for the model is obtained. The dynamics of the linear time-periodic model is similar to that of the linear model.

Application of hepatitis B virus replication mouse model

AIM:To evaluate the value of the hepatitis B virus(HBV) replication mouse model with regard to several aspects of the study of HBV biology.METHODS:To evaluate the HBV replication mouse model in detecting the efficacy of anti-HBV agents,the interferon inducer polyinosinic-polytidylin acid(polyIC) and nucleotide analogues adefovir and entecavir were administered to mice injected with wild type pHBV4.1,and the inhibiting effect of these agents on HBV DNA replication was evaluated.To identify the model's value in a replication ability study of HBV drug-resistant mutants and a HBx-minus mutant,telbivudine resistance mutants(rtM204I,ayw subtype),adefovir resistance mutants(rtA181V + rtN236T,ayw subtype) and HBxminus mutants were injected respectively,and their corresponding HBV DNA replication intermediates in mouse liver were assessed.RESULTS:Compared with the wild type HBV replication mouse model without antiviral agent treatment,the HBV DNA replication intermediates of the polyICtreated group were decreased 1-fold;while in the entecavir-and adefovir-treated groups,the levels of HBV DNA replication intermediates were inhibited 13.6-fold and 1.4-fold,respectively.For the mouse models injected with telbivudine resistance mutant,adefovir resistance mutant and HBx-minus mutant,HBV DNA replication intermediates could still be detected,but the levels of HBV DNA replication intermediates of these mutants decreased 4.5-fold,5.6-fold and 2.9-fold respectively,compared with the mouse model with wild type HBV plasmid.CONCLUSION:The HBV replication mouse model we established was a useful and convenient tool to detect the efficacy of antiviral agents and to study the replication ability of HBV mutants in vivo.

Global Stability of SEIQRS Computer Virus Propagation Model with Non-Linear Incidence Function

In this paper, we present an SEIQRS epidemic model with non-linear incidence function. The proposed model exhibits two equilibrium points, the virus free equilibrium and viral equilibrium. The model stability is connected with the basic reproduction number R0. If R0 R0 > 1, then the model is locally and globally stable at viral equilibrium point. Numerical methods are used for supporting the analytical work.

Simulation modelling of potato virus Y spread in relation to initial inoculum and vector activity

Potato virus Y(PVY)is a non-persistent virus that is transmitted by many aphid species and causes significant damage to potato production.We constructed a spatially-explicit model simulating PVY spread in a potato field and used it to investigate possible effects of transmission efficiency,initial inoculum levels,vector behavior,vector abundance,and timing of peak vector activity on PVY incidence at the end of a simulated growing season.Lower PVY incidence in planted seed resulted in lower virus infection at the end of the season.However,when populations of efficient PVY vectors were high,significant PVY spread occurred even when initial virus inoculum was low.Non-colonizing aphids were more important for PVY spread compared to colonizing aphids,particularly at high densities.An early-season peak in the numbers of noncolonizing aphids resulted in the highest number of infected plants in the end of the season,while mid-and late-season peaks caused relatively little virus spread.Our results highlight the importance of integrating different techniques to prevent the number of PVY-infected plants from exceeding economically acceptable levels instead of trying to control aphids within potato fields.Such management plans should be implemented very early in a growing season.

Hepatitis B virus infection modeling using multi-cellular organoids derived from human induced pluripotent stem cells

Chronic infection with hepatitis B virus(HBV)remains a global health concern despite the availability of vaccines.To date,the development of effective treatments has been severely hampered by the lack of reliable,reproducible,and scalable in vitro modeling systems that precisely recapitulate the virus life cycle and represent virus-host interactions.With the progressive understanding of liver organogenesis mechanisms,the development of human induced pluripotent stem cell(iPSC)-derived hepatic sources and stromal cellular compositions provides novel strategies for personalized modeling and treatment of liver disease.Further,advancements in three-dimensional culture of self-organized liver-like organoids considerably promote in vitro modeling of intact human liver tissue,in terms of both hepatic function and other physiological characteristics.Combined with our experiences in the investigation of HBV infections using liver organoids,we have summarized the advances in modeling reported thus far and discussed the limitations and ongoing challenges in the application of liver organoids,particularly those with multi-cellular components derived from human iPSCs.This review provides general guidelines for establishing clinical-grade iPSC-derived multi-cellular organoids in modeling personalized hepatitis virus infection and other liver diseases,as well as drug testing and transplantation therapy.

Hopf Bifurcation of a Nonresident Computer Virus Model with Delay

In this paper, a delayed nonresident computer virus model with graded infection rate is considered in which the following assumption is imposed: latent computers have lower infection ability than infectious computers. With the aid of the bifurcation theory, sufficient conditions for stability of the infected equilibrium of the model and existence of the Hopf bifurcation are established. In particular, explicit formulae which determine direction and stability of the Hopf bifurcation are derived by means of the normal form theory and the center manifold reduction for functional differential equations. Finally, a numerical example is given in order to show the feasibility of the obtained theoretical findings.

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.

Hepatitis C Virus Experimental Model Systems and Antiviral drug Research

An estimated 130 million people worldwide are chronically infected with hepatitis C virus (HCV) making it a leading cause of liver disease worldwide. Because the currently available therapy of pegylated interferon-alpha and ribavirin is only effective in a subset of patients, the development of new HCV antivirals is a healthcare imperative. This review discusses the experimental models available for HCV antiviral drug research, recent advances in HCV antiviral drug development, as well as active research being pursued to facilitate development of new HCV-specific therapeutics.