On modeling the crowding and psychological effects in network-virus prevalence with nonlinear epidemic model

The fast point-to-group information sharing process within an enterprise network also exposes information to more severe virus attacks. On the other hand, a relative large number of virus attacks may result in psychological effects of inhibition for the network end-users. In this paper, a nonlinear force of infection function for e-SEIR model is presented to study the crowding and psychological effects in network virus prevalence. By carrying out a global analysis of the stability of both the virus-free and endemic equilibrium, this work reveals how the crowding and psychological effects have impacts on network virus propagation process. Furthermore, analysis and simulation results show some managerial insights that are helpful for the practice of antivirus in information sharing networks.

[1]  Zhidong Teng,et al.  Persistence and extinction of disease in non-autonomous SIRS epidemic models with disease-induced mortality , 2008 .

[2]  R. May,et al.  Infection dynamics on scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Giuseppe Serazzi,et al.  Computer Virus Propagation Models , 2003, MASCOTS Tutorials.

[4]  M. Hui,et al.  Perceived Control and the Effects of Crowding and Consumer Choice on the Service Experience , 1991 .

[5]  Yasuhiro Takeuchi,et al.  Global asymptotic stability of an SIR epidemic model with distributed time delay , 2001 .

[6]  Hua Yuan,et al.  Network virus-epidemic model with the point-to-group information propagation , 2008, Appl. Math. Comput..

[7]  Jeffrey O. Kephart,et al.  Measuring and modeling computer virus prevalence , 1993, Proceedings 1993 IEEE Computer Society Symposium on Research in Security and Privacy.

[8]  Shigui Ruan,et al.  Global analysis of an epidemic model with nonmonotone incidence rate , 2006, Mathematical Biosciences.

[9]  S. Valins,et al.  The Role of Group Phenomena in the Experience of Crowding , 1975 .

[10]  N. Madar,et al.  Immunization and epidemic dynamics in complex networks , 2004 .

[11]  R. May,et al.  How Viruses Spread Among Computers and People , 2001, Science.

[12]  J Wakeling,et al.  Intelligent systems in the context of surrounding environment. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  M. Markus,et al.  Oscillations and turbulence induced by an activating agent in an active medium. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  G. Serio,et al.  A generalization of the Kermack-McKendrick deterministic epidemic model☆ , 1978 .

[15]  Donald F. Towsley,et al.  Modeling malware spreading dynamics , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[16]  Joshua Fogel,et al.  Internet social network communities: Risk taking, trust, and privacy concerns , 2009, Comput. Hum. Behav..

[17]  Aadil Lahrouz,et al.  Complete global stability for an SIRS epidemic model with generalized non-linear incidence and vaccination , 2012, Appl. Math. Comput..

[18]  Salvatore Rionero,et al.  On the Lyapunov stability for SIRS epidemic models with general nonlinear incidence rate , 2010, Appl. Math. Comput..

[19]  J. Sime.  Crowd psychology and engineering , 1995 .

[20]  Dinesh Kumar Saini,et al.  SEIRS epidemic model with delay for transmission of malicious objects in computer network , 2007, Appl. Math. Comput..

[21]  R. Robinson,et al.  An Introduction to Dynamical Systems: Continuous and Discrete , 2004 .

[22]  Shigui Ruan,et al.  Dynamical behavior of an epidemic model with a nonlinear incidence rate , 2003 .

[23]  Xia Wang,et al.  Pulse vaccination on SEIR epidemic model with nonlinear incidence rate , 2009, Appl. Math. Comput..

[24]  S. Levin,et al.  Dynamical behavior of epidemiological models with nonlinear incidence rates , 1987, Journal of mathematical biology.

[25]  Alessandro Vespignani,et al.  Epidemic dynamics and endemic states in complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Yukihiko Nakata,et al.  Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates , 2012, Appl. Math. Comput..

[27]  Ruoyan Sun,et al.  Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates , 2011, Appl. Math. Comput..

[28]  Y. Iwasa,et al.  Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models , 1986, Journal of Mathematical Biology.

[29]  Kathleen M. Carley,et al.  The impact of countermeasure propagation on the prevalence of computer viruses , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[30]  David Rakhmilʹevich Merkin,et al.  Introduction to the Theory of Stability , 1996 .

[31]  L. Ho,et al.  The impact of community psychological responses on outbreak control for severe acute respiratory syndrome in Hong Kong , 2003, Journal of epidemiology and community health.