Advertisement

A Literature Review on Dynamic Modeling and Epidemic Dynamics

  • Biswarup SamantaEmail author
Conference paper

Abstract

Malicious codes differ according to the way they attack computer systems and malicious actions they perform. The three classes of computer malware—Virus, Worm and Trojan—can also have hundreds of variants or several slightly modified versions. The main question we are concerned with is “Is that the behavior of infections in the digital world similar to the behavior of infections in the biological world?” Between biological diseases and computer worms, some of the most intriguing similarities lie in the ways in which they infect their hosts and bypass the defences designed to stop them. Transmission of malicious objects in computer network is epidemic in nature. Epidemiology is the study of incidence and distribution of diseases in various populations. Epidemiology has played a very crucial role over the years in planning, implementing, and evaluating programs for control of epidemic outbreaks. Moreover, the combination of epidemic dynamics, epidemiologic theory, biostatistics, and computer simulations will significantly contribute to further improvement of our knowledge of transmission patterns of epidemics, development of epidemiology, and more effective methods in controlling infectious diseases. In this paper, an attempt has been made to present the literature review on dynamic modeling and epidemic dynamics to apply the principles of epidemiological modeling to study and understand the infecting nature, transmission mode, and damaging behavior of worms in computer networks.

Keywords

Cyber attack Computer network Dynamic model Epidemic modeling Malware Stability 

References

  1. 1.
    Tianhan Gao, Quanqi Wang, Xiaojie Wang, and Xiaoxue Gong, “An Anonymous Access Authentication Scheme Based on Proxy Ring Signature for CPS-WMNs”, Mobile Information Systems, Volume 2017 (2017), Article ID 4078521, 11 pages, 2017.Google Scholar
  2. 2.
    Lianwen Wang, Xingan Zhang, Zhijun Liu, “An SEIR Epidemic Model with Relapse and General Nonlinear Incidence Rate with Application to Media Impact”, Qualitative Theory of Dynamical Systems, 2017.Google Scholar
  3. 3.
    Jinliang Wang, Xianning Liu, Toshikazu Kuniya, “Global stability for multi-group SIR and SEIR epidemic models with age-dependent susceptibility”, Discrete and Continuous Dynamical Systems—Series B (DCDS-B), American Institute of Mathematical Science, Pages: 2795–2812, Volume 22, Issue 7, September 2017,  https://doi.org/10.3934/dcdsb.2017151, 2017.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Vyacheslav Kharchenko, and Oleg Illiashenko, “Diversity for security: case assessment for FPGA-based safety-critical systems”, 20th International Conference on Circuits, Systems, Communications and Computers (CSCC 2016), Volume 76, 2016, MATEC Web Conf., 02051, 2016.CrossRefGoogle Scholar
  5. 5.
    Elisa Canzani, Stefan Pickl, Cyber Epidemics: Modelling Attacker-Defender Dynamics in Critical Infrastructure Systems”, Advances in Human Factors in Cyber security pp. 377–389, 2016.Google Scholar
  6. 6.
    Kuldeep Kaur, Dr. Ashutosh Pathak, Parminder Kaur, Karamjeet Kaur, “E-Commerce Privacy and Security System”, Int. Journal of Engineering Research and Applications, ISSN: 2248–9622, Vol. 5, Issue 5, (Part-6) May 2015, pp. 63–73, 2015.Google Scholar
  7. 7.
    Eike Möhlmann, Oliver Theel, “Breaking Dense Structures: Proving Stability of Densely Structured Hybrid Systems”, Electronic Proceedings in Theoretical Computer Science, 2015; 184(Proc. ESSS 2015):49–63  https://doi.org/10.4204/eptcs.184.4, 2015.CrossRefGoogle Scholar
  8. 8.
    Liping Feng et el.; “Modeling and Stability Analysis of Worm Propagation in Wireless Sensor Network”, Mathematical Problems in Engineering (Hindawi Publishing Corporation), Volume 2015 (2015), Article ID 129598, 8 pages 2015; 2015  https://doi.org/10.1155/2015/129598 1024-123X (Print); 1563-5147 (Online), 2015.MathSciNetzbMATHGoogle Scholar
  9. 9.
    Jinhua Ma et el., “Analysis of Two-Worm Interaction Model in Heterogeneous”, M2M Network”, “information”, www.mdpi.com/journal/information, ISSN 2078-2489 2015, 6, 613-632;  https://doi.org/10.3390/info6040613, 2015.CrossRefGoogle Scholar
  10. 10.
    Canzani et al., “Insights from Modeling Epidemics of Infectious Diseases – A Literature Review”, Proceedings of the ISCRAM 2015 Conference—Kristiansand, 2015.Google Scholar
  11. 11.
    Meng Wang et al., “Spread and Control of Mobile Benign Worm Based on Two-Stage Repairing Mechanism”, Journal of Applied Mathematics (Hindawi Publishing Corporation) Volume 2014 (2014), Article ID 746803, 14 pages, http://dx.doi.org/10.1155/2014/746803 2014;2014,  https://doi.org/10.1155/2014/746803 1110-757X (Print); 1687-0042 (Online)”, 2014.Google Scholar
  12. 12.
    Elisa Canzani, Hans-Christian Heldt, Stephan Meyer and Ulrike Lechner, “Towards an Understanding of the IT Security Information Ecosystem”, Autonomous Systems 2014, Proceedings of the 7th GI Conference. VDI Reihe, 2014.Google Scholar
  13. 13.
    XingboLiu, Lijuan Yang, “Stability analysis of an SEIQV epidemic model with saturated incidence rate”, Nonlinear Analysis: Real World Applications, 2671–2679, 2012.Google Scholar
  14. 14.
    Yajuan Zhang, Xinyang Deng, Daijun Wei, Yong Deng, “Assessment of E-Commerce security using AHP and evidential reasoning”, Expert Systems with Applications 39 (2012) 3611–3623 Elsevier, 2012.CrossRefGoogle Scholar
  15. 15.
    “Ryan E Hohimer and Frank L Greitzer, “Modeling Human Behavior to Anticipate Insider Attacks”, Journal of Strategic Security, ISSN: 1944-0464 (Print); 1944-0472 (Online) 2011;4(2):25–48, 2011.CrossRefGoogle Scholar
  16. 16.
    Bimal Kumar Mishra, Samir Kumar Pandey, “Fuzzy epidemic model for the transmission of worms in computer network Nonlinear Analysis: Real World Applications 11, 5, 4335–4341, Oct, 2010.Google Scholar
  17. 17.
    Huang, Gang, “Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate”, Bulletin of Mathematical Biology. 72(5), p. 1192–1207, 01-07-2010.MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Jose R. C., Piqueira and Felipe Barbosa Cesar, “Dynamical Models for Computer Viruses Propagation”, Mathematical Problems in Engineering, Volume 2008, Article ID 940526, 11 pages,  https://doi.org/10.1155/2008/940526, 2008.zbMATHGoogle Scholar
  19. 19.
    Jose R.C. Piqueira, Adolfo A. de Vasconcelos, Carlos E.C.J. Gabriel, Vanessa O. Araujo, “Dynamic models for computer viruses”, computers & security, 27 (2008) 355–359, 2008.CrossRefGoogle Scholar
  20. 20.
    Fangwei Wang, Yunkai Zhang, Jianfeng Ma, “Modeling and Analyzing Passive worms over Unstructured Peer-to-Peer Networks”, Transactions of Tianjin University, 14(1):66–72, 2008.CrossRefGoogle Scholar
  21. 21.
    Li-Ming Cai, Xue-Zhi Li, “Analysis of a SEIV Epidemic Model with a Nonlinear Incidence Rate Applied Mathematical Modelling”, 7-Jan-2008.Google Scholar
  22. 22.
    Zhong Zhao, Lansun Chen, Xinyu Song, “Impulsive vaccination of SEIR epidemic model with time delay and nonlinear incidence rate”, Mathematics and Computers in Simulation, Elsevier, Volume 79, Issue 3, 1 December 2008, Pages 500–510, 2008.Google Scholar
  23. 23.
    Richard J. Boys and Philip R. Giles, “Bayesian inference for stochastic epidemic models with time-inhomogeneous removal rates”, Mathematical Biology, J. Math. Biol. (2007) 55:223–247, 15-March-2007.MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Bimal Kumar Mishra, Dinesh Saini, “Mathematical models on computer viruses”, Applied Mathematics and Computation, Elsevier, 187, 2, 929–936, 2007, 15-April-2007.Google Scholar
  25. 25.
    Bimal Kumar Mishra, Dinesh Kumar Saini, “SEIRS epidemic model with delay for transmission of malicious objects in computer network”, Applied Mathematics and Computation, Elsevier, 188, 1476–1482, 2007.Google Scholar
  26. 26.
    Bimal Kumar Mishra, Navnit Jha, “Fixed period of temporary immunity after run of anti-malicious software on computer nodes Applied Mathematics and Computation, Elsevier, 190, 1207–1212, 2007, 15-July-2007.Google Scholar
  27. 27.
    B.K. Mishra et al., “Differential susceptibility-infectiousness epidemic model of propagation of malicious agents with self-replication in a computer network”, Applied Mathematics and Computation, xxx (2007) xxx–xxx, 2007.Google Scholar
  28. 28.
    Bimal Kumar Mishra, “Generality of the final size formula for infected nodes due to the attack of malicious agents in a computer network, “Applied Mathematics and Computation, xxx (2007) xxx–xxx, 2007.Google Scholar
  29. 29.
    Hisashi Inaba, “Age-structured homogeneous epidemic systems with application to the MSEIR epidemic model Mathematical Biology J. Math. Biol. (2007) 54:101–146, 2007.MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Tailei Zhang, Zhidong Teng, “Global behavior and permanence of SIRS epidemic model with time delay”, Nonlinear Analysis: Real World Applications, ELSEVIER, 14 March 2007.Google Scholar
  31. 31.
    E. Shim, Z. Feng, M. Martcheva, C. Castillo-Chavez, “ An age-structured epidemic model of rotavirus with vaccination”, Mathematical Biology, J. Math. Biol. (2006) 53:719–746, 2006.MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    Arunabha Mukhopadhyay, Samir Chatterjee, Debashis Saha, Ambuj Mahanti, Samir K Sadhukhan, “e-Risk Management with Insurance: A framework using Copula aided Bayesian Belief Networks “, Proceedings of the 39th Hawaii International Conference on System Sciences—2006.Google Scholar
  33. 33.
    Junling Ma, David J.D. Earn, “Generality of the Final Size Formula for an Epidemic of a Newly Invading Infectious Disease, “Bulletin of Mathematical Biology (2006), 68: 679–702, 2006.MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    M.E. Alexander, S.M. Moghadas, P. Rohani, A.R. Summers, “ Modelling the effect of a booster vaccination on disease epidemiology”, Mathematical Biology, J. Math. Biol. 52, 290–306 (2006), 10-November-2005.MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    J. Lopez Gondar and R. Cipolatti, “A mathematical model for virus infection in a system of interacting computers”, Computational and Applied Mathematics, Vol. 22, N. 2, pp. 209–231, 2003.Google Scholar
  36. 36.
    Paul K. Harmer, Paul D. Williams, Gregg H. Gunsch, and Gary B. Lamont, An Artificial Immune System Architecture for Computer Security Applications”, IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 6, NO. 3, JUNE 2002.Google Scholar
  37. 37.
    Wang Wendia, Ma Zhiena, “Global dynamics of an epidemic model with time delay”, Nonlinear Analysis: Real World Applications, 3(2002)365–373, 2002.MathSciNetzbMATHCrossRefGoogle Scholar
  38. 38.
    Herbert Hethcote, Ma Zhien b, Liao Shengbing, “Effects of quarantine in six endemic models for infectious diseases”, Mathematical Biosciences 180 (2002) 141–160, 26-March-2002.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Computer Science & Information Technology, Amity Institute of Information TechnologyAmity UniversityRanchiIndia

Personalised recommendations