Optimal Internet Worm Treatment Strategy Based on the Two‐Factor Model

The security threat posed by worms has steadily increased in recent years. This paper discusses the application of the optimal and sub-optimal Internet worm control via Pontryagin's maximum principle. To this end, a control variable representing the optimal treatment strategy for infectious hosts is introduced into the two-factor worm model. The numerical optimal control laws are implemented by the multiple shooting method and the sub-optimal solution is computed using genetic algorithms. Simulation results demonstrate the effectiveness of the proposed optimal and sub-optimal strategies. It also provides a theoretical interpretation of the practical experience that the maximum implementation of treatment in the early stage is critically important in controlling outbreaks of Internet worms. Furthermore, our results show that the proposed sub-optimal control can lead to performance close to the optimal control, but with much simpler strategies for long periods of time in practical use.

[1]  G. Thompson,et al.  Optimal control theory : applications to management science , 1984 .

[2]  Yang Wang,et al.  Modeling the effects of timing parameters on virus propagation , 2003, WORM '03.

[3]  Yun Zou,et al.  Optimal and sub-optimal quarantine and isolation control in SARS epidemics , 2007, Mathematical and Computer Modelling.

[4]  H. J. Pesch.  Real-time computation of feedback controls for constrained optimal control problems. Part 2: A correction method based on multiple shooting , 1989 .

[5]  Lawrence Davis,et al.  Genetic Algorithms and Simulated Annealing , 1987 .

[6]  J. Stoer,et al.  Introduction to Numerical Analysis , 2002 .

[7]  Eugene H. Spafford,et al.  The Internet Worm Incident , 1989, ESEC.

[8]  Ram Dantu,et al.  Dynamic control of worm propagation , 2004, International Conference on Information Technology: Coding and Computing, 2004. Proceedings. ITCC 2004..

[9]  Sudarshan Dhall,et al.  Optimal Control of Treatment Costs for Internet Worm , 2004 .

[10]  Takashi Yoneyama,et al.  Optimal and sub‐optimal control in Dengue epidemics , 2001 .

[11]  O. Patrick Kreidl,et al.  Feedback control applied to survivability: a host-based autonomic defense system , 2004, IEEE Transactions on Reliability.

[12]  Yun Zou,et al.  Optimal Quarantine and Isolation Control in SEQIJR SARS Model , 2006, 2006 9th International Conference on Control, Automation, Robotics and Vision.

[13]  Jeffrey O. Kephart,et al.  Directed-graph epidemiological models of computer viruses , 1991, Proceedings. 1991 IEEE Computer Society Symposium on Research in Security and Privacy.

[14]  Donald F. Towsley,et al.  Code red worm propagation modeling and analysis , 2002, CCS '02.

[15]  David Moore,et al.  Code-Red: a case study on the spread and victims of an internet worm , 2002, IMW '02.

[16]  Christos Faloutsos,et al.  Epidemic spreading in real networks: an eigenvalue viewpoint , 2003, 22nd International Symposium on Reliable Distributed Systems, 2003. Proceedings..

[17]  D. Kirschner,et al.  Optimal control of the chemotherapy of HIV , 1997, Journal of mathematical biology.

[18]  Steve R. White,et al.  Computers and epidemiology , 1993, IEEE Spectrum.

[19]  Xiefei Yan,et al.  Optimal quarantine and isolation strategies in epidemics control , 2007 .

[20]  Kevin A. Kwiat,et al.  Modeling the spread of active worms , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[21]  Sudarshan K. Dhall,et al.  Measurement and analysis of worm propagation on Internet network topology , 2004, Proceedings. 13th International Conference on Computer Communications and Networks (IEEE Cat. No.04EX969).

[22]  Sridhar Radhakrishnan,et al.  Cost Optimization in SIS Model of Worm Infection , 2006 .

[23]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[24]  R. E. Rink,et al.  Optimum control of epidemics , 1973 .

[25]  Suzanne Lenhart,et al.  Optimal control of treatments in a two-strain tuberculosis model , 2002 .

[26]  Michael D. Intriligator,et al.  Mathematical optimization and economic theory , 1971 .

[27]  Daniel Massey,et al.  Observation and analysis of BGP behavior under stress , 2002, IMW '02.

[28]  Donald F. Towsley,et al.  Worm propagation modeling and analysis under dynamic quarantine defense , 2003, WORM '03.

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

[30]  Sihan Qing,et al.  A survey and trends on Internet worms , 2005, Comput. Secur..