Distributed modelling of propagation of computer viruses/worms by partial differential equations

Abstract

Two distributed Partial Differential Equations-based (PDES-based) mathematical models of propagation of computer viruses are derived for the first time. It is shown that experimental studies and inverse problems should be two main topics of further research of these models. The recently developed so-called globally convergent convexification numerical method of the author and Timonov is a good candidate to be a base of corresponding inverse algorithms.

†Dedicated to Professor Wei Lin on the occasion of his 70th birthday.

Keywords:

• Computer viruses
• Computer worms
• Distributed models
• Geographic locations
• Inverse problems
• Convexification numerical method
• Experiments
• 2000 Mathematics Subject Classifications: 06B35
• 35R20
• 35R25
• 68M14
• 94A13
• 94A40

Acknowledgment

The author is grateful to Doctors Boris Dobrov (Moscow State University), Igor Ternovskiy (Intelligent Optical Systems, Inc., Torrance, California), Alexander Tikhonravov (Moscow State University) and Yuliang Zheng (University of North Carolina at Charlotte) for the useful discussions.

Notes

Present address: The Information Security and Assurance Institute at The University of North Carolina at Charlotte, Canada (http://www.isai.uncc.edu); personal WEB page http://www.math.uncc.edu/people/info.php/mklibanv

†Dedicated to Professor Wei Lin on the occasion of his 70th birthday.

Additional information

Notes on contributors

Michael V. Klibanov

Present address: The Information Security and Assurance Institute at The University of North Carolina at Charlotte, Canada (http://www.isai.uncc.edu); personal WEB page http://www.math.uncc.edu/people/info.php/mklibanv