Computer virus propagation modelled as a stochastic differential game

Mario Lefebvre

Abstract


The propagation of a computer virus is expressed as a stochastic differential game based on the two-dimensional Kermack-McKendrick model for the spread of epidemics. One optimizer tries to maximize the expected value of a cost function with quadratic control costs, while the other one wants to minimize this expected value. A particular problem is solved explicitly by making use of the method of similarity solutions to obtain the solution to the partial differential equation satisfied by the value function, subject to the appropriate conditions.

Keywords


Game theory; first-passage time; Brownian motion; partial differential equations; method of similarity solutions.

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DOI: https://doi.org/10.1478/AAPP.981A3

Copyright (c) 2020 Mario Lefebvre

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