# American Institute of Mathematical Sciences

April  2020, 7(2): 163-174. doi: 10.3934/jdg.2020010

## A stochastic model for computer virus propagation

 Department of Mathematics and Industrial Engineering, Polytechnique Montréal, C.P. 6079, Succursale Centre-ville, Montréal, H3C 3A7, Canada

Received  February 2020 Revised  March 2020 Published  April 2020

A three-dimensional continuous-time stochastic model based on the classic Kermack-McKendrick model for the spread of epidemics is proposed for the propagation of a computer virus. Moreover, control variables are introduced into the model. We look for the controls that either minimize or maximize the expected time it takes to clean the infected computers, or to protect them from the virus. Using dynamic programming, the equations satisfied by the value functions are derived. Particular problems are solved explicitly.

Citation: Mario Lefebvre. A stochastic model for computer virus propagation. Journal of Dynamics & Games, 2020, 7 (2) : 163-174. doi: 10.3934/jdg.2020010
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##### References:
Function $X(t)$ in the interval $[0, 80]$ when $k_1 = k_3 =$ 0.1 and $k_2 =$ 0.001
Function $Y(t)$ in the interval $[0, 80]$ when $k_1 = k_3 =$ 0.1 and $k_2 =$ 0.001
Function $Z(t)$ in the interval $[0, 80]$ when $k_1 = k_3 =$ 0.1 and $k_2 =$ 0.001
Function $Y(t)$ in the interval $[0, 2]$ when $k_i =$ 0.1 for $i = 1, 2, 3$
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