Mathematical analysis of the effectiveness of control strategies to prevent the autorun virus transmission propagation

摘要

In this work, a deterministic model for autorun computer virus propagation is presented and discussed. Two new control parameters; vaccination rate and perfect recovery rate are introduced to validate the existence of computer virus infection via external devices likewise USBs. The model is comprehensively analyzed with and without control parameter for verification of proposed model and strategy. The recovery population of the infected computers has been divided into perfectly recovered with probability ‘p’ and partially recovered with probability ‘1 − p’. The results show that as vaccination rate is increased reproductive number and number of infected computers decreased. Since reproductive number does not depend upon p, change in the value of p does not affect the basic reproductive number. However, as value of p is increased, a reduction in steady state of infected computer is observed. Local and global stability analysis of virus-free equilibrium has been investigated through basic reproductive number. The endemic equilibrium has also been determined under certain conditions.We introduce two control functions which are defined to present successful effort of repairing computers and fixing USBs and propose an optimal control problem with two control functions. The solution to the proposed problem is derived through forward-backward method. The necessary conditions for optimal control have been developed using the Pontryagin's Maximum Principle. Different combination of computer and USBs numbers have been utilized for effective simulation results and comprehensive analysis.