Virus dynamics of a distributed attack on a targeted network: Effect of firewall and optimal control

Abstract An attempt has been made to understand the virus dynamics of a distributed attack in a targeted network adopting firewall security coefficient and treatment rate. A mathematical model is proposed with two sub-frameworks of attacking and targeted class, which further reduces to non-dimensional model system and investigated along with the analysis of virus propagation control measures. Existence and stability of equilibrium points have been discussed. Using central manifold theory, it has been observed that as R0 passes through unity, transcritical bifurcation occurs. In this work, the firewall security is taken as a media coverage factor and detected that it helps to diminish the virus propagation to some extent. The concept of optimal control theory is introduced as an another measure for controlling the virus proliferation. Numerical experiments are accomplished to justify the analytical findings. Finally, a sensitivity analysis is performed that offer insights into the criticality of parameters in determining the virus dispersion in networks. The inclusion of firewall security eradicates the malicious node propagation in a computer network by lowering the infection level although doesn’t affect the value of R0.