Dynamical analysis and optimal control for a malware propagation model in an information network

摘要: Abstract With the rapid development of network information technology, networks security has become a very critical issue in our work and daily life. This paper investigates nonlinear malware propagation model wireless sensor (WSNs) based on SIR epidemic model. Sufficient conditions for local stability positive equilibrium point existence Hopf bifurcation are obtained by analyzing associated characteristic equation. Moreover, formulas determining properties bifurcating periodic oscillations derived applying normal form method center manifold theorem. Furthermore, with help Maximum Principle Pontryagin, we design an optimal control strategy previous to extend region reduce density infected nodes WSNs. Finally, conduct extensive simulations evaluate proposed Numerical evidence shows that dynamic characteristics WSNs closely related immune period recovered node rate constant becoming susceptible again after recovered. Besides, obtain effectively improves performance networks.