Hopf bifurcation and optimal control of a delayed malware propagation model on mobile wireless sensor networks

In present paper, a delayed SEIR model of malware propagation on mobile wireless sensor networks is formulated. Basic reproduction number of the model is calculated by employing the next generation matrix method and impact of the time delay due to incubation period of malware is discussed with the help of eigenvalue method. What is more, properties of the Hopf bifurcation are derived by using center manifold method. To minimize number of the infectious nodes and the cost related with detoxication, an optimal control strategy is presented by constructing a suitable Hamiltonian function. Numerical calculations are performed to justify the obtained theoretical findings.