Effect of Delay in SMS Worm Propagation in Mobile Network with Saturated Incidence Rate

The mobile network has become the social standing pulverized for heaps of novel worms, including the SMS, Bluetooth-built worms and Wi-Fi based worms. Particularly, SMS worms have drawn significant attention owing to their enormous threats to the mobile network. In this article, we proposed and analysed the SMS worm propagation, a delayed SAIDR model (Susceptible-Affected-Infected-Suspended-Recovered) with a saturated incidence rate. A novel express in the SMS model, the suspended state, which gets some margin to affected node to infected node in mobile network. Furthermore, the influence of time delay during the charging behaviour of the affected state nodes needs to be considered. Hopf bifurcation is studied by discussing the time delay that is chosen as the bifurcation parameter. Direction and stability of the Hopf bifurcation are derived using normal form theory and centre manifold theorem. At last, a few numerical simulations are presented to check the analytical outcomes.