State estimation in computer virus epidemic dynamical systems using hybrid extended Kalman filter

This paper considers the problem of state estimations in virus/ worm epidemic dynamic system with time-dependent parameters in arbitrary sparse networks by using continuous-discrete Extended Kalman Filter (so-called Hybrid Extended Kalman Filter [1]). The virus spreading dynamic model has unmeasurable states and with highly nonlinearities which makes the state estimation complicated and not straightforward. Because of the continuous-time dynamic and discrete-time measurement, in this paper, a Hybrid Extended Kalman Filter to estimate states has been introduced. To move one step further, the homogeneity assumption in Kephart and White [2], [3] has been removed and a model that accommodate realistic scenarios where the model parameters may change with respect to time has been introduced. Simulations are taken to demonstrate, via a small sparse network of constant number of nodes, that the Hybrid Kalman Filter still gives a fast and accurate estimation. Of course, there are subtle issues that must be tackled before the problem can be fully addressed.