On modeling epidemics in networks using linear time-invariant dynamics

Can linear time-invariant dynamics be used to model the epidemics on the networks? This paper shows that this is indeed possible. Given the topology of a network in terms of an undirected graph we form a state space representation of a linear system to study the behavior of this network and to compare calculations against simulations of epidemics. In particular, an epidemic modeling approach based on systems theory usable even for lager networks is introduced and its potential is demonstrated. Also, methods to form the state variables of a corresponding LTI system are proposed. Presented results show that this approach is highly effective to evaluate epidemic dynamics analytically in every discrete time step omitting agent-based simulations. Moreover, it is shown that it can be used for network analysis and network optimization against virus spreading. This opens the door for using systems theory tools in network analysis.