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Graph dynamical systems (GDS) model dynamic processes on a (static) graph.Stochastic GDS has been used for network-based epidemics models such as thecontact process and the reversible contact process. In this paper, we considerstochastic GDS that are also continuous-time Markov processes (CTMP), whosetransition rates are linear functions of some dynamics parameters $\theta$ ofinterest (i.e., healing, exogeneous, and endogeneous infection rates). Our goalis to estimate $\theta$ from a single, finite-time, continuously observedtrajectory of the CTMP. Parameter estimation of CTMP is challenging when thestate space is large; for GDS, the number of Markov states are\emph{exponential} in the number of nodes of the graph. We showed that holdingclasses (i.e., Markov states with the same holding time distribution) giveefficient partitions of the state space of GDS. We derived an upperbound on thenumber of holding classes for the contact process, which is polynomial in thenumber of nodes. We utilized holding classes to solve a smaller system oflinear equations to find $\theta$. Experimental results show that findingreasonable results can be achieved even for short trajectories, particularlyfor the contact process. In fact, trajectory length does not significantlyaffect estimation error.

Estimating Parameters of Large CTMP from Single Trajectory with Application to Stochastic Network Epidemics Models