|
Abstract:
|
The last twenty years have seen an increasing interest in the use of network-based stochastic models to model the spread of epidemics. In particular, there has been great interest in the Configuration Model due to its flexibility and mathematical tractability. A key point of interest is studying the sets of Ordinary Differential Equations (ODEs) that emerge as the large population limit of the stochastic model. However, derivation of these sets of differential equations is made more complicated by the presence of the network. For the case of a simple SIR model with Markovian infection and recovery processes the limiting set of ODEs was initially derived heuristically by Volz and Miller (2008,2011). Formal proofs of correctness for this limit were later given by Decreusefond et al. (2012) and Janson et al. (2014). We present an alternate approach that is considerably more simple and relies only on first principle properties of the stochastic processes under study. We further present the first set of estimation methods for the rates of infection and recovery from standard epidemic data and prove essential properties of these estimators which follow from the Law of Large Numbers.
|
