Exact and approximate moment closures for non-Markovian network epidemics

Understand

Moment-closure techniques are commonly used to generate low-dimensional deterministic models to approximate the average dynamics of stochastic systems on networks.

• The quality of such closures is usually difficult to asses and the relationship between model assumptions and closure accuracy are often difficult, if not impossible, to quantify.
• Here we carefully examine some commonly used moment closures, in particular a new one based on the concept of maximum entropy, for approximating the spread of epidemics on networks by reconstructing the probability distributions over triplets based on those over pairs.
• We consider various models (SI, SIR, SEIR and Reed-Frost-type) under Markovian and non-Markovian assumption characterising the latent and infectious periods.