2015/05/13 by Lorenzo Pellis, Thomas House, Pellis, Lorenzo +3
Physics and Astronomy · Psychology · #05C21 #92D30 #Complex Network Analysis Techniques #FOS: Biological sciences #FOS: Mathematics #Mental Health Research Topics #Opinion Dynamics and Social Influence #Populations and Evolution (q-bio.PE) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1505.03354
openalex publication_date 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Moment-closure techniques are commonly used to generate low-dimensional\ndeterministic models to approximate the average dynamics of stochastic systems\non networks. The quality of such closures is usually difficult to asses and the\nrelationship between model assumptions and closure accuracy are often\ndifficult, if not impossible, to quantify. Here we carefully examine some\ncommonly used moment closures, in particular a new one based on the concept of\nmaximum entropy, for approximating the spread of epidemics on networks by\nreconstructing the probability distributions over triplets based on those over\npairs. We consider various models (SI, SIR, SEIR and Reed-Frost-type) under\nMarkovian and non-Markovian assumption characterising the latent and infectious\nperiods. We initially study two special networks, namely the open triplet and\nclosed triangle, for which we can obtain analytical results. We then explore\nnumerically the exactness of moment closures for a wide range of larger motifs,\nthus gaining understanding of the factors that introduce errors in the\napproximations, in particular the presence of a random duration of the\ninfectious period and the presence of overlapping triangles in a network. We\nalso derive a simpler and more intuitive proof than previously available\nconcerning the known result that pair-based moment closure is exact for the\nMarkovian SIR model on tree-like networks under pure initial conditions. We\nalso extend such a result to all infectious models, Markovian and\nnon-Markovian, in which susceptibles escape infection independently from each\ninfected neighbour and for which infectives cannot regain susceptible status,\nprovided the network is tree-like and initial conditions are pure. This works\nrepresent a valuable step in deepening understanding of the assumptions behind\nmoment closure approximations and for putting them on a more rigorous\nmathematical footing.\n