2011/10/17 by István Z. Kiss, Peter Šimon, Kiss, Istvan Z. +1
Mathematics · Medicine · Physics and Astronomy · #COVID-19 epidemiological studies #Complex Network Analysis Techniques #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1110.3723
openalex publication_date 2011/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, research that focuses on the rigorous understanding of the relation\nbetween simulation and/or exact models on graphs and approximate counterparts\nhas gained lots of momentum. This includes revisiting the performance of\nclassic pairwise models with closures at the level of pairs and/or triples as\nwell as effective-degree-type models and those based on the probability\ngenerating function formalism. In this paper, for a fully connected graph and\nthe simple SIS (susceptible-infected-susceptible) epidemic model, a novel\nclosure is introduced. This is done via using the equations for the moments of\nthe distribution describing the number of infecteds at all times combined with\nthe empirical observations that this is well described/approximated by a\nbinomial distribution with time dependent parameters. This assumption allows us\nto express higher order moments in terms of lower order ones and this leads to\na new closure. The significant feature of the new closure is that the\ndifference of the exact system, given by the Kolmogorov equations, from the\nsolution of the newly defined approximate system is of order 1/N2. This is\nin contrast with the \O(1/N) difference corresponding to the\napproximate system obtained via the classic triple closure.\n