cnaa043.pdf (1.45 MB)
PDE limits of stochastic SIS epidemics on networks
Version 2 2023-06-12, 09:34
Version 1 2023-06-09, 22:03
journal contribution
posted on 2023-06-12, 09:34 authored by Francesco Di Lauro, J-C Croix, Luc BerthouzeLuc Berthouze, Istvan KissStochastic epidemic models on networks are inherently high-dimensional and the resulting exact models are intractable numerically even for modest network sizes. Mean-field models provide an alternative but can only capture average quantities, thus offering little or no information about variability in the outcome of the exact process. In this article, we conjecture and numerically demonstrate that it is possible to construct partial differential equation (PDE)-limits of the exact stochastic susceptible-infected-susceptible epidemics on Regular, Erdos–Rényi, Barabási–Albert networks and lattices. To do this, we first approximate the exact stochastic process at population level by a Birth-and-Death process (BD) (with a state space of O(N) rather than O(2N)?) whose coefficients are determined numerically from Gillespie simulations of the exact epidemic on explicit networks. We numerically demonstrate that the coefficients of the resulting BD process are density-dependent, a crucial condition for the existence of a PDE limit. Extensive numerical tests for Regular, Erdos–Rényi, Barabási–Albert networks and lattices show excellent agreement between the outcome of simulations and the numerical solution of the Fokker–Planck equations. Apart from a significant reduction in dimensionality, the PDE also provides the means to derive the epidemic outbreak threshold linking network and disease dynamics parameters, albeit in an implicit way. Perhaps more importantly, it enables the formulation and numerical evaluation of likelihoods for epidemic and network inference as illustrated in a fully worked out example.
History
Publication status
- Published
File Version
- Published version
Journal
Journal of Complex NetworksISSN
2051-1310Publisher
Oxford University PressExternal DOI
Issue
4Volume
8Page range
1-21Pages
21.0Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2020-11-04First Open Access (FOA) Date
2021-01-18First Compliant Deposit (FCD) Date
2020-11-03Usage metrics
Categories
No categories selectedLicence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC