Epidemic dynamics on higher-dimensional small world networks

Haiying Wang; Jack Murdoch Moore; Michael Small; Jun Wang; Huijie Yang; Changgui Gu

doi:10.1016/j.amc.2021.126911

Epidemic dynamics on higher-dimensional small world networks

Appl Math Comput. 2022 May 15:421:126911. doi: 10.1016/j.amc.2021.126911. Epub 2022 Jan 15.

Authors

Haiying Wang¹, Jack Murdoch Moore², Michael Small^{3

4}, Jun Wang⁵, Huijie Yang¹, Changgui Gu¹

Affiliations

¹ Business School, University of Shanghai for Science and Technology, 334 Jungong Road, Shanghai, 200093, China.
² School of Physics Science and Engineering, Tongji University, 1239 Siping Road, Shanghai, 200092, Western Australia, China.
³ Complex Systems Group, Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, 6009, Australia.
⁴ Mineral Resources, CSIRO, 26 Dick Perry Ave, Kensington, 6151, Western Australia, Australia.
⁵ School of Economics and Management, Beihang University, 37 Xueyuan Road, Beijing, 100191, China.

Abstract

Dimension governs dynamical processes on networks. The social and technological networks which we encounter in everyday life span a wide range of dimensions, but studies of spreading on finite-dimensional networks are usually restricted to one or two dimensions. To facilitate investigation of the impact of dimension on spreading processes, we define a flexible higher-dimensional small world network model and characterize the dependence of its structural properties on dimension. Subsequently, we derive mean field, pair approximation, intertwined continuous Markov chain and probabilistic discrete Markov chain models of a COVID-19-inspired susceptible-exposed-infected-removed (SEIR) epidemic process with quarantine and isolation strategies, and for each model identify the basic reproduction number $R_{0}$ , which determines whether an introduced infinitesimal level of infection in an initially susceptible population will shrink or grow. We apply these four continuous state models, together with discrete state Monte Carlo simulations, to analyse how spreading varies with model parameters. Both network properties and the outcome of Monte Carlo simulations vary substantially with dimension or rewiring rate, but predictions of continuous state models change only slightly. A different trend appears for epidemic model parameters: as these vary, the outcomes of Monte Carlo change less than those of continuous state methods. Furthermore, under a wide range of conditions, the four continuous state approximations present similar deviations from the outcome of Monte Carlo simulations. This bias is usually least when using the pair approximation model, varies only slightly with network size, and decreases with dimension or rewiring rate. Finally, we characterize the discrepancies between Monte Carlo and continuous state models by simultaneously considering network efficiency and network size.

Keywords: Epidemic spreading; Model error; Network dimension; Small world model; Spreading dynamics.