Dimension reduction in higher-order contagious phenomena

Subrata Ghosh, Pitambar Khanra, Prosenjit Kundu, Peng Ji, Dibakar Ghosh, Chittaranjan Hens

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We investigate epidemic spreading in a deterministic susceptible-infected-susceptible model on uncorrelated heterogeneous networks with higher-order interactions. We provide a recipe for the construction of one-dimensional reduced model (resilience function) of the N -dimensional susceptible-infected-susceptible dynamics in the presence of higher-order interactions. Utilizing this reduction process, we are able to capture the microscopic and macroscopic behavior of infectious networks. We find that the microscopic state of nodes (fraction of stable healthy individual of each node) inversely scales with their degree, and it becomes diminished due to the presence of higher-order interactions. In this case, we analytically obtain that the macroscopic state of the system (fraction of infectious or healthy population) undergoes abrupt transition. Additionally, we quantify the network’s resilience, i.e., how the topological changes affect the stable infected population. Finally, we provide an alternative framework of dimension reduction based on the spectral analysis of the network, which can identify the critical onset of the disease in the presence or absence of higher-order interactions. Both reduction methods can be extended for a large class of dynamical models.

Original languageEnglish
Article number053117
Issue number5
StatePublished - 1 May 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2023 Author(s).


P.J. was supported by National Science and Technology Innovation 2030 Major Program (Nos. 2021ZD0204500 and 2021ZD0204504), the National Natural Science Foundation of China (NNSFC) (No. 62076071), and Shanghai Municipal Science and Technology Major Project (No. 2018SHZDZX01). C.H. was supported by INSPIRE-Faculty grant (Code: IFA17-PH193).

FundersFunder number
National Science and Technology Innovation 2030 Major Program2021ZD0204500, 2021ZD0204504
National Natural Science Foundation of China62076071
Science and Technology Commission of Shanghai Municipality2018SHZDZX01


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