2021/12/26 by Rohan Nuckchady, Nuckchady, Rohan
Biochemistry, Genetics and Molecular Biology · Mathematics · #Applied mathematics #COVID-19 epidemiological studies #Class (philosophy) #Combinatorics (math.CO) #Computer science #Differential equation #Discrete mathematics #FOS: Biological sciences #FOS: Mathematics #Hypergraph #Mathematical analysis #Mathematics #Notation #Physics #Population #Population model #Populations and Evolution (q-bio.PE) #Probability (math.PR) #Stochastic differential equation #Work (physics) #math.CO #math.PR #q-bio.PE
paper · pdf · doi:10.48550/arxiv.2112.15427
published in arXiv (Cornell University) (Cornell University)
arxiv created 2021/12/26 · openalex publication_date 2021/12/26 · arxiv updated 2022/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This report is based on the work in (1). We first review definitions and notation developped there and provide derivations for the exact mathematical description of an SIS epidemic on a hypergraph. We then generalise the work in (1) to a new class of models that encompass SIS and SIR models. The exact differential equations are derived for the expected values of the population of each state. Focusing on Bi-uniform hypergraphs, we make suitable approximations obtain numerical solutions to those equations. These are compared with stochastic simulations of the model for various systems.