2014/02/07 by Piet Van Mieghem, Van Mieghem, Piet · 2 citations
Physics and Astronomy · Psychology · #Complex Network Analysis Techniques #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #Mental Health Research Topics #Opinion Dynamics and Social Influence #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.1402.1731
openalex publication_date 2014/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Exploiting the power of the expectation operator and indicator (or Bernoulli)\nrandom variables, we present the exact governing equations for both the SIR and\nSIS epidemic models on \networks. Although SIR and SIS are basic epidemic\nmodels, deductions from their exact stochastic equations \without\nmaking approximations (such as the common mean-field approximation) are scarce.\nAn exact analytic solution of the governing equations is highly unlikely to be\nfound (for any network) due to the appearing pair (and higher order)\ncorrelations. Nevertheless, the maximum average fraction yI of infected\nnodes in both SIS and SIR can be written as a quadratic form of the graph's\nLaplacian. Only for regular graphs, the expression for the maximum of yI\ncan be simplied to exhibit the explicit dependence on the spectral radius. From\nour new Laplacian expression, we deduce a general \upper bound for the\nepidemic SIS threshold in any graph.\n