English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Exploiting the power of the expectation operator and indicator (or Bernoulli)random variables, we present the exact governing equations for both the SIR andSIS epidemic models on \emph{networks}. Although SIR and SIS are basic epidemicmodels, deductions from their exact stochastic equations \textbf{without}making approximations (such as the common mean-field approximation) are scarce.An exact analytic solution of the governing equations is highly unlikely to befound (for any network) due to the appearing pair (and higher order)correlations. Nevertheless, the maximum average fraction $y_{I}$ of infectednodes in both SIS and SIR can be written as a quadratic form of the graph'sLaplacian. Only for regular graphs, the expression for the maximum of $y_{I}$can be simplied to exhibit the explicit dependence on the spectral radius. Fromour new Laplacian expression, we deduce a general \textbf{upper} bound for theepidemic SIS threshold in any graph.

Exact Markovian SIR and SIS epidemics on networks and an upper bound for the epidemic threshold