= Resolvent bound for a discrete SIR epidemic
{title2=$\mathbb EZ\leq\mathbf1^T(I-\beta A)^{-1}X(0)$}
When $\beta\rho(A)<1$, summing the <adjacency-matrix bound for a discrete SIR epidemic> gives the displayed <Neumann series> bound on the expected total infected count $Z$. For an undirected <graph>, the <adjacency matrix of a graph> is a <symmetric matrix>, so its Euclidean <operator norm> equals its <spectral radius>. The <Cauchy-Schwarz inequality> then yields $\mathbb EZ\leq\sqrt{nm}/(1-\beta\rho)$ for $m$ initially infected <vertices>.
Back to article page
