2 problems

Let $P_m$ and $P_n$ be paths on $m$ and $n$ vertices, respectively, and let $P_m\square P_n$ denote their Cartesian product. For a graph $G$, write $\sigma_{(p,q)}(G)$ for its…

Let the disease-free states be the equilibria with infectious-state vector … , and let ${\mathcal{Q}}_{xx}$ be the infectious-state block of the linearization matrix defined above.…