11 problems

Let $K$ be the population-size scaling parameter, let $\hat{X}^K$ denote the rescaled epidemic process, and let $\Lambda<0$ be the non-persistence parameter. Consider initial condi…

The pair-approximation approach describes the stochastic epidemic exactly on locally tree-like graphs. Pair-approximation exactness conjecture. The pair approximation is conjecture…

Let $T^N_{\mathrm{MRND}}$ and $T^N_{\mathrm{NSWND}}$ be the final epidemic sizes without dropping of edges on MR and NSW configuration-model random graphs with $N$ vertices. Let…

Let $T^N_{\mathrm{NSW}}$ be the final epidemic size on an NSW random graph with $N$ vertices, let $\rho$ be the limiting final infected fraction, and let $\sigma_D^2$ and $\mu_D$ d…

Let $T^N_{\mathrm{MR}}$ be the final epidemic size on an MR random graph with $N$ vertices, let $\rho$ be the deterministic limiting final fraction infected, and let $z$ be the sol…

Let $\tilde{\boldsymbol{W}}^N(t)$ be the time-changed effective-degree epidemic process, let $\tilde{\tau}^N$ be its random terminal time, and let $\tilde{\boldsymbol{w}}(t)$ and…

Extension conjecture. The results should continue to hold when the condition $d_{\max}<\infty$ is relaxed, provided suitable conditions are imposed on (i) the distribution of $D$ a…

Let theorem1(i) and theorem2(i) denote the asymptotic results for the persistence time of SIS infections in the model with heterogeneous populations or networks, established under…

Let the general stochastic SIR epidemic have susceptible, infected, and recovered population counts, and let the corresponding deterministic Kermack–McKendrick SIR system be initia…

Augmented dynamical-systems conjecture. This analysis should yield a value of $R_0$ equal to the general expression for $R_0$ defined earlier in the paper.

Let $Z_n(t)=(S_n(t),I_n(t),R_n(t))$ be the epidemic process starting from $(S_n(0),I_n(0),R_n(0))=(n-1,1,0)$, and let … On the latter event, namely when $Z_n(t)$ tends to…