9 problems

Let $(n_{1a}^*,n_{1i}^*,n_3^*)$ be an asymptotically stable equilibrium of the three-dimensional virus system, and let…

Assume that $r\kappa\mu_1\neq v\sigma$ and that the $(\operatorname{Coex}_{2,3})$-condition holds, which in particular implies $mv>r+v$. Let $(n_{1a}^*,n_{1i}^*,n_3^*)$ and…

Threshold conjecture. For all such $\gamma$ and $\nu$: if $\mathrm{R}_{0}(\gamma,\nu)<1$, then the $(\gamma,\nu)$-EpiSLFV process goes extinct; if $\mathrm{R}_{0}(\gamma,\nu)>1$, t…

Consider the multi-species SLIR system for $V$ pathogens and $P$ species, with pathogens indexed by $a=1,\dots,k$ satisfying $\mathcal{R}_{0a}<1$ and pathogens indexed by…

Let $G$ be a graph, let $K_N$ be the complete graph on $N$ vertices, let $u$ be the all-infected initial infection-probability vector, and let $V_\infty$ be the endemic steady-stat…

Let $G$ be a graph, let $K_N$ be the complete graph on $N$ vertices, let $u$ denote the all-infected initial infection-probability vector, and let $V(0)$ be an initial infection-pr…

Behaviors in the bistable and endemic domains. For the simplicial SIS model, in the bistable domain and at fixed $\beta_2$, the domain of attraction of the disease-free equilibrium…

Extinction conjecture. If $R_0^S<1$ and

Antal and Krapivsky's conjecture. For each $k=1,\ldots,K$, the expected number of individuals of type $k$ satisfies