4 problems

Let $\overline{\kappa}$ denote the mean curvature of the network, let $\kappa^\star>0$ be a constant, and let $R_0$ denote the basic reproduction number of the unweighted system. T…

Short-period monotonicity conjecture. There exists $\bar{\omega}>0$ such that, for all $\omega<\bar{\omega}$, the asymptotic outbreak size $1-s^{(\infty)}(\infty)$ is decreasing in…

Uniqueness conjecture. The limiting system above has a unique positive and bounded solution on $\mathbb{R}$.

Convergence conjecture. Under these assumptions,