Table 2.

Closed-form expressions for our key results.

	Poisson	Bernoulli
Edge separation rate	σ = α − 2μ	σ = α − 2μ
Edge formation rate	λP = (σ + μ)k	λB = (σ + μ)k/(1 − k)
Expected lifetime partners	$\mathbb{E}\left[D_a(L)\right]=k\alpha /\mu$	$\mathbb{E}\left[D_a(L)\right]=k\alpha /\mu$
Initial FRS growth rate	$g_P=\alpha \frac{k-x}{1-k}$	$g_B=\alpha \left(\frac{\sqrt{1+4k(1-k)}-1}{2(1-k)}(1-x)-x\right)$
Threshold for growth	μ/α < k	$\mu /\alpha <1-\frac{2(1-k)}{\sqrt{1+4k(1-k)+1-2k}}$
Equilibrium prevalence*	$\mathbb{E}[A]/n=\frac{k-x}{k(1-x)}$	$\mathbb{E}[A]/n=1-\frac{x(1-kx)}{k{(1-x)}^2}$
Extinction probability	$z=\frac{p\exp (k(z-1))}{1-(1-p)z}$, solve for z

The expressions depend only on the network parameters k (mean degree), α (edge dissolution rate), and μ (node exit rate). For simplicity, we defined x = μ/α and p = (1 + λ_p/μ)⁻¹.

^*The equilibrium prevalence is shown for the base model, where new nodes are indistinguishable from existing nodes. The prevalence in our simulations, where new nodes enter with degree 0, is derived in Appendix B.