From Individual-Based Stochastic Epidemics to Heterogeneous SIR Equations

What the math gives to ML

The paper derives a general response law for persistent heterogeneity: a population exposed to cumulative pressure A responds through the Laplace transform G(A)=E[exp(-A Lambda)], rather than through a single average susceptibility. Its key transferable asset is the exponentially tilted mean susceptibility, which is the negative log-derivative of G and decreases according to the variance of the tilted susceptibility distribution. This gives neural routing or gating modules a principled family of monotone, saturating pressure penalties with power-law-like tails, instead of a fixed softmax penalty or hand-tuned sigmoid. The most direct experiment is a load-aware MoE router whose expert availability is G(A_e), where A_e is an exponentially averaged measure of recent expert utilization.