Paper links early SIS prevalence to epidemic-threshold uncertainty
Original title: Bayesian inverse problems and epidemic-threshold uncertainty for a heterogeneous SIS reaction-diffusion model
Early prevalence is shown to inform persistence through rate difference and infected diffusivity, with O(epsilon) posterior convergence.
The paper studies Bayesian inference of persistence from early observations of a heterogeneous SIS reaction-diffusion model with standard incidence. It shows leading prevalence depends on unknown coefficients only through the difference of transmission and recovery rates and infected diffusivity, which also sets the principal eigenvalue that governs persistence. The authors prove well-posedness and parameter stability, derive a second-order expansion for small initial infection size epsilon, and prove O(epsilon) Hellinger convergence of nonlinear posteriors to low-prevalence limits when noise scales with epsilon. They also bound eigenvalue and posterior persistence error and illustrate the claims numerically.
- Persistence is governed by the sign of a principal eigenvalue.
- Incidence depends explicitly on transmission at leading order.
- Noise proportional to epsilon yields O(epsilon) Hellinger convergence.
- Bounds cover both forward and eigenvalue approximation error.
From the original article
1 min read at arxiv.orgWe study Bayesian inference of persistence from early observations of a heterogeneous susceptible--infected--susceptible (SIS) reaction--diffusion model with standard incidence. We show that the leading prevalence dynamics depend on the unknown coefficients only through the difference between the transmission and recovery rates and the infected diffusivity.
By Duc-Lam Duong · arxiv.org
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