Pre-Publicación 2026-29
Aníbal Coronel, Fernando Huancas, Mauricio Sepúlveda:
Theoretical analysis and numerical validation of an inverse problem in a SIS reaction–diffusion system, Part 1: Identification of transmission and recovery rates
Abstract:
This work is the first article in a series of studies on inverse problems for this class of epidemiological models. It establishes mathematical and computational foundations by focusing on reaction coefficients, while subsequent parts address the incidence and other unknown model components. The mathematical model is a generalized susceptible-infected-susceptible (SIS) epidemic model with spatial population displacement. We formulate the determination of transmission and recovery rates from final-time observations as a constrained optimization problem. We study existence and uniqueness for the state system, existence of a minimizer, the adjoint problem, first-order necessary optimality conditions, continuous dependence of the state and adjoint solutions, and conditional uniqueness on a fixed-mean admissible subset. We also present numerical experiments for a finite-dimensional parameter-identification problem.
