The Carleman Contraction Mapping Method for a Coefficient Inverse Problem of the Epidemiology

TL;DR

This paper introduces a novel Carleman contraction mapping method to solve a coefficient inverse problem in epidemiology, enabling accurate monitoring of epidemic spread using coupled nonlinear parabolic equations.

Contribution

It develops a new numerical approach combining Carleman estimates and the Quasi-Reversibility Method for solving inverse problems in epidemiology.

Findings

Method demonstrates accurate results with noisy data

Global convergence of the iterative procedure is proven

Numerical experiments confirm effectiveness

Abstract

It is proposed to monitor spatial and temporal spreads of epidemics via solution of a Coefficient Inverse Problem for a system of three coupled nonlinear parabolic equations. To solve this problem numerically, a version of the so-called Carleman contraction mapping method is developed for this problem. On each iteration, a linear problem with the incomplete lateral Cauchy data is solved by the weighted Quasi-Reversibility Method, where the weight is the Carleman Weight Function. This is the function, which is involved as the weight in the Carleman estimate for the corresponding parabolic operator. Convergence analysis ensures the global convergence of this procedure. Numerical results demonstrate an accurate performance of this technique for noisy data.