Observer Design for the State Estimation of Epidemic Processes

TL;DR

This paper introduces a novel observer design for nonlinear epidemic models, improving state estimation accuracy by reducing nonlinearity effects, with proven convergence conditions and demonstrated on a complex epidemic model.

Contribution

It presents a new observer architecture for nonlinear epidemic systems, with algebraic Riccati inequalities ensuring convergence, addressing limitations of existing Lipschitz-based methods.

Findings

Observer achieves asymptotic error convergence.

Applicable to complex epidemic models like SIDARTHE-V.

Provides LMI formulations for design conditions.

Abstract

Although an appropriate choice of measured state variables may ensure observability, designing state observers for the state estimation of epidemic models remains a challenging task. Epidemic spread is a nonlinear process, often modeled as the law of mass action, which is of a quadratic form; thus, on a compact domain, its Lipschitz constant turns out to be local and relatively large, which renders the Lipschitz-based design criteria of existing observer architectures infeasible. In this paper, a novel observer architecture is proposed for the state estimation of a class of nonlinear systems that encompasses the deterministic epidemic models. The proposed observer offers extra leverage to reduce the influence of nonlinearity in the estimation error dynamics, which is not possible in other Luenberger-like observers. Algebraic Riccati inequalities are derived as sufficient conditions for the asymptotic convergence of the estimation error to zero under local Lipschitz and generalized Lipschitz assumptions. Equivalent linear matrix inequality formulations of the algebraic Riccati inequalities are also provided. The efficacy of the proposed observer design is illustrated by its application on the celebrated SIDARTHE-V epidemic model.