Modelling, Analysis, Observability and Identifiability of Epidemic Dynamics with Reinfections

TL;DR

This paper develops a comprehensive SEIRS epidemic model incorporating reinfections, analyzes its mathematical properties, and demonstrates how combined measurements can improve observability and identifiability of disease dynamics.

Contribution

It introduces an infinite differential system for reinfections, establishes existence and uniqueness, and shows how combined data enhances model identifiability.

Findings

Reinfection dynamics are captured by an infinite differential system.

Existence and uniqueness of solutions are proven.

Combined measurements improve model observability and identifiability.

Abstract

We consider in this paper a general SEIRS model describing the dynamics of an infectious disease including latency, waning immunity and infection-induced mortality. We derive an infinite system of differential equations that provides an image of the same infection process, but counting also the reinfections. Existence and uniqueness of the corresponding Cauchy problem is established in a suitable space of sequence valued functions, and the asymptotic behavior of the solutions is characterized, according to the value of the basic reproduction number. This allows to determine several mean numbers of reinfections related to the population at endemic equilibrium. We then show how using jointly measurement of the number of infected individuals and of the number of primo-infected provides observability and identifiability to a simple SIS model for which none of these two measures is sufficient to ensure on its own the same properties.