# Interval observer for uncertain time-varying SIR-SI epidemiological model of vector-borne disease

## TL;DR

This paper develops an interval observer for a seasonal, uncertain SIR-SI epidemiological model of vector-borne diseases, providing asymptotic error bounds using Lyapunov functions for monotone systems.

## Contribution

It introduces a novel interval observer with estimate-dependent gain for a time-varying epidemiological model, ensuring bounded estimation errors.

## Key findings

- The observer guarantees asymptotic error bounds.
- The method is applicable to models with seasonal variations.
- It uses Lyapunov functions for monotone systems to synthesize the observer.

## Abstract

The issue of state estimation is considered for an SIR-SI epidemiological model describing a vector-borne disease such as dengue fever, subject to seasonal variations. Assuming continuous measurement of the incidence rate (that is the number of new infectives in the host population per unit time), a class of interval observers with estimate-dependent gain is constructed, and asymptotic error bounds are provided. The synthesis method is based on the search for a common linear Lyapunov function for monotone systems that represent the evolution of the estimation errors.