Some results on Ricatti Equations, Floquet Theory and Applications

TL;DR

This paper introduces two novel results in Floquet theory for planar periodic systems, including one that computes Floquet multipliers without solving the system, and applies these results to a cholera epidemic model with seasonality.

Contribution

The paper presents new analytical results in Floquet theory, notably a method to determine Floquet multipliers without solving the system, and demonstrates their application to epidemiological modeling.

Findings

New Floquet theory results for planar systems

Floquet multipliers computed independently of solutions

Application to cholera epidemic model with seasonality

Abstract

In this paper, we present two new results to the classical Floquet theory, which provides the Floquet multipliers for two classes of the planar periodic system. One these results provides the Floquet multipliers independently of the solution of system. To demonstrate the application of these analytical results, we consider a cholera epidemic model with phage dynamics and seasonality incorporated.