Box 1.

Recipe to determine the Floquet ratio

(1) Establish a time dependent growth matrix \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bf K}(\varphi _{0} ,t)$$\end{document} (see Eq. 1). This matrix describes the growth of the system (e.g. the increase of population size or the transmission and recovery causing a change in the number of infected hosts)

(2) Determine the Fourier components K −n to K n of the growth matrix K (see Eq. 2)

(3) Formulate the Floquet matrix (see Eq. 9)

(4) Calculate the eigenvalues of the Floquet matrix, if possible analytically or otherwise using a numerical approximation

(5) Compose the Floquet ratio R T from the real part of the largest eigenvalue