Remarks on basic reproduction ratios for periodic abstract functional differential equations

Abstract

In this paper, we extend the theory of basic reproduction ratios \begin{document}$ \mathcal{R}_0 $\end{document} in [Liang, Zhang, Zhao, JDDE], which concerns with abstract functional differential systems in a time-periodic environment. We prove the threshold dynamics, that is, the sign of \begin{document}$ \mathcal{R}_0-1 $\end{document} determines the dynamics of the associated linear system. We also propose a direct and efficient numerical method to calculate \begin{document}$ \mathcal{R}_0 $\end{document} .