Basic Reproduction Ratios for Periodic Abstract Functional Differential Equations (with Application to a Spatial Model for Lyme Disease)

Abstract

In this paper, we develop the theory of basic reproduction ratios $$\mathcal {R}_0$$ for abstract functional differential systems in a time-periodic environment. It is proved that $$\mathcal {R}_0-1$$ has the same sign as the exponential growth bound of an associated linear system. Then we apply it to a time-periodic Lyme disease model with time-delay and obtain a threshold type result on its global dynamics in terms of $$\mathcal {R}_0$$ .