Basic reproduction ratios for almost periodic compartmental models with time delay

The theory of basic reproduction ratio R-0 is established for a large class of almost periodic and time-delayed compartmental population models. We first present some dynamical properties for linear almost periodic functional differential systems. By using the product space and evolution semigroup approach, we then prove that R-0-1 has the same sign as the exponential growth bound of an associated linear system. As an application, we apply the developed theory to an almost periodic SEIR model with an incubation period and obtain a threshold result on its global dynamics in terms of R-0. Finally, we present some numerical simulations. Numerical simulations indicate that prolonging the length of incubation period is beneficial for the control of the disease. In addition, a simple model shows that the basic reproduction ratio may be underestimated or overestimated if an almost periodic coefficient is approximated by a periodic one. (c) 2020 Elsevier Inc. All rights reserved.