A stage-structured SEIR model with time-dependent delays in an almost periodic environment

In this paper, we propose and investigate an almost periodic SEIR model with stage structure and latency, in which time-dependent maturation and incubation periods are incorporated. Two threshold parameters for the persistence and extinction of population and disease are introduced: the basic reproduction ratio (R) over cap (0) for population and the basic reproduction ratio R-0 for disease. If (R) over cap (0) < 1, the population extinction state is globally attractive. In the case where <(R)over cap>(0) > 1, it is shown that the disease tends to die out if R-0 < 1, while remains persistent if R-0 > 1. By virtue of numerical simulations, we verify the analytic results and investigate the effects of the fluctuations of maturation and incubation periods on disease transmission.