A delayed stage-structure brucellosis model with interaction among seasonality, time-varying incubation and density-dependent growth

Abstract

In this paper, a class of brucellosis transmission model with seasonal alternation, density-dependent growth, stage-structure, maturation delay, time-varying incubation is established. The basic reproduction number [Formula: see text] is derived, by which we find that the brucellosis is uniformly persistent if [Formula: see text], while the disease-free periodic solution is globally attractive if [Formula: see text]. The theoretical results are illustrated by numerical simulation, from which we find that the brucellosis transmission would be overestimated (or underestimated) if we ignore the influence of time-varying incubation or maturation delay. If density-dependent growth of animals is ignored, the risk of brucellosis may be far underestimated, the extinction of brucellosis can be obtained by numerical simulation under the same conditions. Seasonality significantly affects the long-term dynamic behavior of brucellosis, and the inconsistency of parameter periods results in complex dynamic behavior.