Analysis on a diffusive two-stage epidemic model with logistic growth and saturated incidence rates. (April 2022)

• Record Type: Journal Article
• Authors: Liu, Guodong; Zhang, Xiaoyan
• Is Part Of: Nonlinear analysis. Volume 64(2022)
• Publication Date: 2022-04
• Subjects: Two-stage epidemic model -- Reaction–diffusion -- Saturated incidence rates -- Basic reproduction number -- Asymptotic profiles; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103444
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we investigate a two-stage epidemic model with logistic growth and saturated incidence rates in a spatially heterogeneous environment. First, the global existence of the nonnegative solution and the existence of global attractor are proved. Then the basic reproduction number R 0 is established as a threshold for the dynamics of the disease with the next generation operator method. It is shown that the disease-free equilibrium is globally attractive if R 0 < 1 and the disease is uniformly persistent if R 0 > 1 . Furthermore, we investigate the asymptotic profiles of positive steady states as the diffusion rate of the susceptible population tends to 0 and ∞, respectively. Additionally, numerical examples are carried out to verify the results and reveal the biological significance. Highlights: A diffusive two-stage epidemic model with saturated incidence rates is proposed. The global existence of the nonnegative solution is proved. The basic reproduction number is established to investigate the epidemic dynamics. Numerical examples are presented to illustrate the theoretical results.