Open AccessGlobal analysis on a class of multi-group SEIR model with latency and relapse
Author(s) -
Jinliang Wang,
Hongying Shu
Publication year - 2016
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2016.13.209
Subject(s) - latency (audio) , basic reproduction number , population , epidemic model , nonlinear system , lyapunov function , computer science , graph , population model , mathematical proof , mathematics , theoretical computer science , demography , physics , telecommunications , geometry , quantum mechanics , sociology
In this paper, we investigate the global dynamics of a multi-group SEIR epidemic model, allowing heterogeneity of the host population, delay in latency and delay due to relapse distribution for the human population. Our results indicate that when certain restrictions on nonlinear growth rate and incidence are fulfilled, the basic reproduction number R0 plays the key role of a global threshold parameter in the sense that the long-time behaviors of the model depend only on R0. The proofs of the main results utilize the persistence theory in dynamical systems, Lyapunov functionals guided by graph-theoretical approach.