Open AccessA stage-structured SEIR model with time-dependent delays in an almost periodic environment
Author(s) -
Lizhong Qiang,
Renhu Wang,
Ruo-fan An,
Zhicheng Wang
Publication year - 2020
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.2020393
Subject(s) - extinction (optical mineralogy) , population , incubation , latency (audio) , reproduction , incubation period , transmission (telecommunications) , basic reproduction number , mathematics , persistence (discontinuity) , stage (stratigraphy) , control theory (sociology) , biology , statistics , demography , computer science , genetics , control (management) , engineering , telecommunications , biochemistry , geotechnical engineering , artificial intelligence , sociology , paleontology
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 $\hat{R}_{0}$ for population and the basic reproduction ratio $R_{0}$ for disease. If $\hat{R}_{0}<1 the="" population="" extinction="" state="" is="" globally="" attractive="" in="" the="" case="" where="" hat="" r="" _="" 0="">1$, 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.