Open AccessStability and bifurcation analysis of $ SIQR $ for the COVID-19 epidemic model with time delay
Author(s) -
Shishi Wang,
Yuting Ding,
Hongfan Lu,
Silin Gong
Publication year - 2021
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.2021278
Subject(s) - hopf bifurcation , mathematics , stability (learning theory) , bifurcation , epidemic model , delay differential equation , saddle node bifurcation , covid-19 , mathematical analysis , differential equation , control theory (sociology) , physics , computer science , nonlinear system , population , medicine , demography , disease , control (management) , pathology , quantum mechanics , machine learning , artificial intelligence , sociology , infectious disease (medical specialty)
Based on the SIQR model, we consider the influence of time delay from infection to isolation and present a delayed differential equation (DDE) according to the characteristics of the COVID-19 epidemic phenomenon. First, we consider the existence and stability of equilibria in the above delayed SIQR model. Second, we analyze the existence of Hopf bifurcations associated with two equilibria, and we verify that Hopf bifurcations occur as delays crossing some critical values. Then, we derive the normal form for Hopf bifurcation by using the multiple time scales method for determining the stability and direction of bifurcation periodic solutions. Finally, numerical simulations are carried out to verify the analytic results.