Open AccessBifurcation analysis and optimal control of SEIR epidemic model with saturated treatment function on the network
Author(s) -
Boli Xie,
AUTHOR_ID,
Maoxing Liu,
Lei Zhang
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.2022079
Subject(s) - epidemic model , population , bifurcation , control theory (sociology) , optimal control , mathematics , stability (learning theory) , function (biology) , range (aeronautics) , mathematical optimization , transmission (telecommunications) , computer science , control (management) , nonlinear system , biology , engineering , artificial intelligence , physics , demography , telecommunications , quantum mechanics , machine learning , evolutionary biology , sociology , aerospace engineering
In order to study the impact of limited medical resources and population heterogeneity on disease transmission, a SEIR model based on a complex network with saturation processing function is proposed. This paper first proved that a backward bifurcation occurs under certain conditions, which means that $ R_{0} < 1 $ is not enough to eradicate this disease from the population. However, if the direction is positive, we find that within a certain parameter range, there may be multiple equilibrium points near $ R_{0} = 1 $. Secondly, the influence of population heterogeneity on virus transmission is analyzed, and the optimal control theory is used to further study the time-varying control of the disease. Finally, numerical simulations verify the stability of the system and the effectiveness of the optimal control strategy.