Bifurcation and stability of a delayed SIS epidemic model with saturated incidence and treatment rates in heterogeneous networks

被引:30
作者
Guan, Gui [1 ]
Guo, Zhenyuan [1 ]
机构
[1] Hunan Univ, Sch Math, Changsha 410082, Hunan, Peoples R China
基金
中国国家自然科学基金;
关键词
Complex network; Epidemic model; Delay; Bifurcation; Stability; Control; SCALE-FREE NETWORKS; BACKWARD BIFURCATION; GLOBAL STABILITY; INFECTIVE VECTOR; MULTIPLE ROUTES; VACCINATION; DYNAMICS; TRANSMISSION; PROPAGATION; BEHAVIORS;
D O I
10.1016/j.apm.2021.08.024
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In this paper, to characterize the limited availability of medical resources, we incorporate a saturated treatment rate into a network-based susceptible-infected-susceptible (SIS) epidemic model with time delay and nonlinear incidence rate. Analytical study shows the boundedness of solutions, the basic reproduction number R-0 and equilibrium points of the proposed system. For any infection delay, we perform both local and global stability analyses for the disease-free equilibrium point by analyzing the characteristic equation and using Lyapunov functional. Furthermore, this system exhibits bifurcation behavior at R-0 = 1 due to the introduction of saturated treatment. More precisely, a backward bifurcation takes place from the disease-free equilibrium point when the saturation constant beta is sufficiently large. Under the given conditions, the unique disease-spreading equilibrium point is also proved to be locally asymptotically stable. In addition, we analyze an optimal control problem with consideration of two time-dependent control measures. Several numerical simulations are presented to validate the obtained theoretical results. (C) 2021 Elsevier Inc. All rights reserved.
引用
收藏
页码:55 / 75
页数:21
相关论文
共 75 条
[1]   Statistical mechanics of complex networks [J].
Albert, R ;
Barabási, AL .
REVIEWS OF MODERN PHYSICS, 2002, 74 (01) :47-97
[2]  
Alkahtani BST, 2020, CHAOS SOLITON FRACT, V138, DOI [10.1016/j.chaos.2020.110006, 10.1016/j.chaos.2020.11006]
[3]   Dynamics of a time-delayed SIR epidemic model with logistic growth and saturated treatment [J].
Avila-Vales, Eric ;
Perez, Angel G. C. .
CHAOS SOLITONS & FRACTALS, 2019, 127 :55-69
[4]   Analysis of tuberculosis model with saturated incidence rate and optimal control [J].
Baba, Isa Abdullahi ;
Abdulkadir, Rabiu Aliyu ;
Esmaili, Parvaneh .
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2020, 540
[5]   Optimal control of an epidemiological model with multiple time delays [J].
Bashier, Eihab B. M. ;
Patidar, Kailash C. .
APPLIED MATHEMATICS AND COMPUTATION, 2017, 292 :47-56
[6]   On the backward bifurcation of a vaccination model with nonlinear incidence [J].
Buonomo, B. ;
Lacitignola, D. .
NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2011, 16 (01) :30-46
[7]   Effects of information-induced behavioural changes during the COVID-19 lockdowns: the case of Italy [J].
Buonomo, Bruno ;
Della Marca, Rossella .
ROYAL SOCIETY OPEN SCIENCE, 2020, 7 (10)
[8]   Oscillations and hysteresis in an epidemic model with information-dependent imperfect vaccination [J].
Buonomo, Bruno ;
Della Marca, Rossella .
MATHEMATICS AND COMPUTERS IN SIMULATION, 2019, 162 :97-114
[9]   GENERALIZATION OF THE KERMACK-MCKENDRICK DETERMINISTIC EPIDEMIC MODEL [J].
CAPASSO, V ;
SERIO, G .
MATHEMATICAL BIOSCIENCES, 1978, 42 (1-2) :43-61
[10]  
Cooke K.L., 1979, The Rocky Mountain Journal of Mathematics, V9, P31, DOI DOI 10.1216/RMJ-1979-9-1-31