具有非单调发生率的时滞随机传染病模型分析

Abstract

Abstract: Epidemic models are often subject to random perturbations. This article proposes a stochastic delayed epidemic model with a non-monotonic incidence rate. By the Lyapunov method and Itô's formula, the existence of a unique global positive solution of the model and the stability of the disease-free equilibrium of the model are proved. The asymptotic behavior around the endemic equilibrium of the associated definite model is obtained. Finally, numerical simulations are presented to illustrate the results.

Key words: Stochastic epidemic model, Stability, Asymptotic behavior, Lyapunov function, Itô's formula

CLC Number:

O175.1

Meng Xiaoying. Analysis of a Stochastic Delayed Epidemic Model with a Non-Monotonic Incidence Rate[J].Acta mathematica scientia,Series A, 2017, 37(6): 1162-1175.

Trendmd

References

[1] 马知恩. 传染病动力学的数学建模与研究. 北京:科学出版社, 2004 Ma Z E. Mathematical Modeling and Research of Infecious Disease Dynamicacs. Beijing:Science Press, 2004
[2] Xiao D M, Ruan S G. Global analysis of an epidemic model with nonmonotone incidence rate. Mathematical Bioscience, 2007, 208:419-429
[3] Huo H F, Ma Z P. Dynamics of a delayed epidemic model with non-monotonic incidence rate. Communications in Nonlinear Science and Numerical Simulations, 2010, 15(2):459-468
[4] Muroya Y, Enatsu Y, Nakata Y. Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate. Journal of Mathematical Analysis and Applications, 2011, 377:1-14
[5] 凌琳, 刘苏雨, 蒋贵荣. 具有饱和接触率和垂直传染的SIRS传染病模型分岔分析. 数学物理学报, 2014, 34A(6):1415-1425 Ling L, Liu S Y, Jiang G R. Bifurcation analysis of a SIRS epidemic model with saturating contact rate and vertical transmission. Acta Mathematica Scientia, 2014, 34A(6):1415-1425
[6] Tornatore E, Buccellato S M, Vetro P. Stability of a stochastic SIR system.Physica A, 2005, 354:111-126
[7] Lu Q. Stability of SIRS system with random perturbations. Physica A, 2009, 688:3677-3686
[8] Beretta E, Kolmanovskii V, Shaikhet L. Stability of epidemic model with time delays influenced by stochastic perturbations. Mathematics and Computers in Simulation, 1998, 45:269-277
[9] Yu J J, Jiang D Q, Shi N Z. Global stability of two-group SIR model with random perturbation. Journal of Mathematical Analysis and Applications, 2009, 360:235-244
[10] Zhao Y N, Jiang D Q. The threshold of a stochastic SIRS epidemic model with saturated incidence. Applied Mathematics Letters, 2014, 34:90-93
[11] Zhao Y N, Jiang D Q. The threshold of a stochastic SIR epidemic model with vaccination. Applied Mathematics and Computation, 2014, 243:718-727
[12] Mao X R. Stochastic Differential Equations and Applications. Chichester:Horwood, 1997
[13] Mao X R, Marion G, Renshaw E. Environmental Brownian noise suppresses explosions in population dynamics. Stochastic Processes and their Applications, 2002, 97:95-110

Metrics

Viewed

Full text

101

HTML			PDF

Just accepted	Online first	Issue	Just accepted	Online first	Issue
0	0	0	0	0	101

From	Others	local

Times	8	93
Rate	8%	92%

Abstract

136

Just accepted	Online first	Issue

0	0	136

From	Others	local

Times	115	21
Rate	85%	15%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed

Comments

Recommended 10

[1]	Fang Hui; Wang Zhicheng. Existence of Positive Periodic Solutions of a Neutral Delay Competition Model with Diffusion and Stock[J]. Acta mathematica scientia,Series A, 2008, 28(4): 719 -730 .
[2]	Su Youhui;Li Wantong. Triple Positive Symmetric Solutions of Two-Point BVPs for p-Laplacian Dynamic Equations on Time Scales[J]. Acta mathematica scientia,Series A, 2008, 28(6): 1232 -1241 .
[3]	Zhang Feijun; Li Kaitai. The Embedded Subbundles over Module Bundles[J]. Acta mathematica scientia,Series A, 2009, 29(1): 151 -157 .
[4]	Yang Shouzhi; Yang Xiaozhong. Orthogonal Multiscaling Functions and Multiwavelets with General Cardinal Property[J]. Acta mathematica scientia,Series A, 2007, 27(3): 470 -475 .
[5]	Xiong Ming; Liu Jiaquan; Zeng Pingan. Positive Solutions for Singular Two-point Boundary Value Problem for p-Laplacian Equation [J]. Acta mathematica scientia,Series A, 2007, 27(3): 549 -558 .
[6]	Lin Xiaoning. MULTIPLICITY OF POSITIVE PERIODIC SOLUTIONS TO SECOND ORDER SINGULAR DIFFERENTIAL SYSTEMS[J]. Acta mathematica scientia,Series A, 2006, 26(6): 1105 .
[7]	Cai Guolan; Ge Weigao. POSITIVE SOLUTION TO FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN[J]. Acta mathematica scientia,Series A, 2006, 26(6): 1077 .
[8]	Shi Dongyang; Zhang Yiran. Rectangular Crouzeix-raviart Anisotropic Finite Element Method for Nonstationary Stokes Problem with Moving Grids [J]. Acta mathematica scientia,Series A, 2006, 26(5): 659 -670 .
[9]	Sun Liying. The Satisfactory Improvements of the Modified Gauss-Seidel Method for H -matrices[J]. Acta mathematica scientia,Series A, 2006, 26(4): 591 -594 .
[10]	Ding Xiangmao;Wang Guidong;Wang Shikun. On the {\boldmath $\widehat{psl(2\|2)^{(2)}}_{k}$ } Current Superalgebra and Conformal Field Theory [J]. Acta mathematica scientia,Series A, 2008, 28(3): 393 -402 .

[1]	Gu Haibo, Gao Caixia. Razumikhin-Type Theorems on P-th Moment and Almost Sure Stability of Neutral Stochastic Switched Nonlinear Systems [J]. Acta mathematica scientia,Series A, 2018, 38(5): 970-983.
[2]	Zheng Lifei, Guo Jie, Wu Meihua, Wang Xiaorui, Wan Aying. The Research on a Class of the Predator-Prey-Mutualist System with Delays [J]. Acta mathematica scientia,Series A, 2018, 38(5): 1001-1013.
[3]	Wu Bin, Gao Ying, Yan Lin, Yu Jun. Carleman Estimate for a 2×2 Strongly Coupled Partial Differential System with Nonsingular Coefficient Matrix of Principal Parts and Application to an Inverse Source Problem [J]. Acta mathematica scientia,Series A, 2018, 38(4): 779-799.
[4]	Wang Junli, Zhang Xingwei, Liu Jian. Instability of Plane Couette-Poiseuille Flow of Compressible Navier-Stokes Equation [J]. Acta mathematica scientia,Series A, 2018, 38(2): 322-333.
[5]	Zhang Mingshu, Zhu Zheqi, Zhao Caidi. Determining Modes and Determining Nodes to the Fluid Flow of Ladyzhenskaya Model [J]. Acta mathematica scientia,Series A, 2018, 38(1): 71-82.
[6]	Wang Wansheng, Zhong Peng, Zhao Xinyang. Long-Time Stability of Nonlinear Neutral Differential Equations with Variable Delay [J]. Acta mathematica scientia,Series A, 2018, 38(1): 96-109.
[7]	Wang Shenghua, Cheng Guofei. The Asymptotic Behavior of the Solution in Structured Bacterial Population Model [J]. Acta mathematica scientia,Series A, 2018, 38(1): 156-167.
[8]	Li Haixia. Stability and Uniqueness of Positive Solutions for a Food-Chain Model [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1094-1104.
[9]	Wei Fengying, Lin Qingteng. Extinction and Distribution for an SIQS Epidemic Model with Quarantined-Adjusted Incidence [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1148-1161.
[10]	Wang Chun, Xu Tianzhou. Solution and Hyers-Ulam-Rassias Stability of a Mixed Type Quadratic-Additive Functional Equation with a Parameter in Quasi-Banach Spaces [J]. Acta mathematica scientia,Series A, 2017, 37(5): 846-859.
[11]	Chen Hongbin, Gan Siqing, Xu Da, Peng Yulong. A Formally Second-Order BDF Compact ADI Difference Scheme for the Two-Dimensional Fractional Evolution Equation [J]. Acta mathematica scientia,Series A, 2017, 37(5): 976-992.
[12]	Yang Jihua, Zhang Erli, Liu Mei. Dynamic Analysis and Chaos Control of a Finance System with Delayed Feedbacks [J]. Acta mathematica scientia,Series A, 2017, 37(4): 767-782.
[13]	Xiong Jun, Li Junmin, He Chao. Fuzzy Boundary Control Design for a Class of First-Order Hyperbolic PDEs [J]. Acta mathematica scientia,Series A, 2017, 37(3): 469-477.
[14]	Wei Aiju, Zhang Xinjian, Wang Junyi, Li Kezan. Dynamics Analysis of an Ebola Epidemic Model [J]. Acta mathematica scientia,Series A, 2017, 37(3): 577-592.
[15]	Wang Wei, Zhu Yucan. Stability of Fusion Frame Systems under Perturbation of the Local Frame Vectors [J]. Acta mathematica scientia,Series A, 2017, 37(2): 228-238.

Analysis of a Stochastic Delayed Epidemic Model with a Non-Monotonic Incidence Rate

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10