基于 Beverton-Holt 出生函数的阶段结构传染病模型的稳定性和分支

doi:10.3969/j.issn.1005-3085.2022.04.008

Chinese Journal of Engineering Mathematics ›› 2022, Vol. 39 ›› Issue (4): 599-609.doi: 10.3969/j.issn.1005-3085.2022.04.008

Previous Articles Next Articles

Stability and Bifurcation in a Stage-structured Epidemic Model with the Beverton-Holt Birth Function

HU Xinli¹, ZHENG Tiantian¹, YANG Yali²

1. School of Science, Xi'an Polytechnic University, Xi'an 710048
2. Fundamentals Department, Air Force Engineering University, Xi'an 710051

Online:2022-08-15 Published:2022-10-15
Supported by:
The China National Foundation for Studying Abroad; the Scientific Research Program Funded by Shaanxi Provincial Education Department (18JK0336).

Abstract

Abstract:

An epidemic model with Beverton-Holt birth rate function and two stage-structure is established, vertical transmission is considered in the model, and the disease is only transmitted among adult individuals. The existence of equilibria of the model is analyzed, and the stability of equilibria of the model is obtained by constructing Lyapunov function, and the condition for the backward bifurcation of the model is determined. Finally, the analysis result is verified by numerical simulation.

Key words: stage structure, equilibrium, stability, backward bifurcation, the basic reproduction number

CLC Number:

O175.13

HU Xinli, ZHENG Tiantian, YANG Yali. Stability and Bifurcation in a Stage-structured Epidemic Model with the Beverton-Holt Birth Function[J]. Chinese Journal of Engineering Mathematics, 2022, 39(4): 599-609.

[1]	WANG Fen. Stability of Stochastic Memristor-based Neural Networks [J]. Chinese Journal of Engineering Mathematics, 2022, 39(4): 522-532.
[2]	ZHAO Dongxia, FAN Dongxia, WANG Tingting, MAO Li. The Control and Eigenvalue Analysis for a Pendulum System with Multiple Time-delay [J]. Chinese Journal of Engineering Mathematics, 2022, 39(3): 439-450.
[3]	ZHANG Suxia, LIU Yanna, XU Xiaxia. Bifurcation Analysis of a SIRS Age-structured Model with General Incidence Function [J]. Chinese Journal of Engineering Mathematics, 2022, 39(3): 463-476.
[4]	CHEN Qingwan, LIU Wenqing. Stability and Hopf Bifurcation of a Reaction Diffusion Predator-prey Model with Prey Fear and Refuge [J]. Chinese Journal of Engineering Mathematics, 2022, 39(3): 495-501.
[5]	ZHANG Mei, WANG Lingshu, JIA Meizhi. Stability of an Eco-epidemiological Model with Disease in the Predators and Stage-structure for the Prey [J]. Chinese Journal of Engineering Mathematics, 2022, 39(2): 224-236.
[6]	GUO Gaihui, GUO Feiyan, LIU Xiaohui. Hopf Bifurcation and Turing Instability in a Reversible Biochemical Reaction-diffusion Model Combining Second-order Saturation [J]. Chinese Journal of Engineering Mathematics, 2022, 39(2): 277-291.
[7]	LIAO Shu, FANG Zhangying, YANG Weiming. A Nonstandard Numerical Methods for a Mathematical Model for Cholera with Multiply Delays and Dispersal [J]. Chinese Journal of Engineering Mathematics, 2022, 39(1): 79-92.
[8]	ZHANG Wang, LI Yanling, ZHOU Hao. Bifurcation Structures for a Class of Ratio-type Holling-Leslie Chemotaxis Models [J]. Chinese Journal of Engineering Mathematics, 2021, 38(5): 679-690.
[9]	WANG Dan-xia, JIA Hong-en, LI Ya-qian. Two Time-mesh Finite Element Method for Cahn-Hilliard Equation [J]. Chinese Journal of Engineering Mathematics, 2021, 38(4): 553-563.
[10]	LI Zhi-min, GAO Jian-zhong, ZHANG Tai-lei, FANG Shu, SONG Xue-li. Influence of Human Behavior on Quitting Smoking Dynamics [J]. Chinese Journal of Engineering Mathematics, 2021, 38(4): 573-585.
[11]	CAO Qian, LI Yan-ling. Bifurcation Solution of a Diffusive Predator-prey Model with Allee Effect in Prey [J]. Chinese Journal of Engineering Mathematics, 2021, 38(3): 377-388.
[12]	MA Xia, CAO Hui, ZHANG Jin-zhu, GUO Zun-guang. Threshold Dynamics of Discrete Meningococcal Meningitis Model with Vaccination and Therapy [J]. Chinese Journal of Engineering Mathematics, 2021, 38(3): 416-430.
[13]	LI Dong-mei, LIU Wei-hua, WANG Qi, GUO Mei-jing. Dynamics Model of Hepatitis B Immunoglobulin Blocking the Transmission of Hepatitis B Virus between Mother and Infant [J]. Chinese Journal of Engineering Mathematics, 2021, 38(2): 151-166.
[14]	ZHU Xue, LIN Xiao-lin, LI Jian-quan. A Dynamic Analysis of Cannibalism Model with Two-stage Structure [J]. Chinese Journal of Engineering Mathematics, 2021, 38(2): 214-228.
[15]	ZHANG Jie-hua, HAN Ming-hua. Stability and Error Estimate of the Second-order Mixed Finite Volume Method for Solving the Navier-Stokes Problems [J]. Chinese Journal of Engineering Mathematics, 2021, 38(2): 229-248.

Stability and Bifurcation in a Stage-structured Epidemic Model with the Beverton-Holt Birth Function

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments