JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (7): 18-32.doi: 10.6040/j.issn.1671-9352.0.2024.369

• Mathematical Biology • Previous Articles    

Dynamics analysis of infectious diseases transmission with vaccination on complex networks

ZHAO Yaqi, ZHANG Ruixia*   

  1. School of Mathematics, North University of China, Taiyuan 030051, Shanxi, China
  • Published:2026-07-01

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Abstract: In this paper, based on complex networks, an SVAIR epidemic model with vaccination is established, in which the asymptomatic infected person(A)and the infected person (I)have different infectivity. The basic reproduction number R0 is calculated by the next generation matrix. By using the Lyapunov function and monotone iterative, it is proved that when R0<1, the disease-free equilibrium is globally asymptotically stable. When R0>1, the endemic equilibrium point exists and is unique, the system is uniformly persistent and the endemic equilibrium point is globally attractive. Finally, we choose the scale-free network for sensitivity analysis and numerical simulation to verify the theoretical results, and results indicate that improving vaccine efficacy and vaccination rate can better control the spread of infectious diseases.

Key words: vaccination, asymptomatic patient, stability, complex networks

CLC Number: 

  • O175
[1] Luo Tianyi, Cao Zhidong, Wang Yuejiao, et al. Role of asymptomatic COVID-19 cases in viral transmission: findings from a hierarchical community contact network model[J]. IEEE Transactions on Automation Science and Engineering, 2021, 19(2):576-585.
[2] Gourieroux C, Jasiak J. Time varying Markov process with partially observed aggregate data: an application to coronavirus[J]. Journal of Econometrics, 2023, 232(1):35-51.
[3] Huang He, Xu Yang, Xing Jingli, et al. Social influence or risk perception? A mathematical model of self-protection against asymptomatic infection in multilayer network[J]. Chaos, Solitons & Fractals, 2023, 166:112925.
[4] 许丽丽,陈艳,陈征宇,等. 疫苗的发展与创新:从天花疫苗到新型冠状病毒疫苗[J]. 医药导报,2021,40(7):876-881. Xu Lili, Chen Yan, Chen Zhengyu, et al. Development and innovation of vaccine: from smallpox vaccine to COVID-19 vaccine[J]. Herald of Medicine, 2021, 40(7):876-881.
[5] Cai Liming, Li Zhaoqing, Song Xinyu. Global analysis of an epidemic model with vaccination[J]. Journal of Applied Mathematics & Computing, 2018, 57(1):605-628.
[6] Roh G H, Lee S, Kim J Y, et al. SNSMiner_VAC: analyzing vaccination based on social network service data for safety surveillance[J]. Expert Systems with Applications, 2024, 255:124684.
[7] Fu Xinjie, Wang Jinrong. Dynamic behaviors and non-instantaneous impulsive vaccination of an SAIQR model on complex networks[J]. Applied Mathematics and Computation, 2024, 465:128425.
[8] La Salle J P. The stability of dynamical systems[M]. Philadelphia: Society for Industrial and Applied Mathematics, 1976:57-70.
[9] Smith H L, De Leenheer P. Virus dynamics: a global analysis[J]. SIAM Journal on Applied Mathematics, 2003, 63(4):1313-1327.
[10] Zhao Xiaoqiang. Dynamical systems in population biology[M]. New York: Springer, 2003:16-22.
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