在疫情防控工作中,医疗资源的合理分配一直是从业人员重点关注的内容。为了探究疫情扩散过程中不同免疫措施在防疫工作中的实际效果,提出了一种复杂网络中考虑双向免疫措施的传染病模型。通过对模型的理论分析和数值仿真,详细讨论了针对不同群体的免疫措施对病毒传播的影响。理论分析中,结合基本再生数分析了模型无病平衡点的稳定性。数值仿真中,通过蒙特卡洛模拟分析了复杂网络中双向免疫和人口流动对传染病传播的影响。仿真结果表明,相较于提高感染个体的康复率,增加易感个体的免疫接种率可以更有效地降低传染病的感染规模。
In epidemic prevention and control efforts, the rational allocation of medical resources has consistently been a focal point of attention for professionals in the field. In order to investigate the practical effectiveness of various immune measures in epidemic prevention during the process of pandemic spread, this study introduces an infectious disease model within complex networks that considers bidirectional immune interventions. Through theoretical analysis and numerical simulations of the model, we delve into a detailed discussion on the impact of immune measures targeted at different population groups on the transmission of the virus. In the theoretical analysis, the stability of the disease-free equilibrium point in the model is examined through the incorporation of the basic reproduction number analysis. In numerical simulations, the impact of bidirectional immunization and population mobility on the spread of infectious diseases is scrutinized through Monte Carlo simulations within the context of complex networks. Simulation results indicate that, compared to enhancing the recovery rate of infected individuals, increasing the immunization rate among susceptible individuals can more effectively reduce the scale of infectious diseases.
[1] KERMACK W O, MCKENDRICK A G. A contribution to the mathematical theory of epidemics[J]. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1927, 115(772): 700721.
[2] KERMACK W O, MCKENDRICK A G. Contributions to the mathematical theory of epidemics. II.—The problem of endemicity[J]. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1932, 138(834): 5583.
[3] NEWMAN M E J. Spread of epidemic disease on networks[J]. Physical Review E, 2002, 66(1): 016128.
[4] MAY R M, LLOYD A L. Infection dynamics on scale-free networks[J]. Physical Review E, 2001, 64(6): 066112.
[5] ZANETTE D H. Dynamics of rumor propagation on small-world networks[J]. Physical Review E, 2002, 65(4): 041908.
[6] PASTOR-SATORRAS R, VESPIGNANI A. Epidemic spreading in scale-free networks[J]. Physical Review Letters, 2001, 86(14): 3200.
[7] PASTOR-SATORRAS R, VESPIGNANI A. Epidemic dynamics in finite size scale-free networks[J]. Physical Review E, 2002, 65(3): 035108.
[8] PASTOR-SATORRAS R, VESPIGNANI A. Epidemic dynamics and endemic states in complex networks[J]. Physical Review E, 2001, 63(6): 066117.
[9] WANG F, LIU M, ZHANG L, et al. Bifurcation analysis and optimal control of a network-based SIR model with the impact of medical resources[J]. Nonlinear Analysis: Modelling and Control, 2023, 28: 119.
[10] PEI H, YAN G, HUANG Y. Impact of contact rate on epidemic spreading in complex networks[J]. The European Physical Journal B, 2023, 96(4): 44.
[11] YANG P, JIA J, SHI W, et al. Stability analysis and optimal control in an epidemic model on directed complex networks with nonlinear incidence[J]. Communications in Nonlinear Science and Numerical Simulation, 2023, 121: 107206.
[12] ZHU L, ZHOU M, ZHANG Z. Dynamical analysis and control strategies of rumor spreading models in both homogeneous and heterogeneous networks[J]. Journal of Nonlinear Science, 2020, 30: 25452576.
[13] ZHOU J, ZHAO Y, YE Y. Complex dynamics and control strategies of SEIR heterogeneous network model with saturated treatment[J]. Physica A: Statistical Mechanics and Its Applications, 2022, 608: 128287.
[14] LÜ X, FAN D, LI Q, et al. Simplicial SIR rumor propagation models with delay in both homogeneous and heterogeneous networks[J]. Physica A: Statistical Mechanics and Its Applications, 2023, 627: 129131.
[15] XIE Y, WANG Z, LU J, et al. Stability analysis and control strategies for a new SIS epidemic model in heterogeneous networks[J]. Applied Mathematics and Computation, 2020, 383: 125381.
[16] PASTOR-SATORRAS R, VESPIGNANI A. Immunization of complex networks[J]. Physical Review E, 2002, 65(3): 036104.
[17] SUN X L, WANG Y G, CANG L Q. Correlation and trust mechanism-based rumor propagation model in complex social networks[J]. Chinese Physics B, 2022, 31(5): 050202.
[18] VAN DEN DRIESSCHE P, WATMOUGH J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission[J]. Mathematical Biosciences, 2002, 180(1/2): 2948.
[19] BARABÁSI A L, ALBERT R. Emergence of scaling in random networks[J]. Science, 1999, 286(5439): 509512.
