Islam M D Shahidul, Sharif Ullah Mohammad, Kabir K M Ariful
Department of Computer Science and Engineering, Green University of Bangladesh, Dhaka, Bangladesh.
Department of Mathematics, Feni University, Feni, Bangladesh.
Infect Dis Model. 2024 Sep 12;10(1):1-27. doi: 10.1016/j.idm.2024.08.006. eCollection 2025 Mar.
Disease severity through an immunized population ensconced on a physical network topology is a key technique for preventing epidemic spreading. Its influence can be quantified by adjusting the common (basic) methodology for analyzing the percolation and connectivity of contact networks. Stochastic spreading properties are difficult to express, and physical networks significantly influence them. Visualizing physical networks is crucial for studying and intervening in disease transmission. The multi-agent simulation method is useful for measuring randomness, and this study explores stochastic characteristics of epidemic transmission in various homogeneous and heterogeneous networks. This work thoroughly explores stochastic characteristics of epidemic propagation in homogeneous and heterogeneous networks through extensive theoretical analysis (positivity and boundedness of solutions, disease-free equilibrium point, basic reproduction number, endemic equilibrium point, stability analysis) and multi-agent simulation approach using the Gilespie algorithm. Results show that Ring and Lattice networks have small stochastic variations in the ultimate epidemic size, while BA-SF networks have disease transmission starting before the threshold value. The theoretical and deterministic aftermaths strongly agree with multi-agent simulations (MAS) and could shed light on various multi-dynamic spreading process applications. The study also proposes a novel concept of void nodes, Empty nodes and disease severity, which reduces the incidence of contagious diseases through immunization and topologies.
通过处于物理网络拓扑结构中的免疫人群来衡量疾病严重程度，是预防疫情传播的一项关键技术。其影响可通过调整用于分析接触网络的渗流和连通性的常规（基本）方法来量化。随机传播特性难以表述，而物理网络会对其产生显著影响。可视化物理网络对于研究和干预疾病传播至关重要。多智能体模拟方法有助于衡量随机性，本研究探讨了各种同构和异构网络中疫情传播的随机特征。这项工作通过广泛的理论分析（解的正性和有界性、无病平衡点、基本再生数、地方病平衡点、稳定性分析）以及使用吉莱斯皮算法的多智能体模拟方法，深入探究了同构和异构网络中疫情传播的随机特征。结果表明，环形网络和格子网络在最终疫情规模方面的随机变化较小，而BA - SF网络在阈值之前就开始了疾病传播。理论和确定性结果与多智能体模拟（MAS）高度一致，可为各种多动态传播过程应用提供启示。该研究还提出了空节点、空穴节点和疾病严重程度的新概念，通过免疫和拓扑结构降低传染病的发病率。
