Large language models for spreading dynamics in complex systems
School of Cyber Science and Engineering, Sichuan University（四川大学计算机科学与工程学院）；Key Laboratory of Data Protection and Intelligent Management (Sichuan University), Ministry of Education（数据保护与智能管理重点实验室（四川大学））；Cyber Science Research Institute, Sichuan University（网络科学研究院）；Royal Melbourne Institute of Technology University（皇家墨尔本理工大学）；Physics Department, University of Fribourg（弗里堡大学物理系）；Chongqing Academy of Preventive Medicine（重庆预防医学研究院）；School of Public Health and Emergency Management, Chongqing Medical and Pharmaceutical College（重庆医药学院公共卫生与应急管理学院）；School of Public Health, Chongqing Medical University（重庆医科大学公共卫生学院）
Shuyu Jiang, Hao Ren, Yichang Gao, Yi-Cheng Zhang, Li Qi, Dayong Xiao, Jie Fan, Rui Tang, Wei Wang
Spreading dynamics is a central topic in the physics of complex systems and network science, providing a unified framework for understanding how information, behaviors, and diseases propagate through interactions among system units. In many propagation contexts, spreading processes are influenced by multiple interacting factors, such as information expression patterns, cultural contexts, living environments, cognitive preferences, and public policies, which are difficult to incorporate directly into classical modeling frameworks. Recently, large language models (LLMs) have exhibited strong capabilities in natural language understanding, reasoning, and generation, enabling explicit perception of semantic content and contextual cues in spreading processes, thereby supporting the analysis of the different influencing factors. Beyond serving as external analytical tools, LLMs can also act as interactive agents embedded in propagation systems, potentially influencing spreading pathways and feedback structures. Consequently, the roles and impacts of LLMs on spreading dynamics have become an active and rapidly growing research area across multiple research disciplines. This review provides a comprehensive overview of recent advances in applying LLMs to the study of spreading dynamics across two representative domains: digital epidemics, such as misinformation and rumors, and biological epidemics, including infectious disease outbreaks. We first examine the foundations of epidemic modeling from a complex-systems perspective and discuss how LLM-based approaches relate to traditional frameworks. We then systematically review recent studies from three key perspectives, which are epidemic modeling, epidemic detection and surveillance, and epidemic prediction and management, to clarify how LLMs enhance these areas. Finally, open challenges and potential research directions are discussed.
Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time -- commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena, which we abbreviate as its `spreading vulnerability', is often surmised to be related to the topology of the temporal network featured by the system. Yet, cleanly extracting spreading vulnerability of a complex system directly from the topological information of the temporal network remains a challenge. Here, using data from a diverse set of real-world complex …
The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and critical phenomena of networked coevolution spreading are extremely important, which provide theoretical foundations for us to control epidemic spreading, predict collective behaviors in social systems, and so on. The coevolution spreading dynamics in complex networks has thus attracted much attention in many disciplines. In this review, we introduce recent pr…
Recent studies on network geometry, a way of describing network structures as geometrical objects, are revolutionizing our way to understand dynamical processes on networked systems. Here, we cope with the problem of epidemic spreading, using the Susceptible-Infected-Susceptible (SIS) model, in simplicial complexes. In particular, we analyze the dynamics of SIS in complex networks characterized by pairwise interactions (links), and three-body interactions (filled triangles, also known as 2-simplices). This higher-order description of the epidemic spreading is analytically formulated using a mi…
Epidemic spreading processes in the real world can interact with each other in a cooperative, competitive, or asymmetric way, requiring a description based on coevolution dynamics. Rich phenomena such as discontinuous outbreak transitions and hystereses can arise, but a full picture of these behaviors in the parameter space is lacking. We develop a theory for interacting spreading dynamics on complex networks through spectral dimension reduction. In particular, we derive from the microscopic quenched mean-field equations a two-dimensional system in terms of the macroscopic variables, which ena…
Identifying the starting point of a spreading process in complex networks
在处理流行病传播时，可以提出的一个重要问题是污染开始的位置。在本文中，我们分析了三种扩频方案，提出并验证了一种有效的方法来识别源节点。该方法是基于对采样网络上的节点的中心性的计算，在这里表示为度，介数，接近度和特征向量中心性。我们表明，源节点往往具有最高的测量值。该方法的潜力说明相对于三个理论复杂的网络模型，以及现实世界的网络，电子邮件网络的大学Rovira i Ravili。
In our daily lives, we rely on the proper functioning of supply networks, from power grids to water transmission systems. A single failure in these critical infrastructures can lead to a complete collapse through a cascading failure mechanism. Counteracting strategies are thus heavily sought after. In this article, we introduce a general framework to analyse the spreading of failures in complex networks and demonstrate that both weak and strong connections can be used to contain damages. We rigorously prove the existence of certain subgraphs, called network isolators, that can completely inhib…
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This paper presents a discrete time probabilistic dynamic for simulating a contact-based epidemic spreading based on discrete time Markov chain process, in particular the attention is addressed to the susceptible-infectious-removed (SIR) model and the phase diagram of such model will be presented. Then, this report presents the set of equations that represent the optimal control strategies, by the means of Pontryagin's maximum principle, in two different cases a vaccination policy and a combined vaccination-hospitalization policy and show a numerical simulation, with the standard forward-backw…
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Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest. In this work we consider the wide-spread compartment model where each node is in one of several states (or compartments). Nodes change their state randomly after an exponentially distributed waiting time and according to a given set of rules. For networks of realistic size, even the generation of only a single stochastic trajectory of a spreading process is…
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The safety and robustness of the network have attracted the attention of people from all walks of life, and the damage of several key nodes will lead to extremely serious consequences. In this paper, we proposed the clustering H-index mixing (CHM) centrality based on the H- index of the node itself and the relative distance of its neighbors. Starting from the node itself and combining with the topology around the node, the importance of the node and its spreading capability were determined. In order to evaluate the performance of the proposed method, we use Susceptible-Infected-Recovered (SIR)…
It is widely acknowledged that the initial spreaders play an important role for the wide spreading of information in complex networks. Thus, a variety of centrality-based methods have been proposed to identify the most influential spreaders. However, most of the existing studies have overlooked the fact that in real social networks it is more costly and difficult to convince influential individuals to act as initial spreaders, resulting in a high risk in maximizing the spreading. In this paper, we address this problem on the basis of the assumption that large-degree nodes are activated with a …
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Albeit epidemic models have evolved into powerful predictive tools for the spread of diseases and opinions, most assume memoryless agents and independent transmission channels. We develop an infection mechanism that is endowed with memory of past exposures and simultaneously incorporates the joint effect of multiple infectious sources. Analytic equations and simulations of the susceptible-infected-susceptible model in unstructured substrates reveal the emergence of an additional phase that separates the usual healthy and endemic ones. This intermediate phase shows fundamentally distinct charac…
Optimal curing strategy of suppressing competing epidemics spreading over complex networks is a critical issue. In this paper, we first establish a framework to capture the coupling between two epidemics, and then analyze the system's equilibrium states by categorizing them into three classes, and deriving their stability conditions. The designed curing strategy globally optimizes the trade-off between the curing cost and the severity of epidemics in the network. In addition, we provide structural results on the predictability of epidemic spreading by showing the existence and uniqueness of th…
Spreading processes have been largely studied in the literature, both analytically and by means of large-scale numerical simulations. These processes mainly include the propagation of diseases, rumors and information on top of a given population. In the last two decades, with the advent of modern network science, we have witnessed significant advances in this field of research. Here we review the main theoretical and numerical methods developed for the study of spreading processes on complex networked systems. Specifically, we formally define epidemic processes on single and multilayer network…
Macroscopic growth laws, solutions of mean field equations, describe in an effective way an underlying complex dynamics. They are applied to study the spreading of infections, as in the case of CoviD-19, where the counting of the cumulated number $N(t)$ of detected infected individuals is a generally accepted, coarse-grain, variable to understand the epidemic phase. However $N(t)$ does not take into account the unknown number of asymptomatic, not detected, cases $A(t)$. Therefore, the question arises if the observed time series of data of $N(t)$ is a reliable tool for monitoring the evolution …
Efficient stochastic simulation algorithms are of paramount importance to the study of spreading phenomena on complex networks. Using insights and analytical results from network science, we discuss how the structure of contacts affects the efficiency of current algorithms. We show that algorithms believed to require $\mathcal{O}(\log N)$ or even $\mathcal{O}(1)$ operations per update---where $N$ is the number of nodes---display instead a polynomial scaling for networks that are either dense or sparse and heterogeneous. This significantly affects the required computation time for simulations o…
The world of network science is fascinating and filled with complex phenomena that we aspire to understand. One of them is the dynamics of spreading processes over complex networked structures. Building the knowledge-base in the field where we can face more than one spreading process propagating over a network that has more than one layer is a challenging task, as the complexity comes both from the environment in which the spread happens and from characteristics and interplay of spreads' propagation. As this cross-disciplinary field bringing together computer science, network science, biology …
Graph drawings are useful tools for exploring the structure and dynamics of data that can be represented by pair-wise relationships among a set of objects. Typical real-world social, biological or technological networks exhibit high complexity resulting from a large number and broad heterogeneity of objects and relationships. Thus, mapping these networks into a low-dimensional space to visualize the dynamics of network-driven processes is a challenging task. Often we want to analyze how a single node is influenced by or is influencing its local network as the source of a spreading process. Her…
Vaccination is an effective way to prevent and control the occurrence and epidemic of infectious diseases. However, many factors influence whether the residents decide to get vaccinated or not, such as the efficacy and side effects while individuals hope to obtain immunity through vaccination. In this paper, the public attitude toward vaccination is investigated, especially how it is influenced by the public estimation of vaccines efficacy and reliance on their neighbors' vaccination behavior. We find that improving people's trust in the vaccination greatly benefits increasing the vaccination …
A common theme among the proposed models for network epidemics is the assumption that the propagating object, i.e., a virus or a piece of information, is transferred across the nodes without going through any modification or evolution. However, in real-life spreading processes, pathogens often evolve in response to changing environments and medical interventions and information is often modified by individuals before being forwarded. In this paper, we investigate the evolution of spreading processes on complex networks with the aim of i) revealing the role of evolution on the threshold, probab…
The propagation of information in social, biological and technological systems represents a crucial component in their dynamic behavior. When limited to pairwise interactions, a rather firm grip is available on the relevant parameters and critical transitions of these spreading processes, most notably the pandemic transition, which indicates the conditions for the spread to cover a large fraction of the network. The challenge is that, in many relevant applications, the spread is driven by higher order relationships, in which several components undergo a group interaction. To address this, we a…
We study a general epidemic model with arbitrary recovery rate distributions. This simple deviation from the standard setup is sufficient to prove that heterogeneity in the dynamical parameters can be as important as the more studied structural heterogeneity. Our analytical solution is able to predict the shift in the critical properties induced by heterogeneous recovery rates. Additionally, we show that the critical value of infectivity tends to be smaller than the one predicted by quenched mean-field approaches in the homogeneous case and that it can be linked to the variance of the recovery…
