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 enables a full phase diagram to be determined analytically. The diagram predicts critical phenomena that were known previously but only numerically, such as the interplay between discontinuous transition and hysteresis as well as the emergence and role of tricritical points.
Identifying the most influential spreaders is important to understand and control the spreading process in a network. As many real-world complex systems can be modeled as multilayer networks, the question of identifying important nodes in multilayer network has attracted much attention. Existing studies focus on the multilayer network structure, while neglecting how the structural and dynamical coupling of multiple layers influence the dynamical importance of nodes in the network. Here we investigate on this question in an information-disease coupled spreading dynamics on multiplex networks. F…
Competition and collaboration are at the heart of multi-agent probabilistic spreading processes. The battle on public opinion and competitive marketing campaigns are typical examples of the former, while the joint spread of multiple diseases such as HIV and tuberculosis demonstrates the latter. These spreads are influenced by the underlying network topology, the infection rates between network constituents, recovery rates and, equally importantly, the interactions between the spreading processes themselves. Here, for the first time we derive dynamic message-passing equations that provide an ex…
Diseases and other contagion phenomena in nature and society can interact asymmetrically, such that one can benefit from the other, which in turn impairs the first, in analogy with predator-prey systems. Here, we consider two models for interacting disease-like dynamics with asymmetric interactions and different associated time scales. Using rate equations for homogeneously mixed populations, we show that the stationary prevalences and phase diagrams of each model behave differently with respect to variations of the relative time scales. We also characterize in detail the regime where transien…
In the early stage of epidemics, individuals' determination on adopting protective measures, which can reduce their risk of infection and suppress disease spreading, is likely to depend on multiple information sources and their mutual confirmation due to inadequate exact information. Here we introduce the inter-layer mutual confirmation mechanism into the information-disease interacting dynamics on multiplex networks. In our model, an individual increases the information transmission rate and willingness to adopt protective measures once he confirms the authenticity of news and severity of dis…
Interactions in biology and social systems are not restricted to pairwise but can take arbitrary sizes. Extensive studies have revealed that the arbitrary-sized interactions significantly affect the spreading dynamics on networked systems. Competing spreading dynamics, i.e., several epidemics spread simultaneously and compete with each other, have been widely observed in the real world, yet the way arbitrary-sized interactions affect competing spreading dynamics still lacks systematic study. This study presents a model of two competing simplicial susceptible-infected-susceptible epidemics on a…
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 investigate the problem of locating the source of a self-interacting signal spreading in a complex networks. We use a well-known rumour model as an example of the process with self-interaction. According to this model based on the SIR epidemic dynamics, the infected nodes may interact and discourage each other from gossiping with probability $α$. We compare three algorithms of source localization: Limited Pinto-Thiran-Vettarli (LPTV), Gradient Maximum Likelihood (GMLA) and one based on Pearson correlation between time and distance. The results of numerical simulations show that additional i…
Nowadays, one of the challenges we face when carrying out modeling of epidemic spreading is to develop methods to control disease transmission. In this article we study how the spreading of knowledge of a disease affects the propagation of that disease in a population of interacting individuals. For that, we analyze the interaction between two different processes on multiplex networks: the propagation of an epidemic using the susceptible-infected-susceptible dynamics and the dissemination of information about the disease --and its prevention methods-- using the unaware-aware-unaware dynamics, …
The dynamics of epidemic spreading is often reduced to the single control parameter $R_0$, whose value, above or below unity, determines the state of the contagion. If, however, the pathogen evolves as it spreads, $R_0$ may change over time, potentially leading to a mutation-driven spread, in which an initially sub-pandemic pathogen undergoes a breakthrough mutation. To predict the boundaries of this pandemic phase, we introduce here a modeling framework to couple the network spreading patterns with the intra-host evolutionary dynamics. For many pathogens these two processes, intra- and inter-…
Population inhomogeneity, in the variation of the individual social contact networks and the individual infectious-recovery rates, renders the dynamics of infectious disease spreading uncertain. As a consequence the overlaying economical production network with its proper collaboration components is to extent impacted unpredictably. Our model proposes a `vector logistic' dynamical approach to SIS dynamics in a social contact network interacting with its economic capacity network. The probabilistic interpretation of the graph state in the vector logistic description provides a method to assess …
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）
