Epidemic spread in adaptive networks with multitype agents

How the individuals’ risk aversion affect the epidemic spreading

People change their physical contacts as a preventive response to infectious disease propagations. Yet, only a few mathematical models consider the coupled dynamics of the disease propagation and the contact adaptation process. This paper presents a model where each agent has a default contact neighborhood set, and switches to a different contact set once she becomes alert about infection among her default contacts. Since each agent can adopt either of two possible neighborhood sets, the overall contact network switches among }{}2^{N} possible configurations. Notably, a two-layer network representation can fully model the underlying adaptive, state-dependent contact network. Contact adaptation influences the size of the disease prevalence and the epidemic threshold—a characteristic measure of a contact network robustness against epidemics—in a nonlinear fashion. Particularly, the epidemic threshold for the presented adaptive contact network belongs to the solution of a nonlinear Perron-Frobenius (NPF) problem, which does not depend on the contact adaptation rate monotonically. Furthermore, the network adaptation model predicts a counter-intuitive scenario where adaptively changing contacts may adversely lead to lower network robustness against epidemic spreading if the contact adaptation is not fast enough. An original result for a class of NPF problems facilitate the analytical developments in this paper.

Effects of delayed recovery and nonuniform transmission on the spreading of diseases in complex networks

It is often useful to represent the infectious dynamics of mobile agents by metapopulation models. In such a model, metapopulations form a static network, and individuals migrate from one metapopulation to another. It is known that heterogeneous degree distributions of metapopulation networks decrease the epidemic threshold above which epidemic spreads can occur. We investigate the combined effect of heterogeneous degree distributions and diffusion on epidemics in metapopulation networks. We show that for arbitrary heterogeneous networks, diffusion suppresses epidemics in the sense of an increase in the epidemic threshold. On the other hand, some diffusion rates are needed to elicit epidemic spreads on a global scale. As a result of these opposing effects of diffusion, epidemic spreading near the epidemic threshold is most pronounced at an intermediate diffusion rate. The result that diffusion can suppress epidemics contrasts with that for diffusive SIS dynamics and its variants when individuals are fixed at nodes on static networks.

Bipartite network with rewiring dynamics exists in many real-world networks. Various models based on the mean-field approximation are successfully proposed for the degree distribution of rewiring dynamics in the bipartite network. However, there are implicit or even obvious differences among these models, despite that they are utilized for modeling the same rewiring problem. How the differences among these models arise and how the differences influence the solution of the degree distribution remain unresolved. Firstly, the models for a bipartite network with rewiring dynamics are categorized into three versions, which are named as a two steps version model (TSV model), a one step version-I model (OSV-I model), and a one step version-II model (OSV-II model) in the present paper. The differences among the three versions models are clarified. Then, we derive an exact solution for the TSV model and that for the OSV-II model. Furthermore, we prove that the exact solution for the steady degree distribution of the TSV model and that of the OSV-II model are globally asymptotically stable. Based on the exact solutions, the differences of the solution of the degree distribution among the three versions models are analyzed.

The information dissemination profoundly influences epidemic spreading, yet their interplay in time-varying systems remains underexplored. To tackle this issue, firstly, a multilayer time-varying network is established to model the coupled information-epidemic dynamics, which comprises a physical layer structured as networked metapopulation with community-preference migration for epidemic transmission and a virtual layer with activity-driven interactions, including media, for information diffusion. Then, using the Microscopic Markov Chain Approach, the temporal evolution of the system state is captured and the expression of the epidemic threshold is derived. Finally, extensive experiments are conducted to explore the role of information dissemination and human mobility in epidemic propagation. Our findings reveal that information dissemination elevates the epidemic threshold, reducing disease prevalence, with media credibility proving more effective than media quantity in mitigating outbreaks. Community heterogeneity and asymmetric mobility further amplify epidemic and awareness spread, particularly in densely connected regions. This study provides a robust theoretical framework for understanding the feedback loop between the coupled information-epidemic spreading dynamics, providing actionable insights for designing public health interventions in spatially and socially complex environments.

Disconnecting impaired or suspicious nodes and rewiring to those reliable, adaptive networks have the potential to inhibit cascading failures, such as DDoS attack and computer virus. The weights of disconnected links, indicating the workload of the links, can be transferred or redistributed to newly connected links to maintain network operations. Distinctively different from existing studies focused on adaptive unweighted networks, this paper presents a new mean-field model to analyze the reliability of adaptive weighted networks against cascading failures. By taking mean-field approximation, we develop a new continuous-time Markov model to capture the propagations of cascading failures and the rewiring actions that individual nodes can take to bypass failed neighbors. We analyze the stability of the model to identify the critical conditions, under which the cascading failures can be eventually inhibited or would proliferate. The conditions are evaluated under different link weight distributions and rewiring strategies. Our model reveals that preferentially disconnecting suspicious peers with high weights can effectively inhibit virus and failures.

We study the effect of heterogeneous temporal activations on epidemic spreading in temporal networks. We focus on the susceptible-infected-susceptible model on activity-driven networks with burstiness. By using an activity-based mean-field approach, we derive a closed analytical form for the epidemic threshold for arbitrary activity and inter-event time distributions. We show that, as expected, burstiness lowers the epidemic threshold while its effect on prevalence is twofold. In low-infective systems burstiness raises the average infection probability, while it weakens epidemic spreading for high infectivity. Our results can help clarify the conflicting effects of burstiness reported in the literature. We also discuss the scaling properties at the transition, showing that they are not affected by burstiness.

The interplay between disease and awareness has been extensively studied in static networks. However, most networks in reality will evolve over time. Based on this, we propose a novel epidemiological model in multiplex networks. In this model, the disease spreading layer is a time-varying network generated by the activity-driven model, while the awareness diffusion layer is a static network, and the heterogeneity of individual infection and recovery ability is considered. First, we extend the microscopic Markov chain approach to analytically obtain the epidemic threshold of the model. Then, we simulate the spread of disease and find that stronger heterogeneity in the individual activities of a physical layer can promote disease spreading, while stronger heterogeneity of the virtual layer network will hinder the spread of disease. Interestingly, we find that when the individual infection ability follows Gaussian distribution, the heterogeneity of infection ability has little effect on the spread of disease, but it will significantly affect the epidemic threshold when the individual infection ability follows power-law distribution. Finally, we find the emergence of a metacritical point where the diffusion of awareness is able to control the onset of the epidemics. Our research could cast some light on exploring the dynamics of epidemic spreading in time-varying multiplex networks.

Recent research results indicate that individual awareness can play an important influence on epidemic spreading in networks. By local stability analysis, a significant conclusion is that the embedded awareness in an epidemic network can increase its epidemic threshold. In this paper, by using limit theory and dynamical system theory, we further give global stability analysis of a susceptible-infected-susceptible (SIS) epidemic model on networks with awareness. Results show that the obtained epidemic threshold is also a global stability condition for its endemic equilibrium, which implies the embedded awareness can enhance the epidemic threshold globally. Some numerical examples are presented to verify the theoretical results.

Adaptive dynamical networks are network systems in which the structure co-evolves and interacts with the dynamical state of the nodes. We study an adaptive dynamical network in which the structure changes on a slower time scale relative to the fast dynamics of the nodes. We identify a phenomenon we refer to as recurrent adaptive chaotic clustering (RACC), in which chaos is observed on a slow time scale, while the fast time scale exhibits regular dynamics. Such slow chaos is further characterized by long (relative to the fast time scale) regimes of frequency clusters or frequency-synchronized dynamics, interrupted by fast jumps between these regimes. We also determine parameter values where the time intervals between jumps are chaotic and show that such a state is robust to changes in parameters and initial conditions.

The connectivity of ranches facilitates the spread of hoof and mouth disease among livestock, even over long distances. This study aimed to investigate the spread of hoof and mouth disease within animal ranch networks and individual ranches using a network-based modelling approach. Two models were developed: the multi-ranch model and the in-ranch model. The multi-ranch model examined how the topology and connectivity of the ranch network influenced the spread of hoof and mouth disease, while the in-ranch compartmental model captured the disease dynamics within individual ranches. The results indicate that the disease can be contained, and the network can remain disease-free as long as the transmission rate is low and the network is not overly dense. In the in-ranch compartmental model, the basic reproduction number was used to gain insights into the vaccination coverage required to maintain a disease-free state within individual ranches, as well as the coverage needed across a larger ranch network. Additionally, the findings highlight the importance of understanding both network-level transmission dynamics and within-ranch disease progression to effectively model and manage hoof and mouth disease outbreaks. Furthermore, disease control strategies, such as vaccination, to minimize the spread of the disease, which can lead to declines in the production of milk, meat, manure, and raw materials, ultimately reducing both national and individual income due to livestock loss also investigated and recommended that maintaining a transmission rate below 0.044 and offering sufficient immunization coverage are essential for a multi-ranch to stay resilient against HMD illnesses. For individual ranches and ranch networks, applying a vaccination level below 0.195 is not essential since disease will not vanish, but a level over 0.327 keep both a single ranch and larger ranch community in disease-free state

Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as n interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or large-scale data centers. Mean field approximation is asymptotically exact for systems composed of n homogeneous objects under mild conditions. In this paper, we study what happens when objects are heterogeneous. This can represent servers with different speeds or contents with different popularities. We define an interaction model that allows obtaining asymptotic convergence results for stochastic systems with heterogeneous object behavior, and show that the error of the mean field approximation is of order $O(1/n)$. More importantly, we show how to adapt the refined mean field approximation, developed by Gast et al., and show that the error of this approximation is reduced to O(1/n^2). To illustrate the applicability of our result, we present two examples. The first addresses a list-based cache replacement model, RANDOM(m), which is an extension of the RANDOM policy. The second is a heterogeneous supermarket model. These examples show that the proposed approximations are computationally tractable and very accurate. They also show that for moderate system sizes (30) the refined mean field approximation tends to be more accurate than simulations for any reasonable simulation time.

The rational allocation of resources is crucial to suppress the outbreak of epidemics. Here, we propose an epidemic spreading model in which resources are used simultaneously to prevent and treat disease. Based on the model, we study the impacts of different resource allocation strategies on epidemic spreading. First, we analytically obtain the epidemic threshold of disease using the recurrent dynamical message passing method. Then, we simulate the spreading of epidemics on the Erdős-Rényi (ER) network and the scale-free network and investigate the infection density of disease as a function of the disease infection rate. We find hysteresis loops in the phase transition of the infection density on both types of networks. Intriguingly, when different resource allocation schemes are adopted, the phase transition on the ER network is always a first-order phase transition, while the phase transition on the scale-free network transforms from a hybrid phase transition to a first-order phase transition. Particularly, through extensive numerical simulations, we find that there is an optimal resource allocation scheme, which can best suppress epidemic spreading. In addition, we find that the degree heterogeneity of the network promotes the spreading of disease. Finally, by comparing theoretical and numerical results on a real-world network, we find that our method can accurately predict the spreading of disease on the real-world network.

The rapid development of modern society continually transforms the social structure which leads to an increasing distinct dualistic social structure pattern that more people gather to large cities, resulting high population density area, and less people remain in the rural area, resulting low population density area. We study the epidemic spreading on such dualistic structure where the infectious disease could be described by SIRS model. We find that distinct from other disease model, the SIRS model has two epidemic threshold. A disease could not persist the spreading when the population density is too high or too low, which is verified both on theoretical analysis and numerical simulations. Moreover, we find that for two areas, one has high population density and the other has low population density such that a disease could not survive in each of them, when they are connected the disease could however spread over the whole system. This phenomenon indicates that the connection of the two areas could radically change the capability of the whole system to resist an infectious disease. Our finding may provide new understanding of epidemic spreading on dualistic structure of modern society and the corresponding immunization strategies.