Search Results (25)

Under the “Dual Carbon” goal, public opinion analysis is crucial for optimizing policy implementation and enhancing social consensus, yet it faces challenges such as insufficient multi-source data integration, limited causal modeling, and delayed interventions. This study proposes a collaborative framework integrating reinforcement learning-enhanced large language models (LLMs), diffusion models, and multi-agent systems (MASs). By constructing a four-dimensional causal network of “policy–technology–economy–public sentiment”, it analyzes multi-source data and simulates multi-agent interactions. The experimental results show that this framework outperforms Latent Dirichlet Allocation (LDA), Bidirectional Encoder Representations from Transformers (BERT), and Susceptible Infected Recovered (SIR) models in causal inference, dynamic intervention, and multi-agent collaboration. Reinforcement Learning from Human Feedback (RLHF) optimizes LLM outputs for reliable policy recommendations, with pass@10 showing strong correlations. This study provides scientific support for “Dual Carbon” policymaking and public opinion guidance, facilitating the green and low-carbon transition. Full article

In this article, we propose a novel nonlinear cross-diffusion framework to model the distribution of susceptible and infected individuals within their habitat using a reduced SIR model that incorporates saturated incidence and treatment rates. The study investigates solution boundedness through the theory of parabolic partial differential equations, thereby validating the proposed spatio-temporal model. Through the implementation of the suggested cross-diffusion mechanism, the model reveals at least one non-constant positive equilibrium state within the susceptible–infected (SI) system. This work demonstrates the potential coexistence of susceptible and infected populations through cross-diffusion and unveils Turing instability within the system. By analyzing codimension-2 Turing–Hopf bifurcation, the study identifies the Turing space within the spatial context. In addition, we explore the results for Turing–Bogdanov–Takens bifurcation. To account for seasonal disease variations, novel perturbations are introduced. Comprehensive numerical simulations illustrate diverse emerging patterns in the Turing space, including holes, strips, and their mixtures. Additionally, the study identifies non-Turing and Turing–Bogdanov–Takens patterns for specific parameter selections. Spatial series and surfaces are graphed to enhance the clarity of the pattern results. This research provides theoretical insights into the implications of cross-diffusion in epidemic modeling, particularly in contexts characterized by localized mobility, clinically evident infections, and community-driven isolation behaviors. Full article

This study enhances the classical deterministic SIR model by incorporating soliton-like dynamics and gradient-induced diffusion, effectively capturing the complex spatiotemporal patterns of disease transmission within nomadic populations. The proposed model incorporates an advection–diffusion mechanism that modulates the spatial gradients in infection dynamics, transitioning from highly localized infection peaks to distributed infection fronts. We discussed the role of diffusion coefficients in shaping the spatial distribution of susceptible, infected, and recovered populations, as well as the impact of gradient-induced advection in mitigating epidemic intensity. Numerical simulations demonstrate the effects of varying key parameters such as transmission rates, recovery rates, and advection–diffusion coefficients on the epidemic’s progression. The soliton-like dynamics ensure the stability of infection waves over time, specifying targeted intervention strategies such as localized quarantines and vaccination campaigns. This model underscores the critical importance of spatial heterogeneity and mobility patterns in managing infectious diseases. The applicability of the model has been tested using the AIDS data from the last 25 years. Full article

In this article, a diffusion component in an SIR model is introduced, and its impact is analyzed using fractional calculus. We have included the diffusion component in the SIR model. in order to illustrate the variations. Here, we have applied the general fractional derivative to analyze the impact. The Laplace decomposition technique is employed to obtain the numerical outcomes of the model. In order to observe the effect of the diffusion component in the SIR model, graphical solutions are also displayed. Full article

In the context of global economic digitalization, financial information is highly susceptible to internet financial public opinion due to the overwhelming and misleading nature of information on internet platforms. This paper delves into the core entities in the diffusion process of internet financial public opinions, including financial institutions, governments, media, and investors, and models the behavioral characteristics of these entities in the diffusion process. On this basis, we comprehensively use the multi-agent model and the SIR model to construct a dynamic evolution model of internet financial public opinion. We conduct a simulation analysis of the impact effects and interaction mechanisms of multi-agent behaviors in the financial market on the evolution of internet financial public opinion. The research results are as follows. Firstly, the financial institutions’ digitalization levels, government guidance, and the media authority positively promote the diffusion of internet financial public opinion. Secondly, the improvement of investors’ financial literacy can inhibit the diffusion of internet financial public opinion. Thirdly, under the interaction of multi-agent behaviors in the financial market, the effects of financial institutions’ digitalization level and investors’ financial literacy are more significant, while the effects of government guidance and media authority tend to converge. Full article

We propose a stochastic model of infectious disease transmission that is more realistic than those found in the literature. The model is based on jump-diffusion processes. However, it is defined in such a way that the number of people susceptible to be infected decreases over time, which is the case for a population of fixed size. Next, we consider the problem of finding the optimal control of the proposed model. The dynamic programming equation satisfied by the value function is derived. Estimators of the various model parameters are obtained. Full article

Our aim is to provide an insight into the procedures and the dynamics that lead the spread of contagious diseases through populations. Our simulation tool can increase our understanding of the spatial parameters that affect the diffusion of a virus. SIR models are based on the hypothesis that populations are “well mixed”. Our model constitutes an attempt to focus on the effects of the specific distribution of the initially infected individuals through the population and provide insights, considering the stochasticity of the transmission process. For this purpose, we represent the population using a square lattice of nodes. Each node represents an individual that may or may not carry the virus. Nodes that carry the virus can only transfer it to susceptible neighboring nodes. This important revision of the common SIR model provides a very realistic property: the same number of initially infected individuals can lead to multiple paths, depending on their initial distribution in the lattice. This property creates better predictions and probable scenarios to construct a probability function and appropriate confidence intervals. Finally, this structure permits realistic visualizations of the results to understand the procedure of contagion and spread of a disease and the effects of any measures applied, especially mobility restrictions, among countries and regions. Full article

For decades, understanding the dynamics of infectious diseases and halting their spread has been a major focus of mathematical modelling and epidemiology. The stochastic SIRS (susceptible–infectious–recovered–susceptible) reaction–diffusion model is a complicated but crucial computational scheme due to the combination of partial immunity and an incidence rate. Considering the randomness of individual interactions and the spread of illnesses via space, this model is a powerful instrument for studying the spread and evolution of infectious diseases in populations with different immunity levels. A stochastic explicit finite difference scheme is proposed for solving stochastic partial differential equations. The scheme is comprised of predictor–corrector stages. The stability and consistency in the mean square sense are also provided. The scheme is applied to diffusive epidemic models with incidence rates and partial immunity. The proposed scheme with space’s second-order central difference formula solves deterministic and stochastic models. The effect of transmission rate and coefficient of partial immunity on susceptible, infected, and recovered people are also deliberated. The deterministic model is also solved by the existing Euler and non-standard finite difference methods, and it is found that the proposed scheme forms better than the existing non-standard finite difference method. Providing insights into disease dynamics, control tactics, and the influence of immunity, the computational framework for the stochastic SIRS reaction–diffusion model with partial immunity and an incidence rate has broad applications in epidemiology. Public health and disease control ultimately benefit from its application to the study and management of infectious illnesses in various settings. Full article

Mathematical modeling in epidemiology, biology, and life sciences requires the use of stochastic models. In this paper, we derive a competitive two-strain stochastic SIR epidemic model by considering the change in state of the epidemic process due to an event. Based on the density-dependent process theory, we construct a six-dimensional deterministic model that can be used to describe the diffusion limit of the stochastic epidemic on a heterogeneous network. Furthermore, we show the explicit expressions for the variances of infectious individuals with strain 1 and strain 2 when the level of infection is increasing exponentially. In particular, we find that the expressions of the variances are symmetric. Finally, simulations for epidemics spreading on networks are performed to confirm our analytical results. We find a close agreement between the simulations and theoretical predictions. Full article

Identifying influential spreaders in complex networks is critical for information spread and malware diffusion suppression. In this paper, we propose a novel influential spreader identification method, called SpreadRank, which considers the path reachability in information spreading and uses its quantitative index as a measure of node spread centrality to obtain the spread influence of a single node. To avoid the overlapping of the influence range of the node spread, this method establishes a dynamic influential node set selection mechanism based on the spread centrality value and the principle of minimizing the maximum connected branch after network segmentation, and it selects a group of nodes with the greatest overall spread influence. Experiments based on the SIR model demonstrate that, compared to other existing methods, the selected influential spreaders of SpreadRank can quickly diffuse or suppress information more effectively. Full article

The mechanisms of information diffusion in Online Social Networks (OSNs) have been studied extensively from various perspectives with some focus on identifying and modeling the role of heterogeneous nodes. However, none of these studies have considered the influence of fake accounts on human accounts and how this will affect the rumor diffusion process. This paper aims to present a new information diffusion model that characterizes the role of bots in the rumor diffusion process in OSNs. The proposed $S{I}_h{I}_{b}R$ model extends the classical SIR model by introducing two types of infected users with different infection rates: the users who are infected by human $\left(I_h\right)$ accounts with a normal infection rate and the users who are infected by bot accounts $\left(I_b\right)$ with a different diffusion rate that reflects the intent and steadiness of this type of account to spread the rumors. The influence of fake accounts on human accounts diffusion rate has been measured using the social impact theory, as it better reflects the deliberate behavior of bot accounts to spread a rumor to a large portion of the network by considering both the strength and the bias of the source node. The experiment results show that the accuracy of the $S{I}_h{I}_{b}R$ model outperforms the SIR model when simulating the rumor diffusion process in the existence of fake accounts. It has been concluded that fake accounts accelerate the rumor diffusion process as they impact many people in a short time. Full article

The explanation of risk contagion among economic players—not only in financial crises—and how they spread across the world has fascinated scholars and scientists in the last few decades. Inspired by the literature dealing with the analogy between financial systems and ecosystems, we model risk contagion by revisiting the mathematical approach of epidemiological models for infectious disease spread in a new paradigm. We propose a time delay differential system describing risk diffusion among companies inside an economic sector by means of a SIR dynamics. Contagion is modelled in terms of credit and financial risks with low and high levels. A complete theoretical analysis of the problem is carried out: well-posedness and solution positivity are proven. The existence of a risk-free steady state together with an endemic equilibrium is verified. Global asymptotic stability is investigated for both equilibria by the classical Lyapunov functional theory. The model is tested on a case study of some companies operating in the food economic sector in a specific Italian region. The analysis allows for understanding the crucial role of both incubation time and financial immunity period in the asymptotic behaviour of any solution in terms of endemic permanence of risk rather than its disappearance. Full article

This paper presents a method to minimize the spread of negative influence on social networks by contact blocking. First, based on the infection-spreading process of COVID-19, the traditional susceptible, infectious, and recovered (SIR) propagation model is extended to the susceptible, non-symptomatic, infectious, and recovered (SNIR) model. Based on this model, we present a method to estimate the number of individuals infected by a virus at any given time. By calculating the reduction in the number of infected individuals after blocking contacts, the method selects the set of contacts to be blocked that can maximally reduce the affected range. The selection of contacts to be blocked is repeated until the number of isolated contacts that need to be blocked is reached or all infection sources are blocked. The experimental results on three real datasets and three synthetic datasets show that the algorithm obtains contact blockings that can achieve a larger reduction in the range of infection than other similar algorithms. This shows that the presented SNIR propagation model can more precisely reflect the diffusion and infection process of viruses in social networks, and can efficiently block virus infections. Full article

Aiming at the problem that the existing rumor dissemination models only focus on the characteristics of rumor dissemination and ignore anti-rumor dissemination, an evolution game model, SDIR, based on heat influence is proposed in this paper. Firstly, in order to solve the problem that rumor and anti-rumor information of emergency events disseminate simultaneously in social networks, the model extracts the factors that affect information dissemination: user behavior characteristics, user closeness and heat influence of participating topics. Secondly, anti-rumor information and an evolutionary game mechanism are introduced into the traditional SIR model, binary information is introduced to analyze the anti-rumor dissemination model SDIR, and the four state transitions and dissemination processes of SDIR are discussed. Finally, the SDIR model is experimentally validated in different datasets and dissemination models. The experimental results show that the SDIR model is in line with the actual dissemination law, and it can be proved that high self-identification ability plays a certain role in suppressing rumors; the anti-rumor information effectively inhibits the spread of rumor information to a certain extent. Compared with other models, the SDIR model is closer to the real diffusion range in the dataset. Full article

Risk propagation is occurring as an exceptional challenge to supply chain management. Identifying which supplier has the greater possibility of interruptions is pivotal for managing the occurrence of these risks, which have a significant impact on the supply chain. Identifying and predicting how these risks propagate and understanding how these risks dynamically diffuse if control strategies are installed can help to better manage supply chain risks. Drawing on the complex systems and epidemiological literature, we research the impact of the global supply network structure on risk propagation and supply network health. The SIR model is used to dynamically identify and predict the risk status of the supply chain risk at different times. The results show that there is a significant relationship between network structure and risk propagation and supply network health. We demonstrate the importance of supply network visibility and of the extraction of the information of node firms. We build up an R package for geometric graphs and epidemics. This paper applies the R package to model the supply chain risk for an automotive manufacturing company. The R package provides a firm to construct the complicated interactions among suppliers and display how these interactions impact on risks. Theoretically, our study adapts a computational approach to contribute to the understanding of risk management and supply networks. Managerially, our study demonstrates how the supply chain network analysis approach can benefit the managers by developing a more holistic framework of system-wide risk propagation. This provides guidance for network governance policies, which will lead to healthier supply chains. Full article