Dynamic analysis and optimal control of a novel fractional-order 2I2SR rumor spreading model

In this paper, a novel fractional-order 2I2SR rumor spreading model is investigated. Firstly, the boundedness and uniqueness of solutions are proved. Then the next-generation matrix method is used to calculate the threshold. Furthermore, the stability of rumor-free/spreading equilibrium is discussed based on fractional-order Routh–Hurwitz stability criterion, Lyapunov function method, and invariance principle. Next, the necessary conditions for fractional optimal control are obtained. Finally, some numerical simulations are given to verify the results

How to Run a Campaign: Optimal Control of SIS and SIR Information Epidemics

Information spreading in a population can be modeled as an epidemic. Campaigners (e.g. election campaign managers, companies marketing products or movies) are interested in spreading a message by a given deadline, using limited resources. In this paper, we formulate the above situation as an optimal control problem and the solution (using Pontryagin's Maximum Principle) prescribes an optimal resource allocation over the time of the campaign. We consider two different scenarios --- in the first, the campaigner can adjust a direct control (over time) which allows her to recruit individuals from the population (at some cost) to act as spreaders for the Susceptible-Infected-Susceptible (SIS) epidemic model. In the second case, we allow the campaigner to adjust the effective spreading rate by incentivizing the infected in the Susceptible-Infected-Recovered (SIR) model, in addition to the direct recruitment. We consider time varying information spreading rate in our formulation to model the changing interest level of individuals in the campaign, as the deadline is reached. In both the cases, we show the existence of a solution and its uniqueness for sufficiently small campaign deadlines. For the fixed spreading rate, we show the effectiveness of the optimal control strategy against the constant control strategy, a heuristic control strategy and no control. We show the sensitivity of the optimal control to the spreading rate profile when it is time varying.Comment: Proofs for Theorems 4.2 and 5.2 which do not appear in the published journal version are included in this version. Published version can be accessed here: http://dx.doi.org/10.1016/j.amc.2013.12.16

Epidemic processes in complex networks

In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)

Dynamic Core Community Detection and Information Diffusion Processes on Networks

Interest in network science has been increasingly shared among various research communities due to its broad range of applications. Many real world systems can be abstracted as networks, a group of nodes connected by pairwise edges, and examples include friendship networks, metabolic networks, and world wide web among others. Two of the main research areas in network science that have received a lot of focus are community detection and information diffusion. As for community detection, many well developed algorithms are available for such purposes in static networks, for example, spectral partitioning and modularity function based optimization algorithms. As real world data becomes richer, community detection in temporal networks becomes more and more desirable and algorithms such as tensor decomposition and generalized modularity function optimization are developed. One scenario not well investigated is when the core community structure persists over long periods of time with possible noisy perturbations and changes only over periods of small time intervals. The contribution of this thesis in this area is to propose a new algorithm based on low rank component recovery of adjacency matrices so as to identify the phase transition time points and improve the accuracy of core community structure recovery. As for information diffusion, traditionally it was studied using either threshold models or independent interaction models as an epidemic process. But information diffusion mechanism is different from epidemic process such as disease transmission because of the reluctance to tell stale news and to address this issue other models such as DK model was proposed taking into consideration of the reluctance of spreaders to diffuse the information as time goes by. However, this does not capture some cases such as the losing interest of information receivers as in viral marketing. The contribution of this thesis in this area is we proposed two new models coined susceptible-informed-immunized (SIM) model and exponentially time decaying susceptible-informed (SIT) model to successfully capture the intrinsic time value of information from both the spreader and receiver points of view. Rigorous analysis of the dynamics of the two models were performed based mainly on mean field theory. The third contribution of this thesis is on the information diffusion optimization. Controlling information diffusion has been widely studied because of its important applications in areas such as social census, disease control and marketing. Traditionally the problem is formulated as identifying the set of k seed nodes, informed initially, so as to maximize the diffusion size. Heuristic algorithms have been developed to find approximate solutions for this NP-hard problem, and measures such as k-shell, node degree and centrality have been used to facilitate the searching for optimal solutions. The contribution of this thesis in this field is to design a more realistic objective function and apply binary particle swarm optimization algorithm for this combinatorial optimization problem. Instead of fixating the seed nodes size and maximize the diffusion size, we maximize the profit defined as the revenue, which is simply the diffusion size, minus the cost of setting those seed nodes, which is designed as a function of degrees of the seed nodes or a measure that is similar to the centrality of nodes. Because of the powerful algorithm, we were able to study complex scenarios such as information diffusion optimization on multilayer networks.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145937/1/wbao_1.pd

A Microscopic-view Infection Model based on Linear Systems

Understanding the behavior of an infection network is typically addressed from either a microscopic or a macroscopic point-of-view. The trade-off is between following the individual states at some added complexity cost or looking at the ratio of infected nodes. In this paper, we focus on developing an alternative approach based on dynamical linear systems that combines the fine information of the microscopic view without the associated added complexity. Attention is shifted towards the problems of source localization and network topology discovery in the context of infection networks where a subset of the nodes is elected as observers. Finally, the possibility to control such networks is also investigated. Simulations illustrate the conclusions of the paper with particular interest on the relationship of the aforementioned problems with the topology of the network and the selected observer/controller nodes

Dynamic Control of Fraud Information Spreading in Mobile Social Networks

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this recordMobile social networks (MSNs) provide real-time information services to individuals in social communities through mobile devices. However, due to their high openness and autonomy, MSNs have been suffering from rampant rumors, fraudulent activities, and other types of misuses. To mitigate such threats, it is urgent to control the spread of fraud information. The research challenge is: how to design control strategies to efficiently utilize limited resources and meanwhile minimize individuals' losses caused by fraud information? To this end, we model the fraud information control issue as an optimal control problem, in which the control resources consumption for implementing control strategies and the losses of individuals are jointly taken as a constraint called total cost, and the minimum total cost becomes the objective function. Based on the optimal control theory, we devise the optimal dynamic allocation of control strategies. Besides, a dynamics model for fraud information diffusion is established by considering the uncertain mental state of individuals, we investigate the trend of fraud information diffusion and the stability of the dynamics model. Our simulation study shows that the proposed optimal control strategies can effectively inhibit the diffusion of fraud information while incurring the smallest total cost. Compared with other control strategies, the control effect of the proposed optimal control strategies is about 10% higher.National Natural Science Foundation of China (NSFC)Fundamental Research Funds for the Central Universitie

Implementation of a Social Network Information Dissemination Model Incorporating Negative Relationships

For the study of information dissemination in online social networks, most existing information dissemination models include only positive relationships, ignoring the existence and importance of negative relationships, and do not consider the influence of inter-individual relationship polarity on dissemination. To solve these problems, we propose a social network information dissemination model incorporating negative relationships in this paper. Drawing on the state concept of the SIR (Susceptible Infected Recovered) model, the three types of SIR states are subdivided into five sub-states. Combining the advantages of the viewpoint evolution model, the influence of relational polarity on node attitudes is added to the modeling of the propagation process. The experiment proves that the method proposed in this paper can show more specifically the changing trend in the number of propagation nodes with different attitudes and portray the process of information propagation in online social networks

An information diffusion model in social networks with carrier compartment and delay

With the wide applications of the communication networks, the topic of information networks security is getting more and more attention from governments and individuals. This paper is devoted to investigating a malware propagation model with carrier compartment and delay to describe the process of malware propagation in mobile wireless sensor networks. Based on matrix theory for characteristic values, the local stability criterion of equilibrium points is established. Applying the linear approximation method of nonlinear systems, we study the existence of Hopf bifurcation at the equilibrium points. At the same time, we identify some sensitive parameters in the process of malware propagation. Finally, numerical simulations are performed to illustrate the theoretical results