Fractional SIS epidemic models

开放网络上的SIS流行病：基于替换的近似

SIS epidemics on open networks: A replacement-based approximation

本文通过基于替换的近似过程分析开放网络中受智能体到达和离开影响的连续时间SIS流行病，推导了感染水平聚合度量的期望和方差上界，并验证了近似过程的有效性。

SIS流行病传播过程中的动态治愈与网络设计

Dynamic Curing and Network Design in SIS Epidemic Processes

针对SIS流行病传播快速消退需求，提出带预算近似保证的高效动态治愈算法及公平版本，同时研究通过边调整降低感染率的网络设计问题以消除等待期，二者结合形成高效缓解方案。

SIS Epidemic Model under Mobility on Multi-layer Networks

We study the influence of heterogeneous mobility patterns in a population on the SIS epidemic model. In particular, we consider a patchy environment in which each patch comprises individuals belonging the different classes, e.g., individuals in different socio-economic strata. We model the mobility of individuals of each class across different patches through an associated Continuous Time Markov Chain (CTMC). The topology of these multiple CTMCs constitute the multi-layer network of mobility. At each time, individuals move in the multi-layer network of spatially-distributed patches according t…

A Mean-field Approach for Controlling Singularly Perturbed Multi-population SIS Epidemics

We consider a multi-population epidemic model with one or more (almost) isolated communities and one mobile community. Each of the isolated communities has contact within itself and, in addition, contact with the outside world but only through the mobile community. The contact rate between the mobile community and the other communities is assumed to be controlled. We first derive a multidimensional ordinary differential equation (ODE) as a mean-field fluid approximation to the process of the number of infected nodes, after appropriate scaling. We show that the approximation becomes tight as th…

Use of Enumerative Combinatorics for proving the applicability of an asymptotic stability result on discrete-time SIS epidemics in complex networks

In this paper, we justify by the use of Enumerative Combinatorics, that the results obtained in \cite{Alarcon1}, where is analysed the complex dynamics of an epidemic model to identify the nodes that contribute the most to the propagation process and because of that are good candidates to be controlled in the network in order to stabilize the network to reach the extinction state, is applicable in almost all the cases. The model analysed was proposed in \cite{Gomez1} %et al. [Phys.Rev.E 84, 036105(2011)] and results obtained in \cite{Alarcon1} implies that it is not necessary to control all no…

再感染风险下耦合的演化行为与疾病动力学

Coupled Evolutionary Behavioral and Disease Dynamics under Reinfection Risk

本文在博弈论框架下研究再感染风险下流行病传播与个体防护决策的耦合演化，完整刻画SIS模型的平衡点及稳定性，并分析时间尺度分离下SIS和SIRI模型的不连续混合动力学，揭示振荡与滑模收敛现象。

如何开展一场活动：SIS和SIR信息流行病的最优控制

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

本文研究了在有限资源下如何通过最优控制策略在截止期限前最大化信息传播效果，针对SIS和SIR模型分别提出最优资源分配方法，并分析了不同控制策略的效果差异。

A purely data-driven framework for prediction, optimization, and control of networked processes: application to networked SIS epidemic model

Networks are landmarks of many complex phenomena where interweaving interactions between different agents transform simple local rule-sets into nonlinear emergent behaviors. While some recent studies unveil associations between the network structure and the underlying dynamical process, identifying stochastic nonlinear dynamical processes continues to be an outstanding problem. Here we develop a simple data-driven framework based on operator-theoretic techniques to identify and control stochastic nonlinear dynamics taking place over large-scale networks. The proposed approach requires no prior…

Effects of fractional derivatives in epidemic models

We study epidemic Susceptible-Infected-Susceptible models in the fractional setting. The novelty is to consider models in which the susceptible and infected populations evolve according to different fractional orders. We study a model based on Caputo derivative, for which we establish existence results of the solutions. Also, we investigate a model based on Caputo-Fabrizio operator, for which we provide existence of solutions and a study of the equilibria. Numerical simulations for both models and a direct numerical comparison are also provided.

On Epidemic Spreading under Mobility on Networks

We study a coupled epidemic-mobility model in which, at each time, individuals move in a network of spatially-distributed regions (sub-populations) according to a Continuous Time Markov Chain (CTMC) and subsequently interact with the local sub-population according to an SIS model. We derive a deterministic continuum limit model describing these interactions. We prove the existence of a disease-free equilibrium and an endemic equilibrium under different parameter regimes and establish their (almost) global asymptotic stability using Lyapunov techniques. For the stability of disease-free equilib…

Event-Triggered Control for Mitigating SIS Spreading Processes

In this paper, we investigate the problem of designing event-triggered controllers for containing epidemic processes in complex networks. We focus on a deterministic susceptible-infected-susceptible (SIS) model, which is one of the well-known, fundamental models that capture the epidemic spreading. The event-triggered control is particularly formulated in the context of viral spreading, in which control inputs (e.g., the amount of medical treatments, a level of traffic regulations) for each subpopulation are updated only when the fraction of the infected people in the subpopulation exceeds a p…