相关论文: Explicit solutions of the Bass and SI models on hy…

We present a detailed set-based analysis of the well-known SIR and SEIR epidemic models subjected to hard caps on the proportion of infective individuals, and bounds on the allowable intervention strategies, such as social distancing,…

The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the…

Recently, Bogu\~{n}\'{a} {\it et. al.} [Phys. Rev. Lett. {\bf 111}, 068701 (2013), arXiv:1305.4819] claimed that the epidemic threshold of the susceptible-infected-susceptible (SIS) model is zero on random scale-free (SF) networks with the…

We consider the well-posedness of a class of hyperbolic partial differential equations on a one dimensional spatial domain. This class includes in particular infinite-dimensional networks of transport, wave and beam equations, or even…

Individual-based models of contagious processes are useful for predicting epidemic trajectories and informing intervention strategies. In such models, the incorporation of contact network information can capture the non-randomness and…

Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing…

The ongoing need for effective epidemic modeling has driven advancements in capturing the complex dynamics of infectious diseases. Traditional models, such as Susceptible-Infected-Recovered, and graph-based approaches often fail to account…

We develop an analytical approach to the susceptible-infected-susceptible (SIS) epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks. We find that a delicate balance…

Many models of virus propagation in Computer Networks inspired by {\bf SIS,SIR,}\\ {\bf SEIR}, etc. epidemic disease propagation mathematical models that can be found in the epidemiology field have been proposed in the last two decades. The…

We study hyperedge-removal strategies for suppressing contagion on synthetic hypergraphs. Hypergraphs are generated from Erd\H{o}s--R\'enyi, Barab\'asi--Albert, and Watts--Strogatz seed graphs by promoting maximal cliques to hyperedges. For…

Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…

While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…

It is in practice impossible to describe the topology of a real network or its message propagation process using a single dynamic model. To address this issue, we constructed a new hybrid network model based on scale-free (SF), small-world…

We present a unified mathematical approach to epidemiological models with parametric heterogeneity, i.e., to the models that describe individuals in the population as having specific parameter (trait) values that vary from one individuals…

Learning from structured data is a core machine learning task. Commonly, such data is represented as graphs, which normally only consider (typed) binary relationships between pairs of nodes. This is a substantial limitation for many domains…

We study the spreading of an infection within an SIS epidemiological model on a network. Susceptible agents are given the opportunity of breaking their links with infected agents. Broken links are either permanently removed or reconnected…

The epidemic spreading has been widely studied when each node may get infected by an infected neighbor with the same rate. However, the infection rate between a pair of nodes is usually heterogeneous and even correlated with their nodal…

In this paper we are concerned with the SIR model with random vertex weights on Erd\H{o}s-R\'{e}nyi graph $G(n,p)$. The Erd\H{o}s-R\'{e}nyi graph $G(n,p)$ is generated from the complete graph $C_n$ with $n$ vertices through independently…

Exact solution of the Susceptible-Infectious-Recovered (SIR) epidemic model is derived, and various properties of solution are obtained directly from the exact solution. It is shown that there exists an exact solution of an initial value…

The contact process is an emblematic model of a non-equilibrium system, containing a phase transition between inactive and active dynamical regimes. In the epidemiological context, the model is known as the susceptible-infected-susceptible…