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In network-based SIS models of infectious disease transmission, infection can only occur between directly connected individuals. This constraint naturally gives rise to spatial correlations between the states of neighboring nodes, as the…

Statistical Mechanics · Physics 2026-03-18 Alexander Leibenzon , Samuel W. S. Johnson , Ruth E. Baker , Michael Assaf

We consider a system in which two viruses of the Susceptible-Infected-Susceptible (SIS) type compete over general, overlaid graphs. While such systems have been the focus of many recent works, they have mostly been studied in the sense of…

Systems and Control · Electrical Eng. & Systems 2022-09-16 Vishwaraj Doshi , Jie Hu , Do Young Eun

We study the spread of discrete-time epidemics over arbitrary networks for well-known propagation models, namely SIS (susceptible-infected-susceptible), SIR (susceptible-infected-recovered), SIRS (susceptible-infected-recovered-susceptible)…

Social and Information Networks · Computer Science 2016-10-03 Navid Azizan Ruhi , Hyoung Jun Ahn , Babak Hassibi

We study the mixing time of a Susceptible--Infected--Susceptible (SIS) model on graphs with external sources of infection, which we refer to as the noisy SIS model. Under suitable assumptions on the parameters of the dynamics, we show that…

Probability · Mathematics 2026-05-14 Wasiur R. KhudaBukhsh , Yangrui Xiang

Propagation of contagion in networks depends on the graph topology. This paper is concerned with studying the time-asymptotic behavior of the extended contact processes on static, undirected, finite-size networks. This is a contact process…

Physics and Society · Physics 2015-07-03 June Zhang , José M. F. Moura

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…

Physics and Society · Physics 2017-02-01 Bo Qu , Huijuan Wang

In this paper, we investigate game-theoretic strategies for containing spreading processes on large-scale networks. Specifically, we consider the class of networked susceptible-infected-susceptible (SIS) epidemics where a large population…

Systems and Control · Electrical Eng. & Systems 2024-07-04 Abhisek Satapathi , Ashish R. Hota

In this paper we study the household-structure SIS epidemic spreading on general complex networks. The household structure gives us the way to distinguish inner and the outer infection rate. Unlike household-structure models on homogenous…

Populations and Evolution · Quantitative Biology 2013-02-14 Jingzhou Liu , Jinshan Wu , Z. R. Yang

We study a discrete Susceptible-Infected-Recovered (SIR) model for the spread of infectious disease on a homogeneous tree and the limit behavior of the model in the case when the tree vertex degree tends to infinity. We obtain the…

Probability · Mathematics 2022-07-08 Alexander Gairat , Vadim Shcherbakov

In previous work, we developed the scaled SIS process, which models the dynamics of SIS epidemics over networks. With the scaled SIS process, we can consider networks that are finite-sized and of arbitrary topology (i.e., we are not…

Social and Information Networks · Computer Science 2014-10-10 June Zhang , José M. F. Moura

Age at infection is often an important factor in epidemic dynamics. In this paper a disease transmission model of SIS type with age dependent infection on a heterogeneous network is discussed. The model allows the infectious rate and the…

Dynamical Systems · Mathematics 2018-06-19 Shanshan Chen , Michael Small , Yizhou Tao , Xinchu Fu

Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible-infected-susceptible setting, spectral conditions characterise whether the disease vanishes. However, modelling human…

Social and Information Networks · Computer Science 2021-09-15 Desmond John Higham , Henry-Louis de Kergorlay

We study a fast-slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model, taking into account that the infection period is much…

Dynamical Systems · Mathematics 2021-12-30 Hildeberto Jardón-Kojakhmetov , Christian Kuehn , Andrea Pugliese , Mattia Sensi

Social interactions are stratified in multiple contexts and are subject to complex temporal dynamics. The systematic study of these two features of social systems has started only very recently mainly thanks to the development of multiplex…

Physics and Society · Physics 2018-12-12 Quan-Hui Liu , Xinyue Xiong , Qian Zhang , Nicola Perra

The paper deals with the spread of two competing viruses over a network of population nodes, accounting for pairwise interactions and higher-order interactions (HOI) within and between the population nodes. We study the competitive…

Systems and Control · Electrical Eng. & Systems 2023-09-26 Sebin Gracy , Brian D. O. Anderson , Mengbin Ye , Cesar A. Uribe

We investigate the Susceptible-Infectious-Recovered contagion dynamics in a system of self-propelled particles with polar alignment. Using agent-based simulations, we analyze the outbreak process for different combinations of the spatial…

Adaptation and Self-Organizing Systems · Physics 2021-06-16 Yinong Zhao , Cristián Huepe , Pawel Romanczuk

Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular…

Populations and Evolution · Quantitative Biology 2017-01-23 Frank Ball , Thomas House

We study an infection-age structured epidemic model in which both the infectivity and the rate of loss of immunity depend on the time-since-infection. The model can be equivalently viewed as a nonlinear renewal equation for the incidence of…

Dynamical Systems · Mathematics 2025-11-13 Francesca Scarabel , Harry Coldwell , Tyler Cassidy

Case isolation, that is, detection and isolation of infected individuals in order to prevent spread, is a strategy to curb infectious disease epidemics. Here, we study the efficiency of a case isolation strategy subject to time delays in…

Optimization and Control · Mathematics 2022-09-20 Jonas Hansson , Alain Govaert , Richard Pates , Emma Tegling , Kristian Soltesz

The evolution of network structure and the spreading of epidemic are common coexistent dynamical processes. In most cases, network structure is treated either static or time-varying, supposing the whole network is observed in a same time…

Physics and Society · Physics 2016-03-23 Yanjun Lei , Xin Jiang , Quantong Guo , Yifang Ma , Meng Li , Zhiming Zheng
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