相关论文: A model for an epidemic with contact tracing and c…

We study the Susceptible-Infected-Susceptible model of the spread of an endemic infection. We calculate an exact expression for the mean number of transmissions for all values of the population and the infectivity. We derive the large-N…

The ability to directly record human face-to-face interactions increasingly enables the development of detailed data-driven models for the spread of directly transmitted infectious diseases at the scale of individuals. Complete coverage of…

This paper proves a new central limit theorem for a sample that exhibits two-way dependence and heterogeneity across clusters. Statistical inference for situations with both two-way dependence and cluster heterogeneity has thus far been an…

In an increasingly interconnected world, a key scientific challenge is to examine mechanisms that lead to the widespread propagation of contagions, such as misinformation and pathogens, and identify risk factors that can trigger large-scale…

A key characteristic of the spread of infectious diseases is their ability to use efficient transmission paths within contact graphs. This enables the pathogen to maximise infection rates and spread within a target population. In this work,…

For a given, arbitrary graph, what is the epidemic threshold? That is, under what conditions will a virus result in an epidemic? We provide the super-model theorem, which generalizes older results in two important, orthogonal dimensions.…

We present a systematic review of some basic results on the derivation of classical epidemiological models from simple agent-based dynamics. The evolution of large populations is coupled with the dynamics of the contact distribution,…

A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form…

The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…

This paper is concerned with Crump-Mode-Jagers branching processes, describing spread of an epidemic depending on the proportion of the population that is vaccinated. Births in the branching process are aborted independently with a…

The spread of an epidemic disease and the population's collective behavioural response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their…

We consider a branching process with Poissonian immigration where individuals have inheritable types. At rate theta, new individuals singly enter the total population and start a new population which evolves like a supercritical,…

After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…

We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix…

Infectious or contagious diseases can be transmitted from one person to another through social contact networks. In today's interconnected global society, such contagion processes can cause global public health hazards, as exemplified by…

This paper considers a stochastic SIR (susceptible$\to$infective$\to$removed) epidemic model in which individuals may make infectious contacts in two ways, both within `households' (which for ease of exposition are assumed to have equal…

Global strategies to contain a pandemic, such as social distancing and protective measures, are designed to reduce the overall transmission rate between individuals. Despite such measures, essential institutions, including hospitals,…

Spatial models for spread of an epidemic may be mapped onto bond percolation. We point out that with disorder in the strength of contacts between individuals patchiness in the spread of the epidemic is very likely, and the criterion for…

We consider the spread of infectious disease through contact networks of Configuration Model type. We assume that the disease spreads through contacts and infected individuals recover into an immune state. We discuss a number of existing…

We explore how heterogeneity in the intensity of interactions between people affects epidemic spreading. For that, we study the susceptible-infected-susceptible model on a complex network, where a link connecting individuals $i$ and $j$ is…