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We present the mathematical analysis of generalized complex contagions in clustered multiplex networks for susceptible-infected-recovered (SIR)-like dynamics. The model is intended to understand diffusion of influence, or any other…
We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by…
Although traditional models of epidemic spreading focus on the number of infected, susceptible and recovered individuals, a lot of attention has been devoted to integrate epidemic models with population genetics. Here we develop an…
The paradigm for compartment models in epidemiology assumes exponentially distributed incubation and removal times, which is not realistic in actual populations. Commonly used variations with multiple exponentially distributed variables are…
The dynamics of the spread of contagions such as viruses, infectious diseases or even rumors/opinions over contact networks (graphs) have effectively been captured by the well known \textit{Susceptible-Infected-Susceptible} ($SIS$) epidemic…
In mathematical studies of the dynamics of multi-strain diseases caused by antigenically diverse pathogens, there is a substantial interest in analytical insights. Using the example of a generic model of multi-strain diseases with…
In this work, we study the epidemic SIR model on a system which takes into consideration face-to-face interaction networks. This approach has been used as prototype to describe people interactions in different kinds of social organizations…
We study a well mixed SIR epidemic model with heterogeneous susceptibility and infectivity, allowing for an arbitrary joint distribution of these traits. Using an exact final size formulation and a branching process approximation for early…
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…
The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the…
Traditional biomedical approaches treat diseases in isolation, but the importance of synergistic disease interactions is now recognized. As a first step we present and analyze a simple coinfection model for two diseases affecting…
We apply the cavity master equation (CME) approach to epidemics models. We explore mostly the susceptible-infectious-susceptible (SIS) model, which can be readily treated with the CME as a two-state. We show that this approach is more…
We introduce a fast simulation technique for modeling epidemics on adaptive networks. Our rejection-based algorithm efficiently simulates the co-evolution of the network structure and the epidemic dynamics. We extend the classical SIS model…
Understanding infectious disease spread remains a critical public health challenge, particularly given the interplay between household dynamics and community transmission patterns. Traditional epidemiological models often oversimplify these…
In this paper we provide the derivation of a super compact pairwise model with only 4 equations in the context of describing susceptible-infected-susceptible (SIS) epidemic dynamics on heterogenous networks. The super compact model is based…
We introduce a kinetic model that couples the movement of a population of individuals with the dynamics of a pathogen in the same population. We consider that transmission occurs when a susceptible and an infectious individual are…
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many…
We formulate a generalized susceptible exposed infectious recovered (SEIR) model on a graph, describing the population dynamics of an open crowded place with an arbitrary topology. As a sample calculation, we discuss three simple cases,…
This paper analyzes a Susceptible-Infected-Susceptible (SIS) model of epidemic propagation over hypergraphs and, motivated by an important special case, we refer to the model as to the simplicial SIS model. Classically, the multi-group SIS…
We derive the master equations for the Susceptible-Infected (SI) model on general hypernetworks with~$N$-body interactions. We solve these equations exactly for infinite~$d$-regular hypernetworks, and obtain an explicit solution for the…