相关论文: Exact equations for SIR epidemics on tree graphs
Contact networks can significantly change the course of epidemics, affecting the rate of new infections and the mean size of an outbreak. Despite this dependence, some characteristics of epidemics are not contingent on the contact network…
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 duration of the infectious period is a crucial determinant of the ability of an infectious disease to spread. We consider an epidemic model that is network based and non-Markovian, containing classic Kermack-McKendrick, pairwise,…
Individual contributions to the spread of an epidemic vary widely due to an individual's location in a social network and their intrinsic ability to spread or contract diseases. While the effect of heterogeneous population structure and…
Time-varying network topologies can deeply influence dynamical processes mediated by them. Memory effects in the pattern of interactions among individuals are also known to affect how diffusive and spreading phenomena take place. In this…
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…
A general formalism is introduced to allow the steady state of non-Markovian processes on networks to be reduced to equivalent Markovian processes on the same substrates. The example of an epidemic spreading process is considered in detail,…
Much effort has been directed towards using mathematical models to understand and predict contagious disease, in particular Ebola outbreaks. Classical SIR (susceptible-infected-recovered) compartmental models capture well the dynamics of…
The exact analytical solution in closed form of a modified SIR system where recovered individuals are removed from the population is presented. In this dynamical system the populations $S(t)$ and $R(t)$ of susceptible and recovered…
Current modeling of infectious diseases allows for the study of complex and realistic scenarios that go from the population to the individual level of description. However, most epidemic models assume that the spreading process takes place…
The SIR model is a three-compartment model of the time development of an epidemic. After normalizing the dependent variables, the model is a system of two non-linear differential equations for the susceptible proportion $S$ and the infected…
We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters---governing within-household…
Mathematical models are formal and simplified representations of the knowledge related to a phenomenon. In classical epidemic models, a neglected aspect is the heterogeneity of disease transmission and progression linked to the viral load…
The outcome of SIR epidemics with heterogeneous infective lifetimes, or heterogeneous susceptibilities, can be mapped onto a directed percolation process on the underlying contact network. In this paper we study SIR models where…
We develop a new methodology for the efficient computation of epidemic final size distributions for a broad class of Markovian models. We exploit a particular representation of the stochastic epidemic process to derive a method which is…
We show that the mean field equations for the SIR epidemic can be exactly solved for a network with arbitrary degree distribution. Our exact solution consists of reducing the dynamics to a lone first order differential equation, which has a…
We consider an SIR epidemic model propagating on a configuration model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three…
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,…
In this paper we study the susceptible-infectious (SI) epidemiological model using dynamical graphs. Dynamical structures have been recently applied in many areas including complex systems. Dynamical structures include the mutual…
In this paper, we study the dynamics of epidemic processes taking place in temporal and adaptive networks. Building on the activity-driven network model, we propose an adaptive model of epidemic processes, where the network topology…