Related papers: Fast variables determine the epidemic threshold in…
Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…
The last decade saw the advent of increasingly realistic epidemic models that leverage on the availability of highly detailed census and human mobility data. Data-driven models aim at a granularity down to the level of households or single…
In this paper, a branching process approximation for the spread of a Reed-Frost epidemic on a network with tunable clustering is derived. The approximation gives rise to expressions for the epidemic threshold and the probability of a large…
Understanding the dynamics of computer virus (malware, worm) in cyberspace is an important problem that has attracted a fair amount of attention. Early investigations for this purpose adapted biological epidemic models, and thus inherited…
We present an exact analytical solution to a one-dimensional model of the Susceptible-Infected-Recovered (SIR) epidemic type, with infection rates dependent on nearest-neighbor occupations. We use a quantum mechanical approach, transforming…
This paper studies the spread dynamics of a stochastic SIRS epidemic model with nonlinear incidence and varying population size, which is formulated as a piecewise deterministic Markov process. A threshold dynamic determined by the basic…
We consider the edge-based compartmental models for infectious disease spread introduced in Part I. These models allow us to consider standard SIR diseases spreading in random populations. In this paper we show how to handle deviations of…
A class of multiple-timescale asymptotic solutions to the equations of the susceptible-infected-recovered (SIR) model is presented for the case of high basic reproduction number, with the inverse of the latter employed as the expansion…
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 multilayer SIR model with two levels of mixing, namely a global level which is uniformly mixing, and a local level with two layers distinguishing household and workplace contacts, respectively. We establish the large population…
Network epidemiology often assumes that the relationships defining the social network of a population are static. The dynamics of relationships is only taken indirectly into account, by assuming that the relevant information to study…
In this paper, we develop a multi-group epidemic framework via virtual dispersal where the risk of infection is a function of the residence time and local environmental risk. This novel approach eliminates the need to define and measure…
Theoretical modeling of computer virus/worm epidemic dynamics is an important problem that has attracted many studies. However, most existing models are adapted from biological epidemic ones. Although biological epidemic models can…
This paper extends the canonical model of epidemiology, the SIRD model, to allow for time-varying parameters for real-time measurement and prediction of the trajectory of the Covid-19 pandemic. Time variation in model parameters is captured…
Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR…
Networked SIR models have become essential workhorses in the modeling of epidemics, their inception, propagation and control. Here, and building on this venerable tradition, we report on the emergence of a remarkable self-organization of…
Wildlife disease surveillance programs and research studies track infection and identify risk factors for wild populations, humans, and agriculture. Often, several types of samples are collected from individuals to provide more complete…
The metapopulation framework is adopted in a wide array of disciplines to describe systems of well separated yet connected subpopulations. The subgroups or patches are often represented as nodes in a network whose links represent the…
In this project, identifiability, observability and uncertainty properties of the deterministic and Chain Binomial stochastic SIR, SEIR and SEIAR epidemiological models are studied. Techniques for modeling overdispersion are investigated…
Multidimensional continuous-time Markov jump processes $(Z(t))$ on $\mathbb{Z}^p$ form a usual set-up for modeling $SIR$-like epidemics. However, when facing incomplete epidemic data, inference based on $(Z(t))$ is not easy to be achieved.…