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We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition…
Background: The global spread of the severe acute respiratory syndrome (SARS) epidemic has clearly shown the importance of considering the long-range transportation networks in the understanding of emerging diseases outbreaks. The…
The Beyond-Linear-Use-of-Equation-Superposition (BLUES) function method is extended to coupled nonlinear ordinary differential equations and applied to the epidemiological SIRS model with vaccination. Accurate analytic approximations are…
Predicting epidemic dynamics is of great value in understanding and controlling diffusion processes, such as infectious disease spread and information propagation. This task is intractable, especially when surveillance resources are very…
This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…
We investigate the SIR epidemic on a dynamic inhomogeneous Erd\H{o}s-R\'enyi random graph, in which vertices are of one of $k$ types and in which edges appear and disappear independently of each other. We establish a functional law of large…
Nowcasting and forecasting of epidemic spreading rely on incidence series of reported cases to derive the fundamental epidemiological parameters for a given pathogen. Two relevant drawbacks for predictions are the unknown fractions of…
Bayesian inference methods are useful in infectious diseases modeling due to their capability to propagate uncertainty, manage sparse data, incorporate latent structures, and address high-dimensional parameter spaces. However, parameter…
This paper is concerned with the growth rate of SIR (Susceptible-Infectious-Recovered) epidemics with general infectious period distribution on random intersection graphs. This type of graph is characterized by the presence of cliques…
Many epidemic models are naturally defined as individual-based models: where we track the state of each individual within a susceptible population. Inference for individual-based models is challenging due to the high-dimensional state-space…
We present a modelling framework for the spreading of epidemics on temporal networks from which both the individual-based and pair-based models can be recovered. The proposed temporal pair-based model that is systematically derived from…
An stochastic SIS epidemic model in an open environment is presented.
The challenges posed by epidemics and pandemics are immense, especially if the causes are novel. This article introduces a versatile open-source simulation framework designed to model intricate dynamics of infectious diseases across diverse…
In this paper, we propose and analyze a reaction-diffusion susceptible-infected-susceptible (SIS) epidemic patch model. The individuals are assumed to reside in different patches, where they are able to move inside and among the patches.…
In regard to infectious diseases socioeconomic determinants are strongly associated with differential exposure and susceptibility however they are seldom accounted for by standard compartmental infectious disease models. These associations…
Structured epidemic models can be formulated as first-order hyperbolic PDEs, where the "spatial" variables represent individual traits, called structures. For models with two structures, we propose a numerical technique to approximate…
This paper develops an individual-based stochastic network SIR model for the empirical analysis of the Covid-19 pandemic. It derives moment conditions for the number of infected and active cases for single as well as multigroup epidemic…
Within epidemiological modeling, the majority of analyses assume a single epidemic process for generating ground-truth data. However, this assumed data generation process can be unrealistic, since data sources for epidemics are often…
Epidemiological models for the spread of pathogens in a population are usually only able to describe a single pathogen. This makes their application unrealistic in cases where multiple pathogens with similar symptoms are spreading…
Containing the recent West African outbreak of Ebola virus (EBOV) required the deployment of substantial global resources. Operationally, health workers and surveillance teams treated cases, collected genetic samples, and tracked case…