Related papers: Discrete epidemic models with two time scales
The SIR model is one of the most prototypical compartmental models in epidemiology. Generalizing this ordinary differential equation (ODE) framework into a spatially distributed partial differential equation (PDE) model is a considerable…
This paper examines an epidemic patch model with mass-action transmission mechanism and asymmetric connectivity matrix. Results on the global dynamics of solutions and the spatial structures of endemic solutions are obtained. In particular,…
Motivated by our intention to use SIR-type epidemiological models in the context of dynamic networks as provided by large-scale highly interacting inhomogeneous human crowds, we investigate in this framework possibilities to reduce the…
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…
We consider in this paper a general SEIRS model describing the dynamics of an infectious disease including latency, waning immunity and infection-induced mortality. We derive an infinite system of differential equations that provides an…
In this paper we first introduce the general stochastic epidemic model for the spread of infectious diseases. Then we give methods for inferring model parameters such as the basic reproduction number $R_0$ and vaccination coverage $v_c$…
A key parameter in models for the spread of infectious diseases is the basic reproduction number $R_0$, which is the expected number of secondary cases a typical infected primary case infects during its infectious period in a large mostly…
In this work, we review the figures used to characterize an epidemic outbreak most. Particular attention is drawn to epidemic spreading at time-varying transition rates. A time-varying SIR-like model is used to describe the epidemic…
We study the spread of susceptible-infected-recovered (SIR) infectious diseases where an individual's infectiousness and probability of recovery depend on his/her "age" of infection. We focus first on early outbreak stages when stochastic…
This work examines the discrete-time networked SIR (susceptible-infected-recovered) epidemic model, where the infection and recovery parameters may be time-varying. We provide a sufficient condition for the SIR model to converge to the set…
Pandemics can cause immense disruption and damage to communities and societies. Thus far, modeling of pandemics has focused on either large-scale difference equation models like the SIR and the SEIR models, or detailed micro-level…
We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate and it is shown the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence.…
We study the susceptible-infective-recovered (SIR) epidemic on a random graph chosen uniformly subject to having given vertex degrees. In this model infective vertices infect each of their susceptible neighbours, and recover, at a constant…
This paper studies the distribution function of the time of extinction of a subcritical epidemic, when a large enough proportion of the population has been immunized and/or the infectivity of the infectious individuals has been reduced, so…
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…
We develop a multi-patch and multi-group model that captures the dynamics of an infectious disease when the host is structured into an arbitrary number of groups and interacts into an arbitrary number of patches where the infection takes…
We show that the basic reproduction number of an SIS patch model with standard incidence is either strictly decreasing and strictly convex with respect to the diffusion coefficient of infected subpopulation if the patch reproduction numbers…
Multivariate count time series models are an important tool for the analysis and prediction of infectious disease spread. We consider the endemic-epidemic framework, an autoregressive model class for infectious disease surveillance counts,…
The SIR model is the cornerstone model for mathematical epidemiology, explaining key epidemic features such as the second-order transition between disease-free and epidemic states, the initial exponential growth of outbreaks or the…
A network epidemic model is studied. The underlying social network has two different types of group structures, households and workplaces, such that each individual belongs to exactly one household and one workplace. The random network is…