Related papers: On SIR-type epidemiological models and population …
We introduce a mathematical description of the impact of sociality in the spread of infectious diseases by integrating an epidemiological dynamics with a kinetic modeling of population-based contacts. The kinetic description leads to study…
Contagious processes, such as spread of infectious diseases, social behaviors, or computer viruses, affect biological, social, and technological systems. Epidemic models for large populations and finite populations on networks have been…
Recent work from public health experts suggests that incorporating human behavior is crucial in faithfully modeling an epidemic. We present a reaction-diffusion partial differential equation SIR-type population model for an epidemic…
We study a SEIR model considered by Gomes et al. \cite{Gomes2020} and Aguas et al. \cite{Aguas2020} where different individuals are assumed to have different levels of susceptibility or exposure to infection. Under this heterogeneity…
We propose a network behavioral-feedback Susceptible-Infected-Recovered (SIR) epidemic model in which the interaction matrix describing the infection rates across subpopulations depends in feedback on the current epidemic state. This model…
We study the long-time behavior of solutions of the SIRS model, a reaction-diffusion system that appears in epidemiology to describe the spread of epidemics. We allow the system to be heterogeneous periodic. Under some hypotheses on the…
We investigate an SIR model of epidemic propagation on networks in the context of mean-field games. In a real epidemic, individuals adjust their behavior depending on the epidemic level and the impact it might have on them in the future.…
In this paper, we study how interactions between populations impact epidemic spread. We extend the classical SEIR model to include both integration-based disease transmission simulation and population flow. Our model differs from existing…
Modeling epidemic dynamics plays an important role in studying how diseases spread, predicting their future course, and designing strategies to control them. In this letter, we introduce a model of SIR (susceptible-infected-removed) type…
Susceptible-Infected-Recovered (SIR) models have been used for decades to understand epidemic outbreak dynamics. We develop an SIR model specifically designed to study the effects of population behavior with respect to health and…
The importance of modeling the spread of epidemics through a population has led to the development of mathematical models for infectious disease propagation. A number of empirical studies have collected and analyzed data on contacts between…
We study a multi-type SIR epidemic process among a heterogeneous population that interacts through a network. When we base social contact on a random graph with given vertex degrees, we give limit theorems on the fraction of infected…
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…
In this paper, we focus on the influence of heterogeneity and stochasticity of the population on the dynamical structure of a basic susceptible-infected-susceptible (SIS) model. First we prove that, upon a suitable mathematical…
We investigate the role of global mixing in epidemic processes. We first construct a simplified model of the SIR epidemic using a realistic population distribution. Using this model, we examine possible mechanisms for destruction of spatial…
The Susceptible-Infectious-Recovered (SIR) model is the canonical model of epidemics of infections that make people immune upon recovery. Many of the open questions in computational epidemiology concern the underlying contact structure's…
The adoption of prophylaxis attitudes, such as social isolation and use of face masks, to mitigate epidemic outbreaks strongly depends on the support of the population. In this work, we investigate a susceptible-infected-recovered (SIR)…
We define and study an open stochastic SIR (Susceptible -- Infected -- Removed) model on a graph in order to describe the spread of an epidemic on a cattle trade network with epidemiological and demographic dynamics occurring over the same…
Infectious diseases are practically represented by models with multiple states and complex transition rules corresponding to, for example, birth, death, infection, recovery, disease progression, and quarantine. In addition, networks…
The transmission dynamics of an epidemic are rarely homogeneous. Super-spreading events and super-spreading individuals are two types of heterogeneous transmissibility. Inference of super-spreading is commonly carried out on secondary case…