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The low-temperature coarsening dynamics of a one-dimensional Ising model, with conserved magnetisation and subject to a small external driving force, is studied analytically in the limit where the volume fraction \mu of the minority phase…
We study seasonal epidemic spreading in a susceptible-infected-removed-susceptible (SIRS) model on smallworld graphs. We derive a mean-field description that accurately captures the salient features of the model, most notably a phase…
Partial differential equation (PDE) models for infectious diseases, while less common than their ordinary differential equation (ODE) counterparts, have found successful applications for many years. Such models are typically of…
We consider SISI epidemic model with discrete-time. The crucial point of this model is that an individual can be infected twice. This non-linear evolution operator depends on seven parameters and we assume that the population size under…
We investigate the long-time dynamics of a SIR epidemic model in the case of a population of pathogens infecting a homogeneous host population. The pathogen population is structured by a genotypic variable. When the initial mass of the…
The aim of this paper is to study the dynamics of a reaction--diffusion SIS (susceptible-infectious-susceptible) epidemic model with a nonlinear incidence rate describing the transmission of a communicable disease between individuals. We…
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…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
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…
This paper analyzes a Susceptible-Infected-Susceptible (SIS) model of epidemic propagation over hypergraphs and, motivated by an important special case, we refer to the model as to the simplicial SIS model. Classically, the multi-group SIS…
Characterizing the spatial extent of epidemics at the outbreak stage is key to controlling the evolution of the disease. At the outbreak, the number of infected individuals is typically small, so that fluctuations around their average are…
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…
Throughout the course of an epidemic, the rate at which disease spreads varies with behavioral changes, the emergence of new disease variants, and the introduction of mitigation policies. Estimating such changes in transmission rates can…
Reaction-diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem.…
The main purpose of this paper is to study the Dynamical behaviors of a stochastic SIS epidemic model using mean-reverting inhomogeneous geometric brownian motion process. First we demonstrate the existence of a global-in-time solution and…
We study domain distributions in the one-dimensional Ising model subject to zero-temperature Glauber and Kawasaki dynamics. The survival probability of a domain, $S(t)\sim t^{-\psi}$, and an unreacted domain, $Q_1(t)\sim t^{-\delta}$, are…
We extend the classical SIR model of infectious disease spread to account for time dependence in the parameters, which also include diffusivities. The temporal dependence accounts for the changing characteristics of testing, quarantine and…
A significant proportion of the infections driving the current {SARS-CoV-2} pandemic are transmitted asymptomatically. Here we introduce and study a simple epidemic model with separate compartments comprising asymptomatic and symptomatic…
Consider a large uniformly mixing dynamic population, which has constant birth rate and exponentially distributed lifetimes, with mean population size $n$. A Markovian SIR (susceptible $\to$ infective $\to$ recovered) infectious disease,…
The SIR model with spatially inhomogeneous infection rate is studied with numerical simulations in one, two, and three dimensions, considering the case that the infection spreads inhomogeneously in densely populated regions or hot spots. We…