Related papers: Large deviation principle for Poisson driven SDEs …
This paper focuses on and analyzes realistic SIR models that take stochasticity into account. The proposed systems are applicable to most incidence rates that are used in the literature including the bilinear incidence rate, the…
Power-law scalings are ubiquitous to physical phenomena undergoing a continuous phase transition. The classic Susceptible-Infectious-Recovered (SIR) model of epidemics is one such example where the scaling behavior near a critical point has…
We establish the large deviation principle for solutions of one-dimensional SDEs with discontinuous coefficients. The main statement is formulated in a form similar to the classical Wentzel--Freidlin theorem, but under the considerably…
This paper is concerned with the study of a diffusive perturbation of the linear LSW model introduced by Carr and Penrose. A main subject of interest is to understand how the presence of diffusion acts as a selection principle, which…
Growing literatures on epidemic and rumor dynamics show that infection and information coevolve. We present a unified framework for modeling the spread of infection and information: a general class of interaction-driven fluid-limit models…
We introduce a stochastic SIR-type partial differential equation model incorporating random diffusion, reinfection, vital dynamics, and a randomly varying transmission rate. For the associated random dynamical system, we prove the existence…
We prove large deviation principles for two versions of fractional Poisson processes. Firstly we consider the main version which is a renewal process; we also present large deviation estimates for the ruin probabilities of an insurance…
Consider an intersection measure $\ell_t ^{\mathrm{IS}}$ of $p$ independent (possibly different) $m$-symmetric Hunt processes up to time $t$ in a metric measure space $E$ with a Radon measure $m$. We derive a Donsker-Varadhan type large…
Different countries -- and sometimes different regions within the same countries -- have adopted different strategies in trying to contain the ongoing COVID-19 epidemic; these mix in variable parts social confinement, early detection and…
The ubiquity of oscillations in epidemics presents a long standing challenge for the formulation of epidemic models. Whether they are external and seasonally driven, or arise from the intrinsic dynamics is an open problem. It is known that…
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…
We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…
We propose a simple SIR model in order to investigate the impact of various confinement strategies on a most virulent epidemic. Our approach is motivated by the current COVID-19 pandemic. The main hypothesis is the existence of two…
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…
In this paper we introduce an agent-based epidemiological model that generalizes the classical SIR model by Kermack and McKendrick. We further provide a multiscale approach to the derivation of a macroscopic counterpart via the mean-field…
We establish a large deviation principle for time dependent trajectories (paths) of the empirical density of $N$ particles with long range interactions, for homogeneous systems. This result extends the classical kinetic theory that leads to…
In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.
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…
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…
We propose an extension of the classical susceptible infectious recovered (SIR) model that incorporates the effects of spatial propagation of an epidemic through a small number of additional compartments. The model is designed to capture…