Related papers: Large deviation principle for Poisson driven SDEs …
The behavior at criticality of spatial SIR (susceptible/infected/recovered) epidemic models in dimensions two and three is investigated. In these models, finite populations of size N are situated at the vertices of the integer lattice, and…
Epidemics have shaped human history, often with devastating consequences, motivating the development of mathematical models to understand and control their dynamics. Among the many aspects of epidemic behavior, the conditions that lead to…
This paper is devoted to the problem of sample path large deviations for the Markov processes on R_+^N having a constant but different transition mechanism on each boundary set {x:x_i=0 for i\notin\Lambda, x_i>0 for i\in\Lambda}. The global…
Threshold theorem is probably the most important development of mathematical epidemic modelling. Unfortunately, some models may not behave according to the threshold. In this paper, we will focus on the final outcome of SIR model with…
This paper considers the Cram\'er-Lundberg model, with the additional feature that the number of clients can fluctuate over time. Clients arrive according to a Poisson process, where the times they spend in the system form a sequence of…
The large deviation principle in the small noise limit is derived for solutions of possibly degenerate It\^o stochastic differential equations with predictable coefficients, which may depend also on the large deviation parameter. The result…
The large deviation principle is established for the distributions of a class of generalized stochastic porous media equations for both small noise and short time.
Why are the epidemic patterns of COVID-19 so different among different cities or countries which are similar in their populations, medical infrastructures, and people's behavior? Why are forecasts or predictions made by so-called experts…
In this paper we introduce a novel method to conduct inference with models defined through a continuous-time Markov process, and we apply these results to a classical stochastic SIR model as a case study. Using the inverse-size expansion of…
We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease…
Limit theorems, including the large deviation principle, are established for random point processes (fields), which describe the position distributions of the perfect boson gas in the regime of the Bose-Einstein condensation. We compare…
The spread of an infectious disease depends on intrinsic properties of the disease as well as the connectivity and actions of the population. This study investigates the dynamics of an SIR type model which accounts for human tendency to…
We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one.…
Compartmental models like the Susceptible-Infected-Recovered (SIR)\cite{Kermack1927} and its extensions such as the Susceptible-Exposed-Infected-Recovered (SEIRS)\cite{Ottar2020,Ignazio2021,Grimm2021,Paoluzzi2021} are commonly used to model…
In this paper, we study the averaging principle and central limit theorem for multi-scale stochastic differential equations with state-dependent switching. To accomplish this, we first study the Poisson equation associated with a Markov…
In this paper, we develop a multi-group epidemic framework via virtual dispersal where the risk of infection is a function of the residence time and local environmental risk. This novel approach eliminates the need to define and measure…
Mathematical modelling of the spread of epidemics has been an interesting challenge in the field of epidemiology. The SIR Model proposed by Kermack and McKendrick in 1927 is a prototypical model of epidemiology. However, it has its…
A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…
We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and noise becomes vanishingly small. The law of large numbers…
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…