Related papers: A consistent discrete version of a non-autonomous …
We consider extinction times for a class of birth-death processes commonly found in applications, where there is a control parameter which determines whether the population quickly becomes extinct, or rather persists for a long time. We…
We analyze a family of methods for statistical causal inference from sample under the so-called Additive Noise Model. While most work on the subject has concentrated on establishing the soundness of the Additive Noise Model, the statistical…
We demonstrate how direct simulation of stochastic, individual-based models can be combined with continuum numerical analysis techniques to study the dynamics of evolving diseases. % Sidestepping the necessity of obtaining explicit…
Stochastic differential equations characterized by uncertainty are effective in modelling virus dynamics and provide an alternative to traditional deterministic models. Epidemic models are inevitably subjected to the randomness within the…
The study of epidemic models plays an important role in mathematical epidemiology. There are many researches on epidemic models using ordinary differential equations, partial differential equations or stochastic differential equations. In…
In this study, we investigate a stochastic SIR model with media effects. The uniqueness and the existence of a global positive solution are studied. The sufficient conditions of extinction and persistence of the disease are established. We…
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…
We consider a discrete-time epidemic SISI model in case when the population size is a constant, so the per capita death rate is equal to per capita birth rate. The evolution operator of this model is a non-linear operator which depends on…
We present a tractable class of one-dimensional McKean-Vlasov equations that allow for unique strong solutions and extend the dynamics of various SIS epidemic models that are well-established in the literature. While the…
We study statistical inference for small-noise-perturbed multiscale dynamical systems under the assumption that we observe a single time series from the slow process only. We construct estimators for both averaging and homogenization…
We review and study the correspondence between discrete linear lattice/chain models of interacting particles and their continuous counterparts represented by linear partial differential equations. In particular, we study the correspondence…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
This is a truncation of the second year group project at Imperial college london. In this paper, we consider a semilinear reaction diffusion system of SIR model which involves the birth rate and the death rate. We first prove the…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes…
We consider multiple diseases spreading in a static Configuration Model network. We make standard assumptions that infection transmits from neighbor to neighbor at a disease-specific rate and infected individuals recover at a…
A numerical study of synchronization and extinction is done for a SIRS model with fixed infective and refractory periods, in the regime of high infectivity, on one- and two-dimensional networks for which the connectivity probability decays…
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…
Diffusion models generate high-dimensional data such as images by learning a process that gradually removes noise from corrupted data. Recent studies have shown that the backward dynamics of diffusion models exhibit two characteristic…
We analyse the problem of stability of a continuous time linear switching system (LSS) versus the stability of its Euler discretization. It is well-known that the existence of a positive {\tau} for which the corresponding discrete time…