Convergence of a particle approximation for the quasi-stationary distribution of a diffusion process: uniform estimates in a compact soft case. p, li { white-space: pre-wrap; }

We establish the convergences (with respect to the simulation time $t$; the number of particles $N$; the timestep $\gamma$) of a Moran/Fleming-Viot type particle scheme toward the quasi-stationary distribution of a diffusion on the $d$-dimensional torus, killed at a smooth rate. In these conditions, quantitative bounds are obtained that, for each parameter ($t\rightarrow \infty$, $N\rightarrow \infty$ or $\gamma\rightarrow 0$) are independent from the two others. p, li { white-space: pre-wrap; }

Quasi-stationary probability distribution for the SIR epidemic model

In this paper, we propose two new approximations to the joint quasi-stationary distribution (QSD) of the number susceptible and infected individuals in the Susceptible-Infected-Recovered (SIR) stochastic epidemic model and we derive the marginal QSD of the infected individuals. These two approximations depend on the basic reproduction number [Formula: see text] and give a positive probability of the QSD to all the transient states. Numerical comparisons are presented to check the accuracy of these approximations.

Speed of convergence to the quasi-stationary distribution for Lévy input fluid queues

In this note, we prove that the speed of convergence of the workload of a Lévy-driven queue to the quasi-stationary distribution is of order 1/t. We identify also the Laplace transform of the measure giving this speed and provide some examples.

2019-nCoV Transmission in Hubei Province, China: Stochastic and Deterministic Analyses

Currently, a novel coronavirus (2019-nCoV) causes an outbreak of viral pneumonia in Hubei province, China. In this paper, stochastic and deterministic models are proposed to investigate the transmission mechanism of 2019-nCoV from 15 January to 5 February 2020 in Hubei province. For the deterministic model, basic reproduction number R0 is defined and endemic equilibrium is given. Under R0>1, quasi-stationary distribution of the stochastic process is approximated by Gaussian diffusion. Residual, sensitivity, dynamical, and diffusion analyses of the models are conducted. Further, control variables are introduced to the deterministic model and optimal strategies are provided. Based on empirical results, we suggest that the first and most important thing is to control input, screening, treatment, and isolation.