Optimal Vaccination in a Stochastic Epidemic Model of Two Non-Interacting Populations

Developing robust, quantitative methods to optimize resource allocations in response to epidemics has the potential to save lives and minimize health care costs. In this paper, we develop and apply a computationally efficient algorithm that enables us to calculate the complete probability distribution for the final epidemic size in a stochastic Susceptible-Infected-Recovered (SIR) model. Based on these results, we determine the optimal allocations of a limited quantity of vaccine between two non-interacting populations. We compare the stochastic solution to results obtained for the traditional, deterministic SIR model. For intermediate quantities of vaccine, the deterministic model is a poor estimate of the optimal strategy for the more realistic, stochastic case.     

Stability of a Stochastic Model of an SIR Epidemic with Vaccination

We prove almost sure exponential stability for the disease-free equilibrium of a stochastic differential equations model of an SIR epidemic with vaccination. The model allows for vertical transmission. The stochastic perturbation is associated with the force of infection and is such that the total population size remains constant in time. We prove almost sure positivity of solutions. The main result concerns especially the smaller values of the diffusion parameter, and describes the stability in terms of an analogue \(\mathcal{R}_\sigma\) of the basic reproduction number \(\mathcal{R}_0\) of the underlying deterministic model, with \(\mathcal{R}_\sigma \le \mathcal{R}_0\). We prove that the disease-free equilibrium is almost sure exponentially stable if \(\mathcal{R}_\sigma <1\).     

一类随机SIR流行病模型的渐近行为研究

考虑了一类恢复率受到噪声影响的随机SIR流行病模型.首先证明了模型非负解的全局存在惟一性;其次证明了当基本再生数R₀≤1时无病平衡点随机渐近稳定,当R₀>1时随机模型的解围绕确定性模型地方病平衡点震荡.最后通过数值仿真验证了所得结论的正确性.     

A Stochastic Epidemic Model with Seasonal Variations in Infection Rate

In this paper we consider a modification of Bailey's stochastic model for the spread of an epidemic when there are seasonal variations in infection rate. The resulting nonlinear model is analyzed by employing the diffusion approximation technique. We have shown that for a large population the process, on suitable scaling and normalization, converges to a non-stationary Ornstein-Uhlenbeck process. Consequently the number of infectives has in the steady state a gaussian distribution.     

真菌基因组数据库概况

阐明不同生物基因组DNA序列信息及破译相关遗传学背景的基因组学是生物学和医学研究的核心学科.最近十年来真菌基因组学研究发生根本性的变化,真菌已成为真核生物基因组研究的最佳模式生物.至2008年6月,近80种隶属于真菌,微孢子虫和卵菌的全基因组序列公布,代表着最广泛的真核生物,它们的基因组大小从2.5 Mb～81.5 Mb.本丈整理了这些数据的相关信息.