期刊文献+
共找到2篇文章
< 1 >
每页显示 20 50 100
Applications of Dynamic-Equilibrium Continuous Markov Stochastic Processes to Elements of Survival Analysis
1
作者 Eugen Mamontov Ziad Taib 《Journal of Applied Mathematics and Physics》 2019年第1期55-71,共17页
In this article, we summarize some results on invariant non-homogeneous and dynamic-equilibrium (DE) continuous Markov stochastic processes. Moreover, we discuss a few examples and consider a new application of DE pro... In this article, we summarize some results on invariant non-homogeneous and dynamic-equilibrium (DE) continuous Markov stochastic processes. Moreover, we discuss a few examples and consider a new application of DE processes to elements of survival analysis. These elements concern the stochastic quadratic-hazard-rate model, for which our work 1) generalizes the reading of its It? stochastic ordinary differential equation (ISODE) for the hazard-rate-driving independent (HRDI) variables, 2) specifies key properties of the hazard-rate function, and in particular, reveals that the baseline value of the HRDI variables is the expectation of the DE solution of the ISODE, 3) suggests practical settings for obtaining multi-dimensional probability densities necessary for consistent and systematic reconstruction of missing data by Gibbs sampling and 4) further develops the corresponding line of modeling. The resulting advantages are emphasized in connection with the framework of clinical trials of chronic obstructive pulmonary disease (COPD) where we propose the use of an endpoint reflecting the narrowing of airways. This endpoint is based on a fairly compact geometric model that quantifies the course of the obstruction, shows how it is associated with the hazard rate, and clarifies why it is life-threatening. The work also suggests a few directions for future research. 展开更多
关键词 Non-Homogeneous Continuous Markov stochastic Process Invariant Process Dynamic Equilibrium Diffusion stochastic Process ito stochastic Ordinary differential Equation Survival Analysis Hazard Rate Obstructive Lung Disease
下载PDF
Stochastic SIS metapopulation models for the spread of disease among species in a fragmented landscape
2
作者 Amy J. Ekanayake 《International Journal of Biomathematics》 2016年第4期97-119,共23页
Two stochastic models are derived for a susceptible-infectious-susceptible epidemic spreading through a metapopulation: a continuous time Markov chain (CTMC) model and an It6 stochastic differential equation (SDE... Two stochastic models are derived for a susceptible-infectious-susceptible epidemic spreading through a metapopulation: a continuous time Markov chain (CTMC) model and an It6 stochastic differential equation (SDE) model. The stochastic models are numerically compared. Close agreement suggests that computationally intense CTMC simulations can be approximated by simpler SDE simulations. Differential equations for the moments of the SDE probability distribution are also derived, the steady states are solved numerically using a moment closure technique, and these results are compared to simulations. The moment closure technique only coarsely approximates simulation results. The effect of model parameters on stability of the disease-free equilibrium is also numerically investigated. 展开更多
关键词 EPIDEMIC METAPOPULATION ito stochastic differential equation Markov chain moment closure.
原文传递
上一页 1 下一页 到第
使用帮助 返回顶部