Stochastic Processes in Epidemiology - HIV/AIDS, Other Infectious Diseases and Computers

Mode, Charles J.; Sleeman, Candace K

doi:10.1142/9789812779250

Cited by 39 publications

(42 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Just remove the Po[DtAE ]/Dt part of the flow rate equations F 1 and F 2 , above. The concept 'embedded model' is important because when an embedded deterministic model behaves similarly to the stochastic model, it is meaningful to perform theoretical analysis on the simpler, deterministic model [5].…”

Section: Making the Macro-model Stochastic And Discretementioning

confidence: 99%

“…This seems reasonable since a population at study develops in continuous time. However discrete-time models such as Markov chain models [4,5], chain-binomial models [15], ARMA models [39], time series models [40], etc. are often used.…”

Section: Appendix B Discrete-time Modellingmentioning

confidence: 99%

“…What makes Markov theory [4,5] important in this context is that it is probably the most powerful method to theoretically analyse population models. For a given conceptual population model, realisations as a Markov model, micro-model and Poisson Simulation model are all consistent.…”

Section: Appendix C Markov Models and Poisson Simulationmentioning

confidence: 99%

“…A population model can be described as a discrete Markov process, also called Markov jump process, in discrete or continuous time [4,5]. However for sufficiently small time-steps in the discrete-time case, the result will be the same as for the continuous time case.…”

Section: C1 Discrete Markov Process In Continuous or Discrete Timementioning

confidence: 99%

“…The most powerful tool for theoretical analysis of population models is probably Markov theory [4,5]. However, a number of more or less distorting simplifications, modifications and additional assumptions are usually needed to perform a mathematical or statistical analysis even on rather simple models.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Bringing consistency to simulation of population models – Poisson Simulation as a bridge between micro and macro simulation

Gustafsson

Sternad

2007

Mathematical Biosciences

View full text Add to dashboard Cite

Population models concern collections of discrete entities such as atoms, cells, humans, animals, etc., where the focus is on the number of entities in a population. Because of the complexity of such models, simulation is usually needed to reproduce their complete dynamic and stochastic behaviour. Two main types of simulation models are used for different purposes, namely micro-simulation models, where each individual is described with its particular attributes and behaviour, and macro-simulation models based on stochastic differential equations, where the population is described in aggregated terms by the number of individuals in different states. Consistency between micro-and macro-models is a crucial but often neglected aspect. This paper demonstrates how the Poisson Simulation technique can be used to produce a population macro-model consistent with the corresponding micro-model. This is accomplished by defining Poisson Simulation in strictly mathematical terms as a series of Poisson processes that generate sequences of Poisson distributions with dynamically varying parameters. The method can be applied to any population model. It provides the unique stochastic and dynamic macro-model consistent with a correct micro-model. The paper also presents a general macro form for stochastic and dynamic population models. In an appendix Poisson Simulation is compared with Markov Simulation showing a number of advantages. Especially aggregation into state variables and aggregation of many events per time-step makes Poisson Simulation orders of magnitude faster than Markov Simulation. Furthermore, you can build and execute much larger and more complicated models with Poisson Simulation than is possible with the Markov approach.

show abstract

Section: Making the Macro-model Stochastic And Discretementioning

confidence: 99%

Section: Appendix B Discrete-time Modellingmentioning

confidence: 99%

Section: Appendix C Markov Models and Poisson Simulationmentioning

confidence: 99%

Section: C1 Discrete Markov Process In Continuous or Discrete Timementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bringing consistency to simulation of population models – Poisson Simulation as a bridge between micro and macro simulation

Gustafsson

Sternad

2007

Mathematical Biosciences

View full text Add to dashboard Cite

show abstract

AIDSStochastic Models

Tan

2005

Encyclopedia of Statistical Sciences

View full text Add to dashboard Cite

To model the HIV epidemic, there are four different approaches: The deterministic models, the stochastic models, the statistical models, and the state space models. The last three models treat the HIV epidemic as random processes. This article presents a systematic review of these random processes. It illustrates how to develop stochastic models and statistical models of the HIV epidemic and how to combine these models into state space models. Using a homosexual population as an example, it illustrates how to develop stochastic equations for the state variables and how to use the state space models to develop a generalized Bayesian method to estimate the unknown parameters and the state variables. The methodology is illustrated by using the AIDS incidence data of the San Francisco homosexual population.

show abstract

On computer‐intensive simulation and estimation methods for rare‐event analysis in epidemic models

Clémençon

Cousien

Felipe

et al. 2015

Statistics in Medicine

View full text Add to dashboard Cite

This article focuses, in the context of epidemic models, on rare events that may possibly correspond to crisis situations from the perspective of public health. In general, no close analytic form for their occurrence probabilities is available, and crude Monte Carlo procedures fail. We show how recent intensive computer simulation techniques, such as interacting branching particle methods, can be used for estimation purposes, as well as for generating model paths that correspond to realizations of such events. Applications of these simulation-based methods to several epidemic models fitted from real datasets are also considered and discussed thoroughly.

show abstract

Stochastic Processes in Epidemiology - HIV/AIDS, Other Infectious Diseases and Computers

Cited by 39 publications

References 0 publications

Bringing consistency to simulation of population models – Poisson Simulation as a bridge between micro and macro simulation

Bringing consistency to simulation of population models – Poisson Simulation as a bridge between micro and macro simulation

AIDSStochastic Models

On computer‐intensive simulation and estimation methods for rare‐event analysis in epidemic models

Contact Info

Product

Resources

About