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

Mathematical Biosciences

Volumn 209, Issue 2, 2007, Pages 361-385

  Gustafsson, Leif ^a   Sternad, Mikael ^b  

^a SWEDISH UNIVERSITY OF AGRICULTURAL SCIENCES   (Sweden)

^b UPPSALA UNIVERSITY   (Sweden)

Author keywords

Consistency; Poisson process; Poisson Simulation; Population model; Stochastic difference equation; Stochastic SIR model

Indexed keywords

ANIMALS; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; POISSON EQUATION; RANDOM PROCESSES;

POISSON PROCESS; POISSON SIMULATION; POPULATION MODELS; STOCHASTIC DIFFERENCE EQUATIONS; STOCHASTIC SIR MODEL;

POPULATION DYNAMICS;

COMPLEXITY; MARKOV CHAIN; POPULATION DISTRIBUTION; POPULATION MODELING; STOCHASTICITY;

ARTICLE; POPULATION DYNAMICS; SIMULATION; STATISTICAL ANALYSIS; STATISTICAL MODEL; STOCHASTIC MODEL; TECHNIQUE;

ANIMALS; HUMANS; MARKOV CHAINS; MATHEMATICS; MODELS, BIOLOGICAL; POISSON DISTRIBUTION; POPULATION DYNAMICS; STOCHASTIC PROCESSES;

ANIMALIA;

EID: 34548548710     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2007.02.004     Document Type: Article

References (41)

1. Bartlett M.S. Stochastic Population Models in Ecology and Epidemiology (1960), Wiley, NY
2. Lande R., Engen S., and Saether B.-E. Stochastic Population Dynamics in Ecology and Conservation: An Introduction (2003), Oxford University, Oxford
3. J.H. Matis, T.R. Kiffe, Stochastic Population Models: A Compartmental Perspective: v. 145, Lecture Notes in Statistics S. Springer, NY, 2000.
4. J.R. Clymer. Systems Analysis Using Simulation and Markov Models Prentice Hall International Series in Industrial & Systems Engineering. NJ, 1991.
5. Mode C.J., and Sleeman C.K. Stochastic Processes in Epidemiology: HIV/AIDS, Other Infectious Diseases and Computers (2000), World Scientific Publishing Co., Singapore
6. Fishman G.S. Principles of Discrete Event Simulation (1978), John Wiley & Sons, NY
7. Banks J., Carson J.S., Nelson B., and Nicol D. Discrete Event Simulation (2005), Prentice Hall, NJ
8. Grimm V., and Railsback S.F. Individual-Based Modeling and Ecology (Princeton Series in Theoretical & Computational Biology) (2005), Princeton University, NJ
9. Korn G.A., and Wait J.V. Digital Continuous-system Simulation (1978), Prentice Hall, NJ
10. Cellier F.E., and Kofman E. Continuous System Simulation (2006), Springer, NY
11. Gustafsson L. Poisson Simulation - A Method for Generating Stochastic Variations in Continuous System Simulation. Simulation 74 5 (2000) 264
12. Kreutzer W. System Simulation: Programming Styles and Languages (1986), Addison-Wesley Publishing Company, Inc., Sydney
13. Hamilton M.S. Estimating Length and Orders of Delays in System Dynamics Models. In: Randers J. (Ed). Elements of the System Dynamics Method (1980), The MIT, MA 162
14. Kermack W.O., and McKendrick A.G. Contributions to the Mathematical Theory of Epidemics. Proc. Royal Soc. A 115 (1927) 700
15. Bailey N.T.J. The Mathematical Theory of Infectious Diseases and its Applications (1975), Griffin, London
16. Anderson R.M., and May R.M. Infectious Diseases of Humans: Dynamics and Control (1991), Oxford University, Oxford
17. Andersson H., and Britton T. Stochastic Epidemic Models and Their Statistical Analysis. Lecture notes in Statistics 151 (2000), Springer, NY
18. Renshaw E. Modelling Biological Populations in Space and Time (1991), Cambridge University, Cambridge, NY
19. Law A.M., and Kelton W.D. Simulation Modeling and Analysis (1991), McGraw-Hill Inc., NY
20. Bratley P., Fox B.L., and Schrage L.E. A Guide to Simulation (1983), Springer, NY
21. Devore J.L. Probability and Statistics for Engineering and Sciences. Sixth edition. (2004), Thomson Learning, Inc., Toronto, Canada
22. Press W.H., Flannery B.P., Teukolsky S.A., and Vetterling W.T. Numerical Recipes in Pascal - The Art of Scientific Computing (1989), Cambridge University, Cambridge, UK The book is also available in FORTRAN or C
23. Gustafsson L. Studying dynamic and stochastic systems using Poisson Simulation. In: Liljenström H., and Svedin U. (Eds). Micro-Meso-Macro: Addressing Complex Systems Couplings (2005), World Scientific Publishing Company, Singapore 131
24. Gustafsson L. Poisson Simulation as an extension of CSS for the modeling of queuing systems. Simulation 79 9 (2003) 528
25. L. Gustafsson, Tools for Statistical Handling of Poisson Simulation: Documentation of StocRes and ParmEst, Dept. of Biometry and Engineering, The Swedish University of Agricultural Sciences, 2004.
26. T. Hedqvist, Wanda for MATLAB. Methods and Tools for Statistical Handling of Poisson Simulation, Uppsala University, ISSN: 1401-5749, UPTEC IT0422, Uppsala, Sweden, 2004.
27. Powersim Reference Manual, Powersim Corporation, 1175 Herndon Parkway, suite 600, Herndon, VA 22170, USA, Powersim Press, 1996. (A free demo to test the examples in this paper is found at: www.powersim.com. Note for using the statistical tools the so called Powersim Constructor should be used.).
28. Using MATLAB, The MathWorks, Inc. Natick, MA., 2002.
29. ® User's Guide. Version 6.0. Borland International, CA, 1990.
30. Greenwood M. On the statistical measure of infectiousness. J. Hyg. Camb. 31 (1931) 336
31. Braun M. Differential Equations and Their Applications (1993), Springer, NY
32. Haefner J.W. Modeling Biological Systems: Principles and Applications (1996), Chapman and Hall, International Thomson Publishing, NY
33. V. Volterra. "Variazioni e fluttuazioni del numero d'individui in specie animali conviventi." Memoire della R. Accademia Nazionale dei Lincei, anno CCCCXXIII, II, 1926, pp. 1-110.
34. Waggoner P.E. Progress curves and Foliar diseases: their interpretation and use. In: Leonard K.J., and Fry W.E. (Eds). Plant Disease Epidemiology - Population Dynamics and Management 1 (1986), Macmillan Publishing Company, NY
35. Clayton D., and Hills M. Statistical Models in Epidemiology (1993), Oxford University, Oxford
36. Elinder F., Frankenhaeuser B., and Århem P. Non-stationary analysis of the Na current in myelinated nerve fibers of Xenopus laevis: experiments and stochastic simulations. BioSystems 62 (2001) 13
37. Luenberger D.G. Introduction to Dynamic Systems: Theory Models and Applications (1979), John Wiley & Sons Inc., NY
38. F. Lanchester, Aircraft in Warfare, the Dawn of the Fourth Arm. Constable: London, UK, 1916.
39. L. Ljung. System Identification - Theory for the User. Prentice-Hall Ptr. Upper Saddle River, New Jersey, second ed., 1999.
40. Tong H. Non-linear Time Series - A Dynamic System Approach (1990), Oxford University, Oxford
41. Cooke D., Craven A.H., and Clarke G.M. Basic Statistical Computing (1982), Edward Arnold Ltd., London