Augmenting Petri nets to model health-care protocols

Abstract An outbreak of an infectious illness can be devastating for a population. Once confirmed, local health-care organizations will attempt to reduce the spread of the disease by adopting a protocol in response. Modelling health-care protocols requires the inclusion of both timing and probability constraints. Choice-point nets , a form of augmented Petri nets, are ideal for the task. In this data structure, time is associated with event-based transitions that may result in several possible outcomes, each of which is given a probability of occurrence. These nets may be analyzed by unravelling them into finite-state automata. By translating questions about the protocol into the mathematical language of the net, recursive algorithms may then be employed to provide health-care professionals with answers.

[1]  Bernard P. Zeigler,et al.  DEVS today: recent advances in discrete event-based information technology , 2003, 11th IEEE/ACM International Symposium on Modeling, Analysis and Simulation of Computer Telecommunications Systems, 2003. MASCOTS 2003..

[2]  Susanna Donatelli,et al.  CSL Model Checking for Generalized Stochastic Petri Nets , 2006, Third International Conference on the Quantitative Evaluation of Systems - (QEST'06).

[3]  W. Wonham,et al.  Supervisory control of timed discrete-event systems , 1994, IEEE Trans. Autom. Control..

[4]  Armand Toguyéni,et al.  State Observer for DES Under Partial Observation with Time Petri Nets , 2009, Discret. Event Dyn. Syst..

[5]  S. Lafortune.  Supervisory Control Of Discrete Event Systems , 2011 .

[6]  Gianfranco Balbo,et al.  Introduction to Generalized Stochastic Petri Nets , 2007, SFM.

[7]  Marco Ajmone Marsan,et al.  Modelling with Generalized Stochastic Petri Nets , 1995, PERV.

[8]  Hanifa Boucheneb,et al.  On-the-fly TCTL model checking for time Petri nets , 2009, Theor. Comput. Sci..

[9]  Hiroki Inoue,et al.  Computer-simulated assessment of methods of transporting severely injured individuals in disaster - Case study of an airport accident , 2006, Comput. Methods Programs Biomed..

[10]  David L. Craft,et al.  Emergency response to a smallpox attack: The case for mass vaccination , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Arunkumar Pennathur,et al.  Modeling hospital response to mild and severe influenza pandemic scenarios under normal and expanded capacities. , 2007, Military medicine.

[12]  Mariel S. Lavieri,et al.  A Florida County Locates Disaster Recovery Centers , 2005, Interfaces.

[13]  Serge Haddad,et al.  Comparison of Different Semantics for Time Petri Nets , 2005, ATVA.

[14]  Christos G. Cassandras,et al.  Introduction to Discrete Event Systems , 1999, The Kluwer International Series on Discrete Event Dynamic Systems.

[15]  Albert Benveniste,et al.  Markov nets: probabilistic models for distributed and concurrent systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[16]  Vijay Gehlot,et al.  An introduction to systems modeling and simulation with Colored Petri Nets , 2010, Proceedings of the 2010 Winter Simulation Conference.

[17]  Q. Hu,et al.  Markov decision processes with their applications , 2007 .

[18]  Nancy G. Leveson.  Model-Based Analysis of Socio-Technical Risk , 2004 .

[19]  S. Chung,et al.  Limited lookahead policies in supervisory control of discrete event systems , 1992 .

[20]  C. S. Oliveira,et al.  Casualty treatment after earthquake disasters: development of a regional simulation model. , 2000, Disasters.

[21]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[22]  Gang Xu,et al.  Reachability Analysis of Real-Time Systems Using Time Petri Nets , 2000 .

[23]  Shirley Dex,et al.  JR 旅客販売総合システム（マルス）における運用及び管理について , 1991 .

[24]  Karen Rudie,et al.  Limited lookahead supervisory control of probabilistic discrete-event systems , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[25]  Mark Lawford,et al.  Probabilistic Supervisory Control of Probabilistic Discrete Event Systems , 2009, IEEE Transactions on Automatic Control.

[26]  Stephan Merz,et al.  Model Checking , 2000 .

[27]  Dominique Pontier,et al.  Modeling transmission of directly transmitted infectious diseases using colored stochastic Petri nets. , 2003, Mathematical biosciences.

[28]  Stefan Haar,et al.  Choice-point nets: A discrete-event modelling technique for analyzing health care protocols , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[29]  K. Rudie,et al.  Discrete-event systems model of an outbreak response , 2008, 2008 American Control Conference.

[30]  Stephen P. Brooks,et al.  Markov Decision Processes. , 1995 .

[31]  Mike Criswell,et al.  Emergency Department Divert Avoidance Using Petri Nets , 2007, 2007 IEEE International Conference on System of Systems Engineering.

[32]  B.P. Zeigler,et al.  Symbolic discrete event system specification , 1992, IEEE Trans. Syst. Man Cybern..

[33]  Frank Drews,et al.  Interactive Agent Based Modeling of Public Health Decision-Making , 2009, AMIA.

[34]  MengChu Zhou,et al.  Modeling and performance analysis of medical services systems using Petri nets , 1994, Proceedings of IEEE International Conference on Systems, Man and Cybernetics.

[35]  C. Macken,et al.  Mitigation strategies for pandemic influenza in the United States. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[36]  A. Mushlin,et al.  Modeling the Public Health Response to Bioterrorism: Using Discrete Event Simulation to Design Antibiotic Distribution Centers , 2002, Medical decision making : an international journal of the Society for Medical Decision Making.

[37]  Nathaniel Hupert,et al.  Recommendations for Modeling Disaster Responses in Public Health and Medicine: A Position Paper of the Society for Medical Decision Making , 2009, Medical decision making : an international journal of the Society for Medical Decision Making.

[38]  René David,et al.  Petri nets and grafcet - tools for modelling discrete event systems , 1992 .

[39]  Michael Sipser,et al.  Introduction to the Theory of Computation , 1996, SIGA.

[40]  W. Wonham,et al.  Control of vector discrete-event systems. I. The base model , 1993, IEEE Trans. Autom. Control..

[41]  Demosthenis Teneketzis,et al.  Diagnosability of stochastic discrete-event systems , 2005, IEEE Transactions on Automatic Control.

[42]  E. Allen Emerson,et al.  The Beginning of Model Checking: A Personal Perspective , 2008, 25 Years of Model Checking.

[43]  Robert K. Kanter,et al.  Strategies to improve pediatric disaster surge response: Potential mortality reduction and tradeoffs , 2007, Critical care medicine.

[44]  Hajo A. Reijers,et al.  Business Process Redesign at a Mental Healthcare Institute: A Coloured Petri Net Approach , 2005 .

[45]  M. Meltzer,et al.  FluSurge—A Tool to Estimate Demand for Hospital Services during the Next Pandemic Influenza , 2006, Medical decision making : an international journal of the Society for Medical Decision Making.

[46]  P. Ramadge,et al.  Supervisory control of a class of discrete event processes , 1987 .

[47]  Wojciech Penczek,et al.  Bounded model checking for knowledge and real time , 2007, Artif. Intell..

[48]  Marta Z. Kwiatkowska,et al.  Model checking for probability and time: from theory to practice , 2003, 18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings..

[49]  M. Brandeau,et al.  Modeling the Logistics of Response to Anthrax Bioterrorism , 2008, Medical decision making : an international journal of the Society for Medical Decision Making.

[50]  T.-J. Ho.  Controller synthesis for some control problems in timed discrete-event systems , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[51]  Xiaolan Xie,et al.  Operating theatre scheduling with patient recovery in both operating rooms and recovery beds , 2010, Comput. Ind. Eng..

[52]  Stephen A. Kotleba,et al.  Inventory modelling for complex emergencies in humanitarian relief operations , 2006 .

[53]  Celso A. A. Kaestner,et al.  Discrete Event Systems with Guards , 2004 .

[54]  W. M. Wonham,et al.  The control of discrete event systems , 1989 .

[55]  Altug Iftar,et al.  Supervisory controller design for timed Petri nets , 2006, 2006 IEEE/SMC International Conference on System of Systems Engineering.

[56]  Mark S. Roberts,et al.  The Cost-Effectiveness of Strategies to Reduce Mortality from an Intentional Release of Aerosolized Anthrax Spores , 2006, Medical decision making : an international journal of the Society for Medical Decision Making.

[57]  Jules Desharnais,et al.  Control of Parameterized Discrete Event Systems , 2009, Discret. Event Dyn. Syst..

[58]  Lars Michael Kristensen,et al.  Coloured Petri Nets - Modelling and Validation of Concurrent Systems , 2009 .

[59]  W. M. Wonham,et al.  Supervisory control of probabilistic discrete event systems , 1993, Proceedings of 36th Midwest Symposium on Circuits and Systems.

[60]  Wlodzimierz M. Zuberek,et al.  Timed Petri nets definitions, properties, and applications , 1991 .

[61]  Xiaolan Xie,et al.  Redesigning pharmacy delivery processes of a health care complex , 2009, Health care management science.

[62]  Marco Ajmone Marsan,et al.  Generalized Stochastic Petri Nets: A Definition at the Net Level and Its Implications , 1993, IEEE Trans. Software Eng..

[63]  Alessandro Giua,et al.  A Survey of Petri Net Methods for Controlled Discrete Event Systems , 1997, Discret. Event Dyn. Syst..

[64]  Tak Kuen Siu,et al.  Markov Chains: Models, Algorithms and Applications , 2006 .

[65]  Joseph Barjis,et al.  The importance of business process modeling in software systems design , 2008, Sci. Comput. Program..

[66]  Marco Ajmone Marsan,et al.  Stochastic Petri nets: an elementary introduction , 1988, European Workshop on Applications and Theory in Petri Nets.