Formalisation et résolution d'un problème en Santé Animale avec le cadre Leader-Follower MDP

Transmissible disease control is a major concern for the livestock sector. For unregulated diseases, each farmer chooses to implement control actions. To help coordination between farmers, organizations propose collective control approaches using incentives. Our objective is to design a tool, based on the Leader-Follower Markov Decision Processes framework (LF-MDP), to help coordination. Exact solution is hard, however we have proposed an exact solution method and an approximate (using state aggregation) one. We have applied these methods to a case study concerning the Porcine Reproductive and Respiratory Syndrome (PRRS) virus. Exact solution is possible for up to n = 20 followers. Approximate solution could be performed for up to n = 100 followers and we observed similar exact and approximate solutions for n ≤ 20.

[1]  Lan Ge,et al.  A modelling approach to support dynamic decision-making in the control of FMD epidemics. , 2010, Preventive veterinary medicine.

[2]  Stéphane Krebs,et al.  Individual and collective management of endemic animal diseases: an economic approach , 2012 .

[3]  G. Nodelijk,et al.  Porcine Reproductive and Respiratory Syndrome (PRRS) with special reference to clinical aspects and diagnosis: A review , 2002, The Veterinary quarterly.

[4]  Christine Fourichon,et al.  Modelling collective effectiveness of voluntary vaccination with and without incentives. , 2010, Preventive veterinary medicine.

[5]  A A Dijkhuizen,et al.  An epidemiological and economic simulation model to evaluate the spread and control of infectious bovine rhinotracheitis in The Netherlands. , 1998, Preventive veterinary medicine.

[6]  M. Begon,et al.  A clarification of transmission terms in host-microparasite models: numbers, densities and areas , 2002, Epidemiology and Infection.

[7]  Alison P. Galvani,et al.  Free-Riding Behavior in Vaccination Decisions: An Experimental Study , 2014, PloS one.

[8]  Gabriel Turinici,et al.  Individual Vaccination as Nash Equilibrium in a SIR Model with Application to the 2009–2010 Influenza A (H1N1) Epidemic in France , 2015, Bulletin of Mathematical Biology.

[9]  Marielle Brunette,et al.  Optimising forest management under storm risk with a Markov decision process model , 2015 .

[10]  Christopher A. Gilligan,et al.  Economic incentives and mathematical models of disease , 2007, Environment and Development Economics.

[11]  J. Ekboir,et al.  The role of the public sector in the development and implementation of animal health policies. , 1999, Preventive veterinary medicine.

[12]  Michael P. Wellman,et al.  Nash Q-Learning for General-Sum Stochastic Games , 2003, J. Mach. Learn. Res..

[13]  Erica L. Plambeck,et al.  Performance-Based Incentives in a Dynamic Principal-Agent Model , 2000, Manuf. Serv. Oper. Manag..

[14]  Marie-Josée Cros,et al.  Risk aversion and optimal management of an uneven-aged forest under risk of windthrow: A Markov decision process approach , 2016 .

[15]  Régis Sabbadin,et al.  A Tractable Leader-Follower MDP Model for Animal Disease Management , 2013, AAAI.

[16]  Rob Deardon,et al.  Optimal reactive vaccination strategies for a foot-and-mouth outbreak in the UK , 2006, Nature.

[17]  E. Albina,et al.  Results of a control programme for the porcine reproductive and respiratory syndrome in the French 'Pays de la Loire' region. , 1997, Veterinary microbiology.

[18]  Anders Ringgaard Kristensen,et al.  A framework for decision support related to infectious diseases in slaughter pig fattening units , 2005 .

[19]  Siddhartha Bhattacharyya,et al.  Single-leader–multiple-follower games with boundedly rational agents , 2009 .

[20]  David L. Smith,et al.  Key strategies for reducing spread of avian influenza among commercial poultry holdings: lessons for transmission to humans , 2006, Proceedings of the Royal Society B: Biological Sciences.

[21]  J. Filar,et al.  Competitive Markov Decision Processes , 1996 .

[22]  Richard E Howitt,et al.  A dynamic, optimal disease control model for foot-and-mouth disease: I. Model description. , 2007, Preventive veterinary medicine.

[23]  L. Jeanpierre,et al.  Using Markov Decision Processes to define an adaptive strategy to control the spread of an animal disease , 2012 .

[24]  Régis Sabbadin,et al.  Leader-Follower MDP Models with Factored State Space and Many Followers - Followers Abstraction, Structured Dynamics and State Aggregation , 2016, ECAI.

[25]  Montserrat Torremorell,et al.  Control and elimination of porcine reproductive and respiratory syndrome virus. , 2010, Virus research.

[26]  Christian Wernz,et al.  Unifying temporal and organizational scales in multiscale decision-making , 2012, Eur. J. Oper. Res..

[27]  Richard Bennett,et al.  The 'Direct Costs'of Livestock Disease: The Development of a System of Models for the Analysis of 30 Endemic Livestock Diseases in Great Britain , 2003 .