Mean-Field Semantics for a Process Calculus for Spatially-Explicit Ecological Models

We define a mean-field semantics for S-PALPS, a process calculus for spatially-explicit, individualbased modeling of ecological systems. The new semantics of S-PALPS allows an interpretation of the average behavior of a system as a set of recurrence equations. Recurrence equations are a useful approximation when dealing with a large number of individuals, as it is the case in epidemiological studies. As a case study, we compute a set of recurrence equations capturing the dynamics of an individual-based model of the transmission of dengue in Bello (Antioquia), Colombia.

[1]  Stephen Gilmore,et al.  Scalable Differential Analysis of Process Algebra Models , 2012, IEEE Transactions on Software Engineering.

[2]  Maria Luisa Guerriero,et al.  Modelling Biological Compartments in Bio-PEPA , 2008, MeCBIC.

[3]  Hyun Mo Yang,et al.  Assessing the effects of vector control on dengue transmission , 2008, Appl. Math. Comput..

[4]  Dimitrios Kouzapas,et al.  A Process Calculus for Dynamic Networks , 2011, FMOODS/FORTE.

[5]  Roberto Barbuti,et al.  Modelling the Dynamics of an Aedes albopictus Population , 2010, AMCA-POP.

[6]  Andrea Bianco,et al.  Model Checking of Probabalistic and Nondeterministic Systems , 1995, FSTTCS.

[7]  Ronald L. Graham,et al.  Concrete Mathematics, a Foundation for Computer Science , 1991, The Mathematical Gazette.

[8]  Paolo Milazzo,et al.  Spatial Calculus of Looping Sequences , 2011, Theor. Comput. Sci..

[9]  Roberto Barbuti,et al.  Spatial Calculus of Looping Sequences , 2009, FBTC@ICALP.

[10]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[11]  Chris M. N. Tofts,et al.  Processes with probabilities, priority and time , 1994, Formal Aspects of Computing.

[12]  Anna Philippou,et al.  Simulation and Verification in a Process Calculus for Spatially-Explicit Ecological Models , 2013, Sci. Ann. Comput. Sci..

[13]  Carron Shankland,et al.  From individuals to populations: A mean field semantics for process algebra , 2011, Theor. Comput. Sci..

[14]  D J Sumpter,et al.  Ants and agents: A process algebra approach to modelling ant colony behaviour , 2001, Bulletin of mathematical biology.

[15]  Luca Cardelli,et al.  BioAmbients: an abstraction for biological compartments , 2004, Theor. Comput. Sci..

[16]  T. Kurtz Solutions of ordinary differential equations as limits of pure jump markov processes , 1970, Journal of Applied Probability.

[17]  Thomas A. Henzinger,et al.  SABRE: A Tool for Stochastic Analysis of Biochemical Reaction Networks , 2010, QEST.

[18]  Giancarlo Mauri,et al.  Tau Leaping Stochastic Simulation Method in P Systems , 2006, Workshop on Membrane Computing.

[19]  Herman H. Shugart,et al.  Avian demography in mosaic landscapes: modeling paradigm and preliminary results , 1984 .

[20]  Carron Shankland,et al.  Process Algebra Models of Population Dynamics , 2008, AB.

[21]  Vashti Galpin,et al.  Modelling Network Performance with a Spatial Stochastic Process Algebra , 2009, 2009 International Conference on Advanced Information Networking and Applications.

[22]  Paolo Milazzo,et al.  A Calculus of Looping Sequences for Modelling Microbiological Systems , 2006, Fundam. Informaticae.

[23]  Mathias John,et al.  A Spatial Extension to the π Calculus , 2007 .

[24]  Gopal Gupta,et al.  Timed π-Calculus , 2013, TGC.

[25]  A. Peterson,et al.  Mapping Environmental Dimensions of Dengue Fever Transmission Risk in the Aburrá Valley, Colombia , 2009, International journal of environmental research and public health.

[26]  Shih Ching Fu,et al.  A Flexible Automata Model for Disease Simulation , 2004, ACRI.

[27]  L. Berec Techniques of spatially explicit individual-based models: construction, simulation, and mean-field analysis , 2002 .

[28]  Giovanni Pardini,et al.  Formal Modelling and Simulation of Biological Systems with Spatiality , 2011 .

[29]  D. Sumpter,et al.  Coupled map lattice approximations for spatially explicit individual-based models of ecology , 2005, Bulletin of mathematical biology.

[30]  John S. Brownstein,et al.  The global distribution and burden of dengue , 2013, Nature.

[31]  Giancarlo Mauri,et al.  An Analysis on the Influence of Network Topologies on Local and Global Dynamics of Metapopulation Systems , 2010, AMCA-POP.

[32]  Marta Z. Kwiatkowska,et al.  Automated Verification Techniques for Probabilistic Systems , 2011, SFM.

[33]  Maciej Koutny,et al.  Petri Nets for Biologically Motivated Computing , 2011, Sci. Ann. Comput. Sci..

[34]  H G Solari,et al.  Stochastic eco-epidemiological model of dengue disease transmission by Aedes aegypti mosquito. , 2010, Mathematical biosciences.

[35]  Paolo Milazzo,et al.  Modular Verification of Interactive Systems with an Application to Biology , 2010, CS2Bio.

[36]  Gheorghe Paun,et al.  Membrane Computing , 2002, Natural Computing Series.

[37]  Qiuwen Chen,et al.  Cellular-automata-based ecological and ecohydraulics modelling , 2009 .

[38]  Camilo Rueda,et al.  Non-determinism and Probabilities in Timed Concurrent Constraint Programming , 2008, ICLP.

[39]  L. Gerber,et al.  Implications of three viability models for the conservation status of the western population of Steller sea lions (Eumetopias jubatus) , 2001 .

[40]  Luca Cardelli,et al.  Brane Calculi Interactions of Biological Membranes , 2004 .

[41]  Ronald L. Graham,et al.  Concrete mathematics - a foundation for computer science , 1991 .

[42]  T. Dawson,et al.  Long-distance plant dispersal and habitat fragmentation: identifying conservation targets for spatial landscape planning under climate change , 2005 .

[43]  Robin Milner,et al.  A Calculus of Communicating Systems , 1980, Lecture Notes in Computer Science.

[44]  G. Michele Pinna,et al.  An Event Based Semantics of P Systems , 2008, Sci. Ann. Comput. Sci..

[45]  Luca Cardelli,et al.  Processes in Space , 2010, CiE.

[46]  Adelinde M. Uhrmacher,et al.  Exploring the performance of spatial stochastic simulation algorithms , 2011, J. Comput. Phys..

[47]  Livio Bioglio,et al.  A Spatial Calculus of Wrapped Compartments , 2011, ArXiv.

[48]  Giancarlo Mauri,et al.  Modelling metapopulations with stochastic membrane systems , 2008, Biosyst..

[49]  Robert I. McDonald,et al.  Uncertainty in spatially explicit population models , 2008 .

[50]  Mario de Jesús Pérez Jiménez,et al.  P System Based Model of an Ecosystem of the Scavenger Birds , 2009 .

[51]  Stephen Gilmore,et al.  Stochastic Process Algebras: From Individuals to Populations , 2012, Comput. J..

[52]  Anna Philippou,et al.  Synchronous Parallel Composition in a Process Calculus for Ecological Models , 2014, ICTAC.