Persistence, extinction and spatio-temporal synchronization of SIRS spatial models

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2009, Issue 7, 2009, Pages

  Liu, Quan Xing ^a   Wang, Rong Hua ^a   Jin, Zhen ^a  

^a NORTH UNIVERSITY OF CHINA   (China)

Author keywords

Cellular automata; Interacting agent models; Pattern formation (theory); Self organized criticality (experiment)

Indexed keywords

EID: 71049124800     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2009/07/P07007     Document Type: Article

References (106)

1. Adler F R 1993 Migration alone can produce persistence of host-parasitoid models Am. Nat. 141 642
2. Allen J C, Schaffer W M and Rosko D 1993 Chaos reduces species extinction by amplifying local population noise Nature 364 229
3. Alonso D, McKane A J and Pascual M 2006 Stochastic amplification in epidemics J. R. Soc. Interface 4 575
4. Alonso D, McKane A J and Pascual M 2007 Stochastic amplification in epidemics J. R. Soc. Interface 4 575
5. Anderson R M and May R M 1991 Infectious Diseases of Humans (Oxford: Oxford University Press)
6. Antal T and Droz M 2001 Phase transitions and oscillations in a lattice prey-predator model Phys. Rev. E 63 056119
7. Antoniazzi A, Fanelli D, Ruffo S and Yamaguchi Y Y 2007 Nonequilibrium tricritical point in a system with long-range interactions Phys. Rev. Lett. 99 040601
8. Ball F, Mollison D and Scalia-Tomba G 1997 Epidemics with two levels of mixing Ann. Appl. Probab. 7 46
9. Bartlett M S 1956 Proc. 3rd Berkeley Symp. on Mathematics, Statistics and Probability vol 4 (Berkeley, CA: University of California Press) Chapter (Deterministic and Stochastic Models for Recurrent Epidemics) p81
10. Bartlett M S 1957 Measles periodicity and community size J. R. Stat. Soc. A 120 48
11. Bartlett M S 1960 The critical community size for measles in the united states J. R. Stat. Soc. A 123 37
12. Bharti N, Xia Y, Bjornstad O N and Grenfell B T 2008 Measles on the edge: coastal heterogeneities and infection dynamics PLoS ONE 3 e1941
13. Blasius B and Stone L 2000 Chaos and phase synchronization in ecological systems Int. J. Bifurc. Chaos 10 2361
14. Boccara N and Cheong K 1992 Automata network sir models for the spread of infectious diseases in populations of moving individuals J. Phys. A: Math. Gen. 25 2447
15. Boccara N and Cheong K 1993 Critical behaviour of a probabilistic automata network sis model for the spread of an infectious disease in a population of moving individuals J. Phys. A: Math. Gen. 26 3707
16. Boccara N, Roblin O and Roger M 1994 Automata network predator-prey model with pursuit and evasion Phys. Rev. E 50 4531
17. Boland R P, Galla T and McKane A J 2008 How limit cycles and quasi-cycles are related in systems with intrinsic noise J. Stat. Mech. P09001
18. Bolker B 1999 Analytic models for the patchy spread of plant disease Bull. Math. Biol. 61 849
19. Bolker B and Grenfell B 1995 Space, persistence and dynamics of measles epidemics Phil. Trans. R. Soc. B 348 309
20. Bolker B and Pacala S W 1997 Using moment equations to understand stochastically driven spatial pattern formation in ecological systems Theor. Popul. Biol. 52 6
21. Boots M and Sasaki A 1999 Small worlds and the evolution of virulence: infection occurs locally and at a distance Proc. R. Soc. B 266 1933
22. Boots M and Sasaki A 2003 Parasite evolution and extinctions Ecol. Lett. 6 176
23. Brauer F and Castillo-Chavez C 1996 Mathematical Models in Population Biology and Epidemiology (New York: Springer)
24. Claussen J C and Traulsen A 2008 Cyclic dominance and biodiversity in well-mixed populations Phys. Rev. Lett. 100 058104
25. Colizza V, Barrat A, Barthelemy M and Vespignani A 2006 The role of the airline transportation network in the prediction and predictability of global epidemics Proc. Nat. Acad. Sci. 103 2015
26. Colizza V and Vespignani A 2008 Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: theory and simulations J. Theor. Biol. 251 450
27. Comins H N and Hassell M P 1996 Persistence of multispecies host-parasitoid interactions in spatially distributed models with local dispersal J. Theor. Biol. 183 19
28. 0 as a predictor of disease invasion in structured populations J. R. Soc. Interface 4 315
29. Cross P C, Lloyd-Smith J O, Johnson P L F and Getz W M 2005 Duelling timescales of host movement and disease recovery determine invasion of disease in structured populations Ecol. Lett. 8 587
30. Czaran T L, Hoekstra R F and Pagie L 2002 Chemical warfare between microbes promotes biodiversity Proc. Nat. Acad. Sci. 99 786
31. DeAngelis D L and Gross L J 1992 Individual-Based Models and Approaches in Ecology: Populations, Communities and Ecosystems (New York: Chapman and Hall)
32. Dieckmann U, Law R and Metz J A J 2000 The Geometry of Ecological Interactions: Simplifying Spatial Complexity (Cambridge: Cambridge University Press)
33. Durrett R 1999 Stochastic spatial models SIAM Rev. 41 677
34. Dushoff J, Plotkin J B, Levin S A and Earn D J D 2004 Dynamical resonance can account for seasonality of influenza epidemics Proc. Nat. Acad. Sci. 101 16915
35. Earn D J, Rohani P, Bolker B M and Grenfell B T 2000 A simple model for complex dynamical transitions in epidemics Science 287 667
36. Earn D J D, Rohani P and Grenfell B T 1998 Persistence, chaos and synchrony in ecology and epidemiology Proc. R. Soc. B 265 7
37. Eubank S, Guclu H, Kumar V S A, Marathe M V, Srinivasan A, Toroczkai Z and Wang N 2004 Modelling disease outbreaks in realistic urban social networks Nature 429 180
38. Ferguson N M, Keeling M J, Edmunds W J, Gani R, Grenfell B T, Anderson R M and Leach S 2003 Planning for smallpox outbreaks Nature 425 681
39. Frank S A 1991 Spatial variation in coevolutionary dynamics Evol. Ecol. 5 193
40. Fukś H, Lawniczak A T and Duchesne R 2006 Effects of population mixing on the spread of sir epidemics Eur. Phys. J. B 50 209
41. Gautreau A, Barrat A and Barthélemy M 2007 Arrival time statistics in global disease spread J. Stat. Mech. L09001
42. Gautreau A, Barrat A and Barthélemy M 2008 Global disease spread: statistics and estimation of arrival times J. Theor. Biol. 251 509
43. Gillespie D T 1977 Exact stochastic simulation of coupled chemical reactions J. Phys. Chem. 81 2340
44. Gillespie D T 2000 The chemical Langevin equation J. Chem. Phys. 113 297
45. Grais R F, Ellis J H and Glass G E 2003 Assessing the impact of airline travel on the geographic spread of pandemic influenza Eur. J. Epidemiol. 18 1065
46. Grassly N C, Fraser C and Garnett G P 2005 Host immunity and synchronized epidemics of syphilis across the United States Nature 433 417
47. Grenfell B and Bolker B 1998 Cities and villages: infection hierarchies in a measles metapopulation Ecol. Lett. 1 63
48. Grenfell B T, Bjørnstad O N and Kappey J 2001 Travelling waves and spatial hierarchies in measles epidemics Nature 414 716
49. Grenfell B T and Harwood J 1997 Metapopulation dynamics of infectious diseases Trends Ecol. Evol. 12 395
50. Harris S and Trewhella W J 1988 An analysis of some of the factors affecting dispersal in an urban fox (vulpes vulpes) population J. Appl. Ecol. 25 409
51. Hassell M P, Comins H N and May R M 1994 Species coexistence and self-organizing spatial dynamics Nature 370 290
52. He D and Stone L 2003 Spatio-temporal synchronization of recurrent epidemics Proc. R. Soc. B 270 15919
53. Heino M, Kaitala V, Ranta E and Lindstrom J 1997 Synchronous dynamics and rates of extinction in spatially structured populations Proc. R. Soc. B 264 481
54. Hufnagel L, Brockmann D and Geisel T 2004 Forecast and control of epidemics in a globalized world Proc. Nat. Acad. Sci. 101 15124
55. Jeltsch F, Muller M S, Grimm V, Wissel C and Brandl R 1997 Pattern formation triggered by rare events: lessons from the spread of rabies Proc. R. Soc. B 264 495
56. Adamek J, Senftleben A, Keller M and Hinrichsen H 2005 Epidemic spreading with long-range infections and incubation times J. Stat. Mech. P09002
57. Kamo M, Sasaki A and Boots M 2007 The role of trade-off shapes in the evolution of parasites in spatial host populations: an approximate analytical approach J. Theor. Biol. 244 588
58. Keeling M J 1999 The effects of local spatial structure on epidemiological invasions Proc. R. Soc. B 266 859
59. Keeling M J, Brooks S P and Gilligan C A 2004 Using conservation of pattern to estimate spatial parameters from a single snapshot Proc. Nat. Acad. Sci. 101 9155
60. Keeling M J and Rohani P 2002 Estimating spatial coupling in epidemiological systems: a mechanistic approach Ecol. Lett. 5 20
61. Kuperman M and Abramson G 2001 Small world effect in an epidemiological model Phys. Rev. Lett. 86 2909
62. Kuske R, Gordillo L F and Greenwood P 2007 Sustained oscillations via coherence resonance in sir J. Theor. Biol. 245 459
63. Lewis M, Renclawowicz J and van den Driessche P 2006 Traveling waves and spread rates for a West Nile Virus model Bull. Math. Biol. 68 3
64. Lima S L and Zollner P A 1996 Towards a behavioural ecology of ecological landscapes Trends Ecol. Evol. 11 131
65. Liu Q-X and Jin Z 2007 Formation of spatial patterns in an epidemic model with constant removal rate of the infectives J. Stat. Mech. P05002
66. Liu Q-X, Jin Z and Liu M-X 2006 Spatial organization and evolution period of the epidemic model using cellular automata Phys. Rev. E 74 031110
67. Liu Q-X, Wang R-H, Jin Z and van de Koppel J 2009 The spatial dynamics and evolution of two strains: power law as an indicator for coexistence manuscript www.nioo.knaw.nl/users/qliu
68. Lloyd A L and Jansen V A A 2004 Spatiotemporal dynamics of epidemics: synchrony in metapopulation models Math. Biosci. 188 1
69. Lloyd A L and May R M 1996 Spatial heterogeneity in epidemic models J. Theor. Biol. 179 1
70. Lloyd A L and May R M 2001 Epidemiology: how viruses spread among computers and people Science 292 1316
71. Medlock J and Kot M 2003 Spreading disease: integro-differential equations old and new Math. Biosci. 184 201
72. Mobilia M, Georgiev I T and Täuber U C 2006 Fluctuations and correlations in lattice models for predator-prey interaction Phys. Rev. E 73 040903
73. Murray J D 1993 Mathematical Biology (Berlin: Springer)
74. Nasell I 1999 On the time to extinction in recurrent epidemics J. R. Stat. Soc. B 61 309
75. Nasell I 2005 A new look at the critical community size for childhood infections Theor. Popul. Biol. 67 203
76. Newman M E J 2002 Spread of epidemic disease on networks Phys. Rev. E 66 016128
77. Nguyen H T H and Rohani P 2008 Noise, nonlinearity and seasonality: the epidemics of whooping cough revisited J. R. Soc. Interface 5 403
78. Noble J V 1974 Geographic and temporal development of plague Nature 250 726
79. Pascual M and Guichard F 2005 Criticality and disturbance in spatial ecological systems Trends Ecol. Evol. 20 88
80. Pastor-Satorras R and Vespignani A 2001 Epidemic spreading in scale-free networks Phys. Rev. Lett. 86 3200
81. Petrovskii S and Li B-L 2001 Increased coupling between subpopulation in a spatially structured environment can lead to population outbreaks J. Theor. Biol. 212 549
82. Rand D A, Keeling M and Wilson H B 1995 Invasion, stability and evolution to criticality in spatially extended, artificial host-pathogen ecology Proc. R. Soc. B 259 55
83. Rauch E M and Bar-Yam Y 2006 Long-range interactions and evolutionary stability in a predator-prey system Phys. Rev. E 73 020903
84. Read J M and Keeling M J 2003 Disease evolution on networks: the role of contact structure Proc. R. Soc. B 270 699
85. Reichenbach T, Mobilia M and Frey E 2006 Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model Phys. Rev. E 74 051907
86. Reichenbach T, Mobilia M and Frey E 2007 Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games Nature 448 1046
87. Reichenbach T, Mobilia M and Frey E 2007 Noise and correlations in a spatial population model with cyclic competition Phys. Rev. Lett. 99 238105
88. Reichenbach T, Mobilia M and Frey E 2008 Self-organization of mobile population in cyclic competition J. Theor. Biol. 254 368 [arXiv:0801.1798]
89. Rhodes C J and Anderson R M 1996 Power laws governing epidemics in isolated populations Nature 381 600
90. Rosenblum M G, Pikovsky A S and Kurths J 1996 Phase synchronization of chaotic oscillators Phys. Rev. Lett. 76 1804
91. Rozenfeld A F and Albano E V 2001 Critical and oscillatory behavior of a system of smart preys and predators Phys. Rev. E 63 061907
92. Rozenfeld A F and Albano E V 2004 A self-organized system of smart preys and predators Phys. Lett. A 332 361
93. Rozenfeld A F, Tessone C J, Albano E V and Wio H S 2001 On the influence of noise on the critical and oscillatory behavior of a predator-prey model: coherent stochastic resonance at the proper frequency of the system Phys. Lett. A 280 45
94. Schippers P, Verboon J, Knaapen J P and van Apeldoorn R C 1996 Dispersal and habitat connectivity in complex heterogeneous landscapes: an analysis with a gis-based random walk model Ecography 19 97
95. Sherratt J A, Eagan B T and Lewis M A 1997 Oscillations and chaos behind predator-prey invasion: mathematical artifact or ecological reality? Phil. Trans. R. Soc. B 352 21
96. Simoes M, da Gama M M T and Nunes A 2008 Stochastic fluctuations in epidemics on networks J. R. Soc. Interface 5 555
97. Stone L, Olinky R and Huppert A 2007 Seasonal dynamics of recurrent epidemics Nature 446 533
98. Sun G, Jin Z, Liu Q-X and Li L 2007 Pattern formation in a spatial s-i model with non-linear incidence rates J. Stat. Mech. P11011
99. Swinton J 1998 Extinction times and phase transitions for spatially structured closed epidemics Bull. Math. Biol. 60 215
100. Tan Z-J, Zou X-W and Jin Z-Z 2000 Percolation with long-range correlations for epidemic spreading Phys. Rev. E 62 8409
101. Tessone C J, Cencini M and Torcini A 2006 Synchronization of extended chaotic systems with long-range interactions: an analogy to Levy-flight spreading of epidemics Phys. Rev. Lett. 97 224101
102. van Ballegooijen W M and Boerlijst M C 2004 Emergent trade-offs and selection for outbreak frequency in spatial epidemics Proc. Nat. Acad. Sci. 101 18246
103. van den Bosch F, Metz J A J and Zadoks J C 1999 Pandemics of focal plant disease, a model Phytopathology 89 495
104. van den Bosch F, Zadoks J and Metz J 1988 Focus expansion in plant disease. i. the constant rate of focus expansion Phytopathology 78 54
105. Viboud C, Bjornstad O N, Smith D L, Simonsen L, Miller M A and Grenfell B T 2006 Synchrony, waves, and spatial hierarchies in the spread of influenza Science 312 447
106. Xia Y, Bjornstad O and Grenfell B 2004 Measles metapopulation dynamics: a gravity model for epidemiological coupling and dynamics Am. Nat. 164 267