Dynamics of infectious diseases

Reports on Progress in Physics

Volumn 77, Issue 2, 2014, Pages

  Rock, Kat ^a   Brand, Sam ^a   Moir, Jo ^a   Keeling, Matt J ^a,b  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

epidemic; infection; risk structure; spatial spread; stochasticity; vaccination

Indexed keywords

EID: 84893398311     PISSN: 00344885     EISSN: None     Source Type: Journal    
DOI: 10.1088/0034-4885/77/2/026602     Document Type: Review

References (254)

1. Abramson P R and Rothschild B 1988 Sex, drugs and matrices: mathematical prediction of HIV infection J. Sex Res. 25 106-22 (Pubitemid 18069361)
2. Albert R and Barabási A L 2002 Statistical mechanics of complex networks Rev. Mod. Phys. 74 47-97
3. Albert R, Jeong H and Barabási A-L 2000 Error and attack tolerance of complex networks Nature 406 378-82 (Pubitemid 30625551)
4. Alexander M E, Moghadas S M, Rohani P and Summers A R 2006 Modelling the effect of a booster vaccination on disease epidemiology J. Math. Biol. 52 290-306 (Pubitemid 43237825)
5. Alonso D, McKane A J and Pascual M 2007 Stochastic amplification in epidemics J. R. Soc. Interface 4 575 (Pubitemid 46846685)
6. Aly S S, Anderson R J, Whitlock R H, Fyock T L, McAdams S C, Byrem T M, Jiang J, Adaska J M and Gardner I A 2012 Cost-effectiveness of diagnostic strategies to identify mycobacterium avium subspecies paratuberculosis super-shedder cows in a large dairy herd using antibody enzyme-linked immunosorbent assays, quantitative real-time polymerase chain reaction, and bacterial culture J. Veterinary Diagnostic Investigation 24 821-32
7. Anderson R M, Jackson H C, May R M and Smith A M 1981 Population dynamics of fox rabies in Europe Nature 289 765-71 (Pubitemid 11150412)
8. Anderson R M and May R M 1983 Vaccination against rubella and measles: quantitative investigations of different policies J. Hygiene 90 259-325 (Pubitemid 13086184)
9. Anderson R M, Blythe S P, Gupta S, Konings E, Anderson R M, Blythe S P, Gupta S and Konings E 1989 The transmission dynamics of the human immunodeficiency virus type 1 in the male homosexual community in the United Kingdom: the influence of changes in sexual behaviour Phil. Trans. R. Soc. Lond. B 325 45-98
10. Anderson R M, Gupta S and Ng W 1990 The significance of sexual partner contact networks for the transmission dynamics of HIV J. Acquired Immune Deficiency Syndromes 3 417-29 (Pubitemid 20154956)
11. Anderson R M, May R M, Boily M C, Garnett G P and Rowley J T 1991 The spread of HIV-1 in Africa: sexual contact patterns and the predicted demographic impact of AIDS Nature 352 581-9 (Pubitemid 21912382)
12. Anderson R M, May R M and McLean A R 1988 Possible demographic consequences of AIDS in developing countries Nature 332 228-34 (Pubitemid 18076652)
13. Anderson R M, May R M, Ng T W, Rowley J T, Anderson R M, May R M, Ng T W and Rowley J T 1992 Age-dependent choice of sexual partners and the transmission dynamics of HIV in sub-Saharan Africa Phil. Trans. R. Soc. Lond. B 336 135-55
14. Anderson R M, Medley G F, May R M and Johnson A M 1986 A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS IMA J. Math. Appl. Med. Biol. 3 229-63
15. Anderson R M and May R M 1979 Population biology of infectious diseases: I Nature 280 361-6 (Pubitemid 9233606)
16. Anderson R M and May R M 1992 Infectious Diseases of Humans (Oxford: Oxford University Press)
17. Aparicio J P and Pascual M 2007 Building epidemiological models from R0 an implicit treatment of transmission in networks Proc. R. Soc. B 274 505 (Pubitemid 47055523)
18. Baguelin M, Van Hoek A J, Jit M, Flasche S, White P J and Edmunds W J 2010 Vaccination against pandemic influenza A/H1N1v in England: a real-time economic evaluation Vaccine 28 2370-84
19. Bailey N T J 1950 A simple stochastic epidemic Biometrika 37 193-202
20. Bailey N T J 1975 The Mathematical Theory of Infectious Diseases and its Applications 2nd edn (London: Charles Griffin & Co Ltd)
21. Bak P, Chen K and Tang C 1990 A forest-fire model and some thoughts on turbulence Phys. Lett. A 147 297-300
22. Balcan D, Colizza V, Gonçalves B, Hu H, Ramasco J J and Vespignani A 2009 Multiscale mobility networks and the spatial spreading of infectious diseases Proc. Natl Acad. Sci. 106 21484-9
23. Ball F 1983 The threshold behaviour of epidemic models J. Appl. Probab. 20 227-41
24. Ball F 1986 A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models Adv. Appl. Probab. 18 289-310
25. Ball F and Clancy D 1993 The final size and severity of a generalised stochastic multitype epidemic model Adv. Appl. Probab. 25 721-36
26. Ball F and Lyne O D 2001 Stochastic multi-type SIR epidemics among a population partitioned into households Adv. Appl. Probab. 33 99-123 (Pubitemid 32443971)
27. Ball F, Mollison D and Scalia-Tomba G 1997 Epidemics with two levels of mixing Ann. Appl. Probab. 7 46-89
28. Ball F, Sirl D and Trapman P 2010 Analysis of a stochastic SIR epidemic on a random network incorporating household structure Math. Biosci. 224 53-73
29. Ball F G and Lyne O D 2002 Optimal vaccination policies for stochastic epidemics among a population of households Math. Biosci. 177 333-54 (Pubitemid 34457397)
30. Ball F, Britton T and Lyne O 2004 Stochastic multitype epidemics in a community of households: estimation and form of optimal vaccination schemes Math. Biosci. 191 19-40 (Pubitemid 39092949)
31. Ball F, Britton T and Sirl D 2012 A network with tunable clustering, degree correlation and degree distribution, and an epidemic thereon J. Math. Biol. 66 979-1019
32. Barabasi A L and Albert R 1999 Emergence of scaling in random networks Science 286 509-12
33. Barbour A and Mollison D 1990 Epidemics and random graphs Stochastic Processes in Epidemic Theory ed J-P Gabriel et al (Berlin: Springer) pp 86-9
34. Bartlett M S 1956 Deterministic and stochastic models for recurrent epidemics Proc. 3rd Berkeley Symp. Math. Stat. Probab. 4 81-108
35. Bartlett M S 1957 Measles periodicity and community size J. R. Stat. Soc. A 120 48-70
36. Bartlett M S 1960 Stochastic Population Models in Ecology and Epidemiology (New York: Wiley)
37. Bartlett M S 1960 The critical community size for measles in the United States J. R. Stat. Soc. A 123 37-44
38. Basta N E, Halloran M E, Matrajt L and Longini I M 2008 Estimating influenza vaccine efficacy from challenge and community-based study data Am. J. Epidemiol. 168 1343-52
39. Bastos A D S, Boshoff C I, Keet D F, Bengis R G and Thomson G R 2000 Natural transmission of Foot-and-Mouth disease virus between African buffalo (syncerus caffer) and Impala (aepyceros melampus) in the Kruger National Park, South Africa Epidemiol. Infection 124 591-8 (Pubitemid 30623875)
40. Becker N G 1989 Analysis of Infectious Disease Data 1st edn (London: Chapman and Hall)
41. Bellan S E 2010 The importance of age dependent mortality and the extrinsic incubation period in models of mosquito-borne disease transmission and control PLoS ONE 5 e10165
42. Bjørnstad O N, Finkenstädt B F and Grenfell B T 2002 Dynamics of measles epidemics: estimating scaling of transmission rates using a time series SIR model Ecol. Monogr. 72 169-84 (Pubitemid 36198821)
43. Black A J, House T, Keeling M J and Ross J V 2013 Epidemiological consequences of household-based antiviral prophylaxis for pandemic influenza J. R. Soc. Interface 10 20121019
44. Black A J and McKane A J 2012 Stochastic formulation of ecological models and their applications Trends Ecol. Evol. 27 337-45
45. Blundell S J and Blundell K M 2012 Concepts in Thermal Physics (Oxford: Oxford University Press)
46. Blythe S P and Anderson R M 1988 Distributed incubation and infectious periods in models of the transmission dynamics of the human immunodeficiency virus (HIV) Math. Med. Biol. 5 1-19
47. Blythe S P and Anderson R M 1988 Heterogeneous sexual activity models of HIV transmission in male homosexual populations Math. Med. Biol. 5 237-60
48. Blythe S P and Anderson R M 1988 Variable infectiousness in HFV transmission models Math. Med. Biol. 5 181-200
49. Boccaletti S, Latora V, Moreno Y, Chavez M and Hwang D-U 2006 Complex networks: structure and dynamics Phys. Rep. 424 175-308 (Pubitemid 43135890)
50. Bolker B and Grenfell B 1995 Space, persistence and dynamics of measles epidemics Phil. Trans. R. Soc. Lond. B 348 309-20
51. Bolker B M 1999 Analytic models for the patchy spread of plant disease Bull. Math. Biol. 61 849-74 (Pubitemid 29480059)
52. Bolker B M and Grenfell B T 1993 Chaos and biological complexity in measles dynamics Proc. R. Soc Lond. B 251 75-81 (Pubitemid 23068977)
53. Boltyanskii R V 1993 Chaos and complexity in measles models - a comparative numerical study IMA J. Math. Appl. Med. Biol. 10 83-95
54. Boots M and Sasaki A 1999 Small worlds and the evolution of virulence: infection occurs locally and at a distance Proc. R. Soc. Lond. B 266 1933-8 (Pubitemid 29479195)
55. Britton N F 2003 Essential Mathematical Biology (Berlin: Springer)
56. Broberg E, Nicoll A and Amato-Gauci A 2011 Seroprevalence to influenza A(H1N1) 2009 virus - where are we? Clin. Vaccine Immunology : CVI 18 1205-12
57. Brochier B, Kieny M P, Costy F, Coppens P, Bauduin B, Lecocq J P, Languet B, Chappuis G, Desmettre P and Afiademanyo K 1991 Large-scale eradication of rabies using recombinant vaccinia-rabies vaccine Nature 354 520-2
58. Brookmeyer R and Gail M H 1988 A method for obtaining short-term projections and lower bounds on the size of the AIDS epidemic J. Am. Stat. Assoc. 83 301-8
59. Brown J K M and Hovmøller M S 2002 Aerial dispersal of pathogens on the global and continental scales and its impact on plant disease Science 297 537-41 (Pubitemid 34815327)
60. Cairns B J and Pollett P K 2005 Approximating persistence in a general class of population processes Theor. Population Biol. 68 77-90 (Pubitemid 41127971)
61. du Preez L H, Hyatt A D, Muller R, Speare R and Weldon C 2004 Origin of the amphibian chytrid fungus Emerging Infectious Diseases 10 2100
62. Conlan A J K, Pej R, Lloyd Andrew L, Keeling Matt J and Grenfell Bryan T 2010 Resolving the impact of waiting time distributions on the persistence of measles J. R. Soc. Interface 7 623-40
63. Conlan A J K, Rohani P, Lloyd A L, Keeling M and Grenfell B T 2010 Resolving the impact of waiting time distributions on the persistence of measles J. R. Soc. Interface 7 623-40
64. Cook A R, Gibson G J, Gottwald T R and Gilligan C A 2008 Constructing the effect of alternative intervention strategies on historic epidemics J. R. Soc. Interface 5 1203-13
65. Cooper B S, Pitman R J, Edmunds W J and Gay N J 2006 Delaying the international spread of pandemic influenza PLoS Med. 3 e212 (Pubitemid 43987827)
66. Cornet S, Nicot A, Rivero A and Gandon S 2012 Malaria infection increases bird attractiveness to uninfected mosquitoes Ecol. Lett. 16 323-9
67. Cox D R and Isham V 1980 Point Processes (London: Chapman and Hall)
68. Cox D R and Medley G F 1989 A process of events with notification delay and the forecasting of AIDS Phil. Trans. R. Soc. Lond. B 325 135-45
69. Danon L, Ford A P, House T, Jewell C P, Keeling M J, Roberts G O, Ross J V and Vernon M C 2011 Networks and the epidemiology of infectious disease Interdisciplinary Perspectives on Infectious Diseases 2011 284909
70. Danon L, House T and Keeling M J 2009 The role of routine versus random movements on the spread of disease in Great Britain Epidemics 1 250-8
71. Danon L, House T A, Read J M and Keeling M J 2012 Social encounter networks: collective properties and disease transmission J. R. Soc. Interface 9 2826-33
72. Deardon R, Brooks S, Grenfell B T, Keeling M J, Tildesley M J, Savill N J, Shaw D J and Woolhouse M E J 2010 Inference for individual-level models of infectious diseases in large populations Stat. Sin. 20 239-61
73. Diekmann O, De Jong M C M and Metz J A J 1998 A deterministic epidemic model taking account of repeated contacts between the same individuals J. Appl. Probab. 35 462-8
74. Diekmann O, Heesterbeek H and Britton T 2012 Mathematical Tools for Understanding Infectious Disease Dynamics (Princeton, NJ: Princeton University Press)
75. Diekmann O, Heesterbeek J A and Metz J A 1990 On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations J. Math. Biol. 28 365-82
76. Diekmann O and Heesterbeek J A P 2000 Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis, and Interpretation (New York: Wiley)
77. Diekmann O 1978 Thresholds and travelling waves for the geographical spread of infection J. Math. Biol. 6 109-30 (Pubitemid 8406817)
78. Eames K T D and Keeling M J 2002 Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases Proc. Natl Acad. Sci. USA 99 13330-5
79. Eames K T D and Keeling M J 2003 Contact tracing and disease control Proc. R. Soc. Lond. B 270 2565-71 (Pubitemid 38082943)
80. Earn D J 2000 A simple model for complex dynamical transitions in epidemics Science 287 667-70 (Pubitemid 30070917)
81. Eaton J W, Hallett T B and Garnett G P 2011 Concurrent sexual partnerships and primary HIV infection: a critical interaction AIDS Behav. 15 687-92
82. Epstein H and Morris M 2011 Concurrent partnerships and HIV: an inconvenient truth J. Int. AIDS Soc. 14 13
83. Erds P and Renyi A 1960 Graphs with prescribed degrees of vertices Publ. Math. Inst. Hung. Acad. Sci. 5 17-61 (in Hungarian)
84. Ethier S and Kurtz T 1986 Markov Processes: Characterization and Convergence (New York: Wiley)
85. 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 429 180-4 (Pubitemid 38656193)
86. Evans J D, Saegerman C, Mullin C and Haubruge E 2009 Colony collapse disorder: a descriptive study PLoS One 4 e6481
87. Evans L C 2010 Partial Differential Equations 2nd edn (Providene, RI: American Mathematical Society)
88. Ferguson N M, Cummings D A T, Cauchemez S, Fraser C, Riley S, Meeyai A, Iamsirithaworn S and Burke D S 2005 Strategies for containing an emerging influenza pandemic in Southeast Asia Nature 437 209-14 (Pubitemid 41294478)
89. Ferguson N M, Donnelly C A and Anderson R M 2001 The Foot-and-Mouth epidemic in Great Britain: pattern of spread and impact of interventions Science 292 1155-60 (Pubitemid 32440936)
90. Ferguson N M, Donnelly C A and Anderson R M 2001 Transmission intensity and impact of control policies on the Foot-and-Mouth epidemic in Great Britain Nature 413 542-8 (Pubitemid 32938755)
91. Ferguson N M and Garnett G P 2000 More realistic models of sexually transmitted disease transmission dynamics: sexual partnership networks, pair models, and moment closure Sexually Transmitted Diseases 27 600-9
92. Ferguson N M, Keeling M J, Edmunds W J, Gant R, Grenfell B T, Amderson R M and Leach S 2003 Planning for smallpox outbreaks Nature 425 681-5 (Pubitemid 37314306)
93. Ferguson N M, Cummings D A T, Fraser C, Cajka J C, Cooley P C and Burke D S 2006 Strategies for mitigating an influenza pandemic Nature 442 448-52 (Pubitemid 44264793)
94. Filipe J A N, Cobb R C, Meentemeyer R K, Lee C A, Valachovic Y S, Cook A R, Rizzo D M and Gilligan C A 2012 Landscape epidemiology and control of pathogens with cryptic and long-distance dispersal: sudden oak death in northern Californian forests PLoS Comput. Biol. 8 e1002328
95. Finkenstädt B F and Grenfell B T 2000 Time series modelling of childhood diseases: a dynamical systems approach J. R. Stat. Soc. C 49 187-205
96. Fleming W and Soner H M 2006 Controlled Markov Processes and Viscosity Solutions (Berlin: Springer)
97. Fraser C 2007 Estimating individual and household reproduction numbers in an emerging epidemic PLoS One 2 758 (Pubitemid 351377243)
98. Freidlin M I and Wentzell A D 1998 Random Perturbations of Dynamical Systems 2nd edn (Berlin: Springer)
99. Fyock T, Whitlock R and Sweeney R 2009 Some Johne's cows do more harm than others Hoard's Dairyman 10 615
100. Ghani A C and Garnett G P 2000 Risks of acquiring and transmitting sexually transmitted diseases in sexual partner networks Sexually Transmitted Diseases 27 579-87
101. Gibson G J, Otten W, Filipe J A N, Cook A, Marion G and Gilligan C A 2006 Bayesian estimation for percolation models of disease spread in plant populations Stat. Comput. 16 391-402 (Pubitemid 44581752)
102. Gilbert M, Mitchell A, Bourn D, Mawdsley J, Clifton-Hadley R and Wint W 2005 Cattle movements and bovine tuberculosis in Great Britain Nature 435 491-6 (Pubitemid 40734245)
103. Gillespie D T 1977 Exact stochastic simulation of coupled chemical reactions J. Phys. Chem. 81 2340-61
104. Gillespie D T 2001 Approximate accelerated stochastic simulation of chemically reacting systems J. Chem. Phys. 115 1716-33 (Pubitemid 32715518)
105. Gillespie D T and Petzold L R 2003 Improved leap-size selection for accelerated stochastic simulation J. Chem. Phys. 119 8229-34
106. Glendinning P 1994 Stability, Instability, and Chaos: An Introduction to the Theory of Nonlinear Differential Equations (Cambridge: Cambridge University Press)
107. Goodman L A 1961 Snowball sampling Ann. Math. Statist. 32 148-70
108. Grenfell B 1997 (Meta)population dynamics of infectious diseases Trends Ecol. Evol. 12 395-9 (Pubitemid 28093523)
109. Grenfell B, Bjørnstad O and Kappey J 2001 Travelling waves and spatial hierarchies in measles epidemics Nature 414 716-23 (Pubitemid 34000763)
110. Grenfell B T and Anderson R M 1985 The estimation of age related rates of infection from case notifications and serological data J. Hygiene 95 419-36 (Pubitemid 16227122)
111. Griffiths D A 1973 Multivariate birth-and-death processes as approximations to epidemic processes J. Appl. Probab. 10 15-26
112. Grimmett G 1999 What is Percolation? (Berlin: Springer)
113. Grimmett G 2010 Probability on Graphs: Random Processes on Graphs and Lattices vol 1 1st edn (Cambridge: Cambridge University Press)
114. Guimera R, Mossa S, Turtschi A and Nunes Amaral L A 2005 The worldwide air transportation network: anomalous centrality, community structure, and cities' global roles Proc. Natl Acad. Sci. 102 7794-9 (Pubitemid 40781017)
115. Gullan P J 2005 The Insects: an Outline of Entomology (Chicago, IL: University of Chicago Press)
116. Gupta S et al 1989 Networks of sexual contacts: implications for the pattern of spread of HIV AIDS 3 807
117. Halloran M E, Haber M and Longini I M 1992 Interpretation and estimation of vaccine efficacy under heterogeneity Am. J. Epidemiol. 136 328-43
118. Hanski I and Gaggiotti O E 2004 Ecology, evolution and genetics of metapopulations (New York: Academic)
119. Harris T E 1974 Contact interactions on a lattice Ann. Probab. 2 969-88
120. Harris T E 1963 The Theory of Branching Processes (Berlin: Springer)
121. Hassell M P, Comins H N and May R M 1991 Spatial structure and chaos in insect population dynamics Nature 353 255-8 (Pubitemid 21896765)
122. Healy M J R and Tillett H E 1988 Short-term extrapolation of the AIDS epidemic J. R. Statist. Soc. A 151 50-65
123. Heesterbeek J A P 2002 A brief history of R° and a recipe for its calculation Acta Biotheor. 50 189-204 (Pubitemid 35218664)
124. Hollingsworth T D, Anderson R M and Fraser C 2008 HIV-1 transmission, by stage of infection J. Infectious Diseases 198 687-93
125. Hollingsworth T D, Ferguson N M and Anderson R M 2006 Will travel restrictions control the international spread of pandemic influenza? Nature Med. 12 497-9
126. Holme P, Kim B J, Yoon C N and Han S K 2002 Attack vulnerability of complex networks Phys. Rev. E 65 056109 (Pubitemid 40606846)
127. House T and Keeling M J 2008 Household structure and infectious disease transmission Epidemiol. Infection 137 654
128. House T, Ross J V and Sirl D 2012 How big is an outbreak likely to be? Methods for epidemic final-size calculation Proc. R. Soc. A 469 20120436
129. House T, Davies G, Danon L and Keeling M J 2009 A motif-based approach to network epidemics Bull. Math. Biol. 71 1693-706
130. House T, Hall I, Danon L and Keeling M J 2010 Contingency planning for a deliberate release of smallpox in Great Britain - the role of geographical scale and contact structure BMC Infectious Diseases 10 25
131. House T and Keeling M J 2011 Epidemic prediction and control in clustered populations J. Theor. Biol. 272 1-7
132. House T and Keeling M J 2011 Insights from unifying modern approximations to infections on networks J. R. Soc. Interface 8 67-73
133. Hufnagel L, Brockmann D and Geisel T 2004 Forecast and control of epidemics in a globalized world Proc. Natl Acad. Sci. USA 101 15124-9 (Pubitemid 39391729)
134. Hyman J M and Stanley E 1988 Using mathematical models to understand the AIDS epidemic Math. Biosci. 90 415-73
135. Isham V 2005 Stochastic models for epidemics: current issues and developments Celebrating Statistics: Papers in Honour of Sir David Cox on his 80th Birthday ed A C Davidson, Y Dodge and N Wermuth (Oxford: Oxford University Press) pp 27-54
136. Jacquez J A, Simon C P, Koopman J, Sattenspiel L and Perry T 1988 Modeling and analyzing HIV transmission: the effect of contact patterns Math. Biosci. 92 119-99 (Pubitemid 19046874)
137. Jalvingh A W, Nielen M, Maurice H, Stegeman A J, Elbers A R W and Dijkhuizen A A 1999 Spatial and stochastic simulation to evaluate the impact of events and control measures on the 1997-1998 classical swine fever epidemic in The Netherlands: I. Description of simulation model Preventive Veterinary Med. 42 271-95
138. Jolly A M, Muth S Q, Wylie J L and Potterat J J 2001 Sexual networks and sexually transmitted infections: a tale of two cities J. Urban Health-Bull. New York Acad. Med. 78 433-45 (Pubitemid 32852783)
139. Kallenberg O 2002 Foundations of Modern Probability (Berlin: Springer)
140. Kaplan E H and Lee Y S 1990 How bad can it get? bounding worst case endemic heterogenous mixing models of HIV/AIDS Math. Biosci. 99 157-80 (Pubitemid 20293837)
141. Karatzas I and Shreve S E 1991 Brownian Motion and Stochastic Calculus (Berlin: Springer)
142. Karon J M et al 1988 The projected incidence of AIDS and estimated prevalence of HIV infection in the United States J. Acquired Immune Deficiency Syndromes 1 542
143. Keeling M J 1999 The effects of local spatial structure on epidemiological invasions Proc. R. Soc. B 266 859-67 (Pubitemid 29204217)
144. Keeling M J, Bjornstad O N and Grenfell B T 2004 Metapopulation dynamics of infectious diseases Ecology, Genetics and Evolution of Metapopulations ed I Hanski and O E Gaggiotti (Amsterdam: Elsevier)
145. Keeling M J and Grenfell B T 1998 Effect of variability in infection period on the persistence and spatial spread of infectious diseases Math. Biosci. 147 207-26 (Pubitemid 28009761)
146. Keeling M J and Ross J V 2008 On methods for studying stochastic disease dynamics J. R. Soc. Interface 5 171-81 (Pubitemid 350274453)
147. Keeling M J, Woolhouse M E, Shaw D J, Matthews L, Chase-Topping M, Haydon D T, Cornell S J, Kappey J, Wilesmith J and Grenfell B T 2001 Dynamics of the 2001 UK foot and mouth epidemic: stochastic dispersal in a heterogeneous landscape Science 294 813-7 (Pubitemid 33032092)
148. Keeling M 2005 The implications of network structure for epidemic dynamics Theor. Population Biol. 67 1-8 (Pubitemid 40084668)
149. Keeling M J, Danon L, Vernon M C and House T A 2010 Individual identity and movement networks for disease metapopulations Proc. Natl Acad. Sci. 107 8866-70
150. Keeling M J and Rohani P 2002 Estimating spatial coupling in epidemiological systems: a mechanistic approach Ecol. Lett. 5 20-9 (Pubitemid 34140314)
151. Keeling M J and Rohani P 2008 Modeling Infectious Diseases in Humans and Animals (Princeton, NJ: Princeton University Press)
152. Keeling M J and Grenfell B T 1997 Disease extinction and community size: modeling the persistence of measles Science 275 65-7 (Pubitemid 27020307)
153. Keeling M J, Rohani P and Grenfell B T 2001 Seasonally forced disease dynamics explored as switching between attractors Physica D - Nonlinear Phenom. 148 317-35 (Pubitemid 33651593)
154. Keeling M J 1999 The effects of local spatial structure on epidemiological invasions Proc. R. Soc. Lond. B 266 859-67 (Pubitemid 29204217)
155. Kermack W O and McKendrick A G 1927 Contributions to the mathematical theory of epidemics: I Proc. R. Soc. A 115 700-21
156. King D 2007 Bovine tuberculosis in cattle and badgers: a report by the chief scientific adviser
157. Kiss I Z, Green D M and Kao R R 2006 The network of sheep movements within Great Britain: network properties and their implications for infectious disease spread J. R. Soc. Interface 3 669-77 (Pubitemid 44696252)
158. Klebaner F C 2005 Introduction to Stochastic Calculus With Applications 2nd edn (London: Imperial College Press)
159. Klovdahl A S 1985 Social networks and the spread of infectious diseases: the AIDS example Social Sci. Med. 21 1203-16 (Pubitemid 16175376)
160. Koelle K and Pascual M 2004 Disentangling extrinsic from intrinsic factors in disease dynamics: a nonlinear time series approach with an application to cholera Am. Naturalist 163 901-13 (Pubitemid 38852143)
161. Kot M, Lewis M A and van den Driessche P 1996 Dispersal data and the spread of invading organisms Ecology 77 2027-42
162. Krebs J R 1997 Bovine Tuberculosis in Cattle and Badgers (London: Ministry of Agriculture, Fisheries and Food)
163. Kretzschmar M and Dietz K 1998 The effect of pair formation and variable infectivity on the spread of an infection without recovery Math. Biosci. 148 83-113 (Pubitemid 28236902)
164. Kurtz T 1970 Solutions of ordinary differential equations as limits of pure jump Markov processes J. Appl. Probab. 7 49-58
165. Kurtz T 1971 Limit theorems for sequences of jump Markov processes approximating ordinary differential processes J. Appl. Probab. 8 344-56
166. Feng J and Kurtz T G 2007 Large Deviations for Stochastic Processes (Mathematical Survey & Monographs N 131) (Providence, RI: American Mathematical Society)
167. Kurtz T G 1971 Limit theorems for sequences of jump markov processes approximating ordinary differential processes J. Appl. Probab. 8 344-56
168. Kuske R, Gordillo L F and Greenwood P 2007 Sustained oscillations via coherence resonance in SIR J. Theor. Biol. 245 459-69 (Pubitemid 46365738)
169. Levi T, Kilpatrick A M, Mangel M and Wilmers C C 2012 Deer, predator, and the emergence of Lyme disease Proc. Natl Acad. Sci. 109 10942-7
170. Levins R 1969 Some demographic and genetic consequences of environmental heterogeneity for biological control Bull. Entomol. Soc. Am. 15 237-40
171. Liljeros F, Edling C R, Amaral L A N, Stanley H E and Aberg Y 2001 The web of human sexual contacts Nature 411 907-8 (Pubitemid 32601479)
172. Lipster R S and Shiryaev A N 2001 Statistics of Random Processes I: General Theory 2nd edn (Berlin: Springer)
173. Liu Q X, Wang R H and Jin Z 2009 Persistence, extinction and spatio-temporal synchronization of SIRS spatial models J. Stat. Mech.: Theory Exp. 2009 P07007
174. Lloyd A L 2001 Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods Proc. R. Soc. B 268 985-93 (Pubitemid 32453390)
175. Longini I M, Nizam A, Xu S F, Ungchusak K, Hanshaoworakul W, Cummings D A T and Halloran M E 2005 Containing pandemic influenza at the source Science 309 1083-7 (Pubitemid 41134467)
176. MacArthur R H and Wilson E O 1967 The Theory of Island Biogeography (Princeton, NJ: Princeton University Press)
177. Macdonald G 1957 The Epidemiology and Control of Malaria (Oxford: Oxford University Press)
178. Mah T L and Halperin D T 2010 Concurrent sexual partnerships and the HIV epidemics in Africa: evidence to move forward AIDS Behav. 14 11-6
179. Marm Kilpatrick A, Daszak P, Jones M J, Marra P P and Kramer L D 2006 Host heterogeneity dominates West Nile virus transmission Proc. R. Soc. B 273 2327-33 (Pubitemid 44387340)
180. May R M and Anderson R M 1979 Population biology of infectious diseases: II Nature 280 455-61 (Pubitemid 9234555)
181. May R M 1988 The transmission dynamics of human immunodeficiency virus (HIV) Phil. Trans. R. Soc. Lond. B 321 565-607
182. McCaig C, Begon M, Norman R and Shankland C 2010 A symbolic investigation of superspreaders Bull. Math. Biol. 73 777-94
183. McClelland G A H and Conway G R 1971 Frequency of blood feeding in the mosquito Aedes aegypti Nature 232 485-6
184. McLean A R and Anderson R M 1988 Measles in developing-countries: II. The predicted impact of mass vaccination Epidemiol. Infection 100 419-42
185. Medlock J and Galvani A P 2009 Optimizing influenza vaccine distribution Science 325 1705-8
186. Meyers L A, Pourbohloul B, Newman M E J, Skowronski D M and Brunham R C 2005 Network theory and SARS: predicting outbreak diversity J. Theor. Biol. 232 71-81 (Pubitemid 39388375)
187. Miller B R, Nasci R S, Godsey M S, Savage H M, Lutwama J J, Lanciotti R S and Peters C J 2000 First field evidence for natural vertical transmission of West Nile virus in Culex Univittatus complex mosquitoes from rift valley province, Kenya Am. J. Tropical Med. Hygiene 62 240-6 (Pubitemid 30257584)
188. Miller J C, Slim A C and Volz E M 2012 Edge-based compartmental modelling for infectious disease spread J. R. Soc. Interface 9 890-906
189. Miller J C 2011 A note on a paper by Erik Volz: SIR dynamics in random networks J. Math. Biol. 62 349-58
190. Mitchell A, Bourn D, Mawdsley J, Wint W, Clifton-Hadley R and Gilbert M 2007 Characteristics of cattle movements in Britain - an analysis of records from the cattle tracing system Animal Sci. 80 265-73
191. Mollison D 1991 Dependence of epidemic and population velocities on basic parameters Math. Biosci. 107 255-87 (Pubitemid 23396931)
192. Molloy M and Reed B 1995 A critical-point for random graphs with a given degree sequence Random Struct. Algor. 6 161-79
193. Molloy M and Reed B 1995 A critical point for random graphs with a given degree sequence Random Struct. Algor. 6 161-80
194. Morgan D, Mahe C, Mayanja B, Okongo J M, Lubega R and Whitworth J A G 2002 HIV-1 infection in rural Africa: is there a difference in median time to AIDS and survival compared with that in industrialized countries? AIDS 16 597-603 (Pubitemid 34218855)
195. Morgan W M and Curran J W 1986 Acquired immunodeficiency syndrome: current and future trends Public Health Rep. 101 459
196. Morris M and Kretzschmar M 1997 Concurrent partnerships and the spread of HIV AIDS 11 641-8 (Pubitemid 27135886)
197. Morris R S, Stern M W, Stevenson M A, Wilesmith J W and Sanson R L 2001 Predictive spatial modelling of alternative control strategies for the Foot-and-Mouth disease epidemic in Great Britain, 2001 Veterinary Rec. 149 137-44 (Pubitemid 33606915)
198. Mossong J et al 2008 Social contacts and mixing patterns relevant to the spread of infectious diseases PLoS Medicine 5 e74 (Pubitemid 351471689)
199. Mossong J J et al 2008 Social contacts and mixing patterns relevant to the spread of infectious diseases PLoS Med. 5 e74 (Pubitemid 351471689)
200. Murray J D 2002 Mathematical Biology: An Introduction vol 1 3 edn (Berlin: Springer)
201. Murray J D, Stanley E A and Brown D L 1986 On the spatial spread of rabies among foxes Proc. R. Soc. Lond. B 229 111-50 (Pubitemid 17182383)
202. Newman M 2010 Networks: An Introduction (Oxford: Oxford University Press)
203. Newman M E J 2003 Random graphs as models of networks Handbook of Graphs and Networks ed S Bornholdt and H G Schuster (New York: Wiley)
204. Newman M E J 2002 Assortative mixing in networks Phys. Rev. Lett. 89 208701
205. Newman M E J 2002 Spread of epidemic disease on networks Phys. Rev. E 66 016128 (Pubitemid 40599061)
206. Newman M E J and Watts D J 1999 Renormalization group analysis of the small-world network model Phys. Lett. A 263 341-6
207. Nobel J V 1974 Geographic and temporal development of plagues Nature 250 726-8
208. Okiro E A, White L J, Ngama M, Cane P A, Medley G F and Nokes D J 2010 Duration of shedding of respiratory syncytial virus in a community study of Kenyan children BMC Infectious Diseases 10 15
209. Okubo A and Levin S A 2002 Diffusion and Ecological Problems: Modern Perspectives 2nd edn (New York: Springer)
210. Olsen L F, Truty G L and Schaffer W M 1988 Oscillations and chaos in epidemics: a nonlinear dynamic study of six childhood diseases in Copenhagen, Denmark Theor. Population Biol. 33 344-70
211. Ott S L, Wells S J and Wagner B A 1999 Herd-level economic losses associated with Johne's disease on US dairy operations Preventive Veterinary Med. 40 179-92 (Pubitemid 29291757)
212. Pastor-Satorras R and Vespignani A 2001 Epidemic spreading in scale-free networks Phys. Rev. Lett. 86 3200 (Pubitemid 32317894)
213. Puterman M L 2005 Markov Decision Processes: Discrete Stochastic Dynamic Programming 2nd edn (New York: Wiley)
214. Ren J and Zhang X 2008 Freidlin-Wentzell's large deviations for stochastic evolution equations J. Funct. Anal. 254 3148-72
215. Rhodes C J and Anderson R M 1997 Epidemic thresholds and vaccination in a lattice model of disease spread Theor. Population Biol. 52 101-18 (Pubitemid 27493190)
216. Rizzo D M and Garbelotto M 2003 Sudden oak death: endangering California and Oregon forest ecosystems Frontiers Ecol. Environ. 1 197-204
217. Rohani P, Keeling M J and Grenfell B T 2002 The interplay between determinism and stochasticity in childhood diseases Am. Naturalist 159 469-81 (Pubitemid 34443778)
218. Rohani P, Zhong X and King A A 2010 Contact network structure explains the changing epidemiology of pertussis Science 330 982-5
219. Ross J V, House T and Keeling M J 2010 Calculation of disease dynamics in a population of households PLoS One 5 e9666
220. Ross R 1911 The Prevention of Malaria (London: Murray)
221. Sachs J and Malaney P 2002 The economic and social burden of malaria Nature 415 680-5 (Pubitemid 34136401)
222. Sattenspiel L and Simon C P 1988 The spread and persistence of infectious diseases in structured populations Math. Biosci. 90 341-66
223. Savary S, Teng P S, Willocquet L and Nutter F W 2006 Quantification and modeling of crop losses: a review of purposes Ann. Rev. Phytopathol. 44 89-112 (Pubitemid 44435699)
224. Schenzle D 1984 An age-structured model of pre- and post-vaccination measles transmission IMA J. Math. Appl. Med. Biol. 1 169-91
225. Sellke T 1983 On the asymptotic distribution of the size of a stochastic epidemic J. Appl. Probab. 20 390-4
226. Shaw M W 1995 Simulation of population expansion and spatial pattern when individual dispersal distributions do not decline exponentially with distance Proc. R. Soc. B 259 243-8
227. Simpson J E, Hurtado P J, Medlock J, Molaei G, Andreadis T G, Galvani A P and Diuk-Wasser M A 2012 Vector host-feeding preferences drive transmission of multi-host pathogens: West Nile virus as a model system Proc. R. Soc. B 279 925-33
228. Smith D L, Lucey B, Waller L A, Childs J E and Real L A 2002 Predicting the spatial dynamics of rabies epidemics on heterogeneous landscapes Proc. Natl Acad. Sci. USA 99 3668-72 (Pubitemid 34252164)
229. Ster I C and Ferguson N M 2007 Transmission parameters of the 2001 Foot-and-Mouth epidemic in Great Britain PLoS One 2 e502
230. Styer L M, Carey J R and Wang J L 2007 Mosquitoes do senesce: departure from the paradigm of constant mortality Am. J. Tropical Med. Hyg. 76 111-7 (Pubitemid 351627811)
231. Szmaragd C, Wilson A J, Carpenter S, Wood J L N, Mellor P S and Gubbins S 2009 A modeling framework to describe the transmission of bluetongue virus within and between farms in Great Britain PLoS One 4 e7741
232. Thieme H R and Castillo-Chavez C 1993 How may infection-age-dependent infectivity affect the dynamics of HIV/AIDS? SIAM J. Appl. Math. 53 1447-79
233. Tildesley M, House T, Bruhn M, Curry R J, O'Neil M, Allpress J L E, Smith G and Keeling M J 2010 Impact of spatial clustering on disease transmission and optimal control Proc. Natl Acad. Sci. USA 107 1041-6
234. Tildesley M J, Bessell P R, Keeling M J and Woolhouse M E J 2009 The role of pre-emptive culling in the control of foot-and-mouth disease Proc. R. Soc. Lond. B 276 3239-48
235. Tildesley M J, Gally D L, McNeilly T N, Low J C, Mahajan A and Savill N J 2012 Insights into mucosal innate responses to Escherichia coli O157: H7 colonization of cattle by mathematical modelling of excretion dynamics J. R. Soc. Interface 9 518-27
236. Tildesley M J, Savill N J, Shaw D J, Deardon R, Brooks S P, Woolhouse M E J, Grenfell B T and Keeling M J 2006 Optimal reactive vaccination strategies for a Foot-and-Mouth outbreak in the UK Nature 440 83-6 (Pubitemid 43336271)
237. Tildesley M J, Deardon R, Savill N J, Bessell P R, Brooks S P, Woolhouse M E J, Grenfell B T and Keeling M J 2008 Accuracy of models for the 2001 foot-and-mouth epidemic Proc. R. Soc. B 275 1459-68 (Pubitemid 351653018)
238. Touchette H 2009 The large deviation approach to statistical mechanics Phys. Rep. 478 1-69
239. Truscott J, Fraser C, Cauchemez S, Meeyai A, Hinsley W, Donnelly C A, Ghani A and Ferguson N 2011 Essential epidemiological mechanisms underpinning the transmission dynamics of seasonal influenza J. R. Soc. Interface 9 304-12
240. Tveito A and Winther R 1998 Introduction to Partial Differential Equations: A Computational Approach (New York: Springer)
241. UNAIDS 2010 Global Report Fact Sheet
242. UNAIDS 2012 2012 Report on the Global AIDS Epidemic
243. van Herwaarden O A and Grasman J 1995 Stochastic epidemics: major outbreaks and the duration of the endemic period J. Math. Biol. 33 581-601
244. van Hoek A J, Melegaro A, Zagheni E, Edmunds J W and Gay N 2011 Modelling the impact of a combined varicella and zoster vaccination programme on the epidemiology of varicella zoster virus in England Vaccine 29 2411-20
245. Van Kampen N G 1992 Stochastic Processes in Physics and Chemistry (Amsterdam: Elsevier)
246. Vernon M C and Keeling M J 2009 Representing the UK's cattle herd as static and dynamic networks Proc. R. Soc. B 276 469-76
247. Volz E 2008 SIR dynamics in random networks with heterogeneous connectivity J. Math. Biol. 56 293-310 (Pubitemid 350212021)
248. Wallinga J, Edmunds W J and Kretzschmar M 1999 Perspective: human contact patterns and the spread of airborne infectious diseases TRENDS Microbiol. 7 372-7 (Pubitemid 29421663)
249. Watts C H and May R M 1992 The influence of concurrent partnerships on the dynamics of HIV/AIDS Math. Biosci. 108 89-104
250. Watts D J and Strogatz S H 1998 Collective dynamics of 'small-world' networks Nature 393 440-2 (Pubitemid 28292183)
251. Watts D and Strogatz S 1998 The small world problem Collective Dyn. Small-World Networks 393 440-2
252. White P C and Harris S 1995 Bovine tuberculosis in badger (Meles meles) populations in southwest England: the use of a spatial stochastic simulation model to understand the dynamics of the disease Phil. Trans. R. Soc. Lond. B 349 391-413 (Pubitemid 26452746)
253. WHO 1997 (Switzerland: World Health Organization) Report on Infectious Diseases
254. Wylie J L and Jolly A 2001 Patterns of chlamydia and gonorrhea infection in sexual networks in Manitoba, Canada Sexually Transmitted Diseases 28 14-24 (Pubitemid 32064204)