Mathematical modeling of infectious disease dynamics

Virulence

Volumn 4, Issue 4, 2013, Pages 295-306

  Siettos, Constantinos I ^a   Russo, Lucia ^b  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

^b CNR   (Italy)

Author keywords

Agent based models; Dynamical models; Machine learning models; Mathematical epidemiology; Statistical models

Indexed keywords

DEATH; DISEASE SURVEILLANCE; DISEASE TRANSMISSION; DYNAMICS; HIDDEN MARKOV MODEL; HOST PATHOGEN INTERACTION; HUMAN; INFECTION; INFECTION CONTROL; MATHEMATICAL MODEL; NONHUMAN; PREDICTION AND FORECASTING; PROBABILITY; REGRESSION ANALYSIS; RELIABILITY; REVIEW; RISK ASSESSMENT; SPATIOTEMPORAL ANALYSIS; STOCHASTIC MODEL; TIME SERIES ANALYSIS;

EID: 84878068986     PISSN: 21505594     EISSN: 21505608     Source Type: Journal    
DOI: 10.4161/viru.24041     Document Type: Review

References (142)

1. Trevisanato SI. The biblical plague of the Philistines now has a name, tularemia. Med Hypotheses 2007; 69:1144-1146; PMID:17467189; http://dx.doi.org/10.1016/j.mehy.2007.02.036
2. Acuna-Soto RD, Stahle DW, Therrell MD, Gomez Chavez S, Cleaveland MK. Drought, epidemic disease, and the fall of classic period cultures in Mesoamerica (AD 750-950). Hemorrhagic fevers as a cause of massive population loss. Med Hypotheses 2005; 65:405-409; PMID:15922121; http://dx.doi.org/10.1016/j.mehy.2005.02.025
3. World Health Organization, UNAIDS, Global Report 2011.
4. World Health Organization. "Avian influenza: assessing the pandemic threat." January, 2005. WHO/ CDS/2005.29
5. Stöhr K, Esveld M. Public health. Will vaccines be available for the next influenza pandemic? Science 2004; 306:2195-2196; PMID:15618505; http://dx.doi.org/10.1126/science.1108165
6. Bernoulli D. Essai d'une nouvelle analyse de la mor-talité causée par la petite vérole. Mém. Math Phys Acad Roy Sci Paris 1766; 1:1-45.
7. Blower S, Bernoulli D. An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it. 1766. Rev Med Virol 2004; 14:275-288; PMID:15334536; http://dx.doi.org/10.1002/rmv.443
8. Dietz K, Heesterbeek JAP. Daniel Bernoulli's epidemio-logical model revisited. Math Biosci 2002; 180:1-21; PMID:12387913; http://dx.doi.org/10.1016/S0025-5564(02)00122-0
9. Lambert JH. Die Toedlichkeit der Kinderblattern. Beytrage zum Gebrauche der Mathematik und deren Anwendung. Buchhandlung der Realschule 1772; 3:568.
10. Laplace PS. T h'eorie analytique des probabilit'es. Courcier, Paris, 1812.
11. Ross R. The prevention of malaria. London: John Murray, 1911; 651-686.
12. Smith DL, Battle KE, Hay SI, Barker CM, Scott TW, McKenzie FE. Ross, macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens. PLoS Pathog 2012; 8:e1002588; PMID:22496640; http://dx.doi.org/10.1371/journal.ppat.1002588
13. Kermack WO, McKendrick AG. Contribution to the mathematical theory of epidemics. Proc R Soc Lond, A Contain Pap Math Phys Character 1927; 115:700-721; http://dx.doi.org/10.1098/rspa.1927.0118
14. Kermack WO, McKendrick AG. Contributions to the mathematical theory of epidemics, part II. Proc R Soc Lond 1932; 138:55-83; http://dx.doi.org/10.1098/rspa.1932.0171
15. Kermack WO, McKendrick AG. Contributions to the mathematical theory of epidemics, part III. Proc R Soc Lond 1933; 141:94-112; http://dx.doi.org/10.1098/rspa.1933.0106
16. Guldberg CM, Waage P. Studies Concerning Affinity. C. M. Forhandlinger: Videnskabs-Selskabet i Christiana 1864; 111.
17. En'ko PD. On the course of epidemics of some infectious diseases. Vrach. St. Petersburg 1889; 1008-1010. 1039-1042, 1061-1063.
18. En'ko PD. On the course of epidemics of some infectious diseases. Int J Epidemiol 1989; 18:749-755; PMID:2695472; http://dx.doi.org/10.1093/ije/18.4.749
19. Dietz K. The first epidemic model: a historical note on P.D. En'ko. Aust J Stat 1988; 30A:56-65; http://dx.doi.org/10.1111/j.1467-842X.1988.tb00464.x
20. Frost WH. Some conceptions of epidemics in general by Wade Hampton Frost. Am J Epidemiol 1976; 103:141-151; PMID:766618.
21. McLeod KS. Our sense of Snow: the myth of John Snow in medical geography. Soc Sci Med 2000; 50:923-35; PMID:10714917; http://dx.doi.org/10.1016/S0277-9536(99)00345-7
22. Greenwood M. The application of mathematics to epidemiology. Nature 1916; 243-244; http://dx.doi.org/10.1038/097243a0
23. Unkel S, Farrington PC, Paul H, Garthwaite PH, Robertson C, Andrew N. Statistical methods for the prospective detection of infectious disease outbreaks: a review. J R Stat Soc Ser A Stat Soc 2012; 175:49-82; http://dx.doi.org/10.1111/j.1467-985X.2011.00714.x
24. Serfling RE. Methods for current statistical analysis of excess pneumonia-influenza deaths. Public Health Rep 1963; 78:494-506; PMID:19316455; http://dx.doi.org/10.2307/4591848
25. Stroup D F, Thacker SB, Herndon JL. Application of multiple time series analysis to the estimation of pneumonia and influenza mortality by age 1962-1983. Stat Med 1988; 7:1045-1059; PMID:3264612; http://dx.doi.org/10.1002/sim.4780071006
26. Costagliola D, Flahault A, Galinec D, Garnerin P, Menares J, Valleron AJ. When is the epidemic warning cut-off point exceeded? Eur J Epidemiol 1994; 10:475-476; PMID:7843360; http://dx.doi.org/10.1007/BF01719680
27. Greenland S. Regression Methods for Epidemiologic Analysis. Handbook of Epidemiology. Part II, 2005, 625-691; http://dx.doi.org/10.1007/978-3-540-26577-1_17
28. Pelat C, Boëlle PY, Cowling BJ, Carrat F, Flahault A, Ansart S, et al. Online detection and quantification of epidemics. BMC Med Inform Decis Mak 2007; 7:29; PMID:17937786; http://dx.doi.org/10.1186/1472-6947-7-29
29. Dafni UG, Tsiodras S, Panagiotakos D, Gkolfinopoulou K, Kouvatseas G, Tsourti Z, et al. Algorithm for statistical detection of peaks-syndromic surveillance system for the Athens 2004 Olympic Games. MMWR Morb Mortal Wkly Rep 2004; 24(Suppl):86-94.
30. Choi K, Thacker SB. An evaluation of influenza mortality surveillance, 1962-1979. I. Time series forecasts of expected pneumonia and influenza deaths. Am J Epidemiol 1981; 113:215-226; PMID:6258426.
31. Abeku TA, de Vlas SJ, Borsboom G, Teklehaimanot A, Kebede A, Olana D, et al. Forecasting malaria incidence from historical morbidity patterns in epidemic-prone areas of Ethiopia: a simple seasonal adjustment method performs best. Trop Med Int Health 2002; 7:851-857; PMID:12358620; http://dx.doi.org/10.1046/j.1365-3156.2002.00924.x
32. Soebiyanto R P, Adimi F, Kiang RK. Modeling and predicting seasonal influenza transmission in warm regions using climatological parameters. PLoS One 2010; 5:e9450; PMID:20209164; http://dx.doi.org/10.1371/journal.pone.0009450
33. Nunes B, Viboud C, Machado A, Ringholz C, Rebelo-de-Andrade H, Nogueira P, et al. Excess mortality associated with influenza epidemics in Portugal, 1980 to 2004. PLoS One 2011; 6:e20661; PMID:21713040; http://dx.doi.org/10.1371/journal.pone.0020661
34. Bai Y, Jin Z. Prediction of SARS epidemic by BP neural networks with online prediction strategy. Chaos Solitons Fractals 2005; 26:559-569; http://dx.doi.org/10.1016/j.chaos.2005.01.064
35. Akaike H. A new look at the statistical model identification. IEEE Trans Automat Contr 1974; 19:716-723; http://dx.doi.org/10.1109/TAC.1974.1100705
36. Page ES. Continuous inspection scheme. Biometrika 1954; 41:100-115.
37. Raubertas R F. An analysis of disease surveillance data that uses the geographic locations of the reporting units. Stat Med 1989; 8:267-271, discussion 279-81; PMID:2711060; http://dx.doi.org/10.1002/sim.4780080306
38. Cowling BJ, Wong IOL, Ho LM, Riley S, Leung GM. Methods for monitoring influenza surveillance data. Int J Epidemiol 2006; 35:1314-1321; PMID:16926216; http://dx.doi.org/10.1093/ije/dyl162
39. Höhle M, Paul M. Count data regression charts for the monitoring of surveillance time series. Comput Stat Data Anal 2008; 52:4357-4368; http://dx.doi.org/10.1016/j.csda.2008.02.015
40. Watkins RE, Eagleson S, Veenendaal B, Wright G, Plant AJ. Applying cusum-based methods for the detection of outbreaks of Ross River virus disease in Western Australia. BMC Med Inform Decis Mak 2008; 8:37; PMID:18700044; http://dx.doi.org/10.1186/1472-6947-8-37
41. Spanos A, Theocharis G, Karageorgopoulos DE, Peppas G, Fouskakis D, Falagas ME. Surveillance of community outbreaks of respiratory tract infections based on house-call visits in the metropolitan area of Athens, Greece. PLoS One 2012; 7:e40310; PMID:22905091; http://dx.doi.org/10.1371/journal.pone.0040310
42. Roberts S W. Control chart tests based on geometric moving averages. Technomearics 1959; 1:239-250; http://dx.doi.org/10.1080/00401706.1959.10489860
43. Elbert Y, Burkom HS. Development and evaluation of a data-adaptive alerting algorithm for univariate temporal biosurveillance data. Stat Med 2009; 28:3226-3248; PMID:19725023; http://dx.doi.org/10.1002/sim.3708
44. Shiryaev AN. On optimum methods in quickest detection problems. Theory Probab Appl 1963; 8:22-46; http://dx.doi.org/10.1137/1108002
45. Frisen M, de Mare J. Optimal surveillance. Biometrika 1991; 78:271-280.
46. Kulldorff M. Prospective time periodic geographical disease surveillance using a scan statistic. J Royal Stat Soc A 2001; 164:61-72; http://dx.doi.org/10.1111/1467-985X.00186
47. Bock D, Andersson E, Frisén M. Statistical surveillance of epidemics: peak detection of influenza in Sweden. Biom J 2008; 50:71-85; PMID:17849383; http://dx.doi.org/10.1002/bimj.200610362
48. Zhou Q, Luo Y, Wang Z. A control chart based on likelihood ratio test for detecting patterned mean and variance shifts. Comput Stat Data Anal 2010; 54:1634-1645; http://dx.doi.org/10.1016/j.csda.2010.01.020
49. Frisén M, Andersson E, Schiöler L. Sufficient reduction in multivariate surveillance. Comm Statist Theory Methods 2011; 40:1821-1838; http://dx.doi.org/10.1080/03610921003714162
50. Naus JI. Clustering of random points in two dimensions. Biometrika 1965; 52:263-267.
51. Kulldorff M, Heffernan R, Hartman J, Assunção RM, Mostashari F. A space-time permutation scan statistic for the early detection of disease outbreaks. PLoS Med 2005; 2:e59; PMID:15719066; http://dx.doi.org/10.1371/journal.pmed.0020059
52. Le Strat Y, Carrat F. Monitoring epidemio-logic surveillance data using hidden Markov models. Stat Med 1999; 18:3463-3478; PMID:10611619; http://dx.doi.org/10.1002/(SICI)1097-0258(19991230)18:243463::AID-SIM4093.0.CO;2-I
53. Rath TM, Carreras M, Sebastiani P. Automated detection of influenza epidemics with hidden Markov models. Berthold MR, Lenz HJ, Bradley E, Kruse R, Borgelt C, editors. Berlin: Springer, 2003.
54. Cooper B, Lipsitch M. The analysis of hospital infection data using hidden Markov models. Biostatistics 2004; 5:223-237; PMID:15054027; http://dx.doi.org/10.1093/biostatistics/5.2.223
55. Rabiner LR, Juang BH. An introduction to hidden Markov models. IEEE ASSP Mag 1986; 3:4-16; http://dx.doi.org/10.1109/MASSP.1986.1165342
56. Viterbi AJ. Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Trans Inf Theory 1967; 13:260-269; http://dx.doi.org/10.1109/TIT.1967.1054010
57. Dempster A P, Laird NM, Rubin DB. Maximum likelihood from incomplete data via the EM Algorithm. J R Stat Soc, B 1977; 39:1-38.
58. Best N, Richardson S, Thomson A. A comparison of Bayesian spatial models for disease mapping. Stat Methods Med Res 2005; 14:35-59; PMID:15690999; http://dx.doi.org/10.1191/0962280205sm388oa
59. Knorr-Held L, Rasser G. Bayesian detection of clusters and discontinuities in disease maps. Biometrics 2000; 56:13-21; PMID:10783772; http://dx.doi.org/10.1111/j.0006-341X.2000.00013.x
60. Gangnon RE, Clayton MK. Bayesian detection and modeling of spatial disease clustering. Biometrics 2000; 56:922-935; PMID:10985238; http://dx.doi.org/10.1111/j.0006-341X.2000.00922.x
61. Denison DGT, Holmes CC. Bayesian partitioning for estimating disease risk. Biometrics 2001; 57:143-149; PMID:11252589; http://dx.doi.org/10.1111/j.0006-341X.2001.00143.x
62. MacNab YC. Hierarchical Bayesian modeling of spatially correlated health service outcome and utilization rates. Biometrics 2003; 59:305-316; PMID:12926715; http://dx.doi.org/10.1111/1541-0420.00037
63. Frisèn M. Spatial outbreak detection based on inference principles for multivariate surveillance. Research Report 2012; 1: ISSN 0349-8034.
64. Robertson C, Nelson TA, MacNab YC, Lawson AB, Lawson AB. Review of methods for space-time disease surveillance. Spat Spatiotemporal Epidemiol 2010; 1:105-116; PMID:22749467; http://dx.doi.org/10.1016/j.sste.2009.12.001
65. Lawson AB, Kleinman K, eds. Spatial and Syndromic Surveillance for Public Health. Chichester: Wiley, 2005.
66. Rencher AC. Methods of Multivariate Analysis. John Wiley and Sons, 2002.
67. Kleinschmidt I, Bagayoko M, Clarke GPY, Craig M, Le Sueur D. A spatial statistical approach to malaria mapping. Int J Epidemiol 2000; 29:355-361; PMID:10817136; http://dx.doi.org/10.1093/ije/29.2.355
68. Carrat F, Valleron AJ. Epidemiologic mapping using the "kriging" method: application to an influenza-like illness epidemic in France. Am J Epidemiol 1992; 135:1293-1300; PMID:1626546.
69. Cohen AA, Dhingra N, Jotkar RM, Rodriguez PS, Sharma V P, Jha P. The Summary Index of Malaria Surveillance (SIMS): a stable index of malaria within India. Popul Health Metr 2010; 8:1; PMID:20181218; http://dx.doi.org/10.1186/1478-7954-8-1
70. Coleman M, Coleman M, Mabuza AM, Kok G, Coetzee M, Durrheim DN. Using the SaTScan method to detect local malaria clusters for guiding malaria control programmes. Malar J 2009; 8:68; PMID:19374738; http://dx.doi.org/10.1186/1475-2875-8-68
71. Kulldorff M. Prospective time-periodic geographical disease surveillance using a scan statistic. J R Stat Soc Ser A Stat Soc 2001; A164:61-72; http://dx.doi.org/10.1111/1467-985X.00186
72. Kulldorff M, Nagarwalla N. Spatial disease clusters: detection and inference. Stat Med 1995; 14:799-810; PMID:7644860; http://dx.doi.org/10.1002/sim.4780140809
73. Kulldorff M, Heffernan R, Hartman J, Assunção R, Mostashari F. A space-time permutation scan statistic for disease outbreak detection. PLoS Med 2005; 2:e59; PMID:15719066; http://dx.doi.org/10.1371/journal.pmed.0020059
74. Gaudart J, Poudiougou B, Dicko A, Ranque S, Toure O, Sagara I, et al. Space-time clustering of childhood malaria at the household level: a dynamic cohort in a Mali village. BMC Public Health 2006; 6:286; PMID:17118176; http://dx.doi.org/10.1186/1471-2458-6-286
75. Sklar A. Random variables, joint distributions, and copulas. Kybernetica 1973; 9:449-460.
76. nd edition. NewYork: Springer, 2006.
77. Cox DR. Regression Models and Life Tables (with Discussion). J R Stat Soc, B 1972; 34:187-220.
78. Cox DR, Oakes D. Analysis of Survival Data. London: Chapman and Hall. 1984.
79. Molenberghs G, Lessafre E. Marginal modeling of correlated ordina data using a multivariate Plackett distribution. J Am Stat Assoc 1994; 89:633-644; http://dx.doi.org/10.1080/01621459.1994.10476788
80. Hawkins C, Chalamilla G, Okuma J, Spiegelman D, Hertzmark E, Aris E, et al. Gender differences in antiretroviral treatment outcomes among HIV-infected adults in Dar es Salaam, Tanzania. AIDS 2011; 25:1189-1197; PMID:21505309; http://dx.doi.org/10.1097/QAD.0b013e3283471deb
81. Louzada F, Suzuki AK, Cancho VG, Prince FL, Pereira GA. The long-term bivariate survival FGM copula model: an application to a brazilian HIV Data. J Data Sci 2012; 10:511-535.
82. Hogan DR, Salomon JA, Canning D, Hammitt JK, Zaslavsky AM, Bärnighausen T, et al. National HIV prevalence estimates for sub-Saharan Africa: controlling selection bias with Heckman-type selection models. Sex Transm Infect 2012; 88(Suppl 2):i17-23; PMID:23172342; http://dx.doi.org/10.1136/sex-trans-2012-050636
83. Cornell M, Schomaker M, Garone DB, Giddy J, Hoffmann CJ, Lessells R, et al.; International Epidemiologic Databases to Evaluate AIDS Southern Africa Collaboration. Gender differences in survival among adult patients starting antiretroviral therapy in South Africa: a multicentre cohort study. PLoS Med 2012; 9:e1001304; PMID:22973181; http://dx.doi.org/10.1371/journal.pmed.1001304
84. Tibaldi F, Molenberghs G, Burzykowski T, Geys H. Pseudo-likelihood estimation for a marginal mul-tivariate survival model. Stat Med 2004; 23:947-963; PMID:15027082; http://dx.doi.org/10.1002/sim.1664
85. Kor CT, Cheng KF, Chen YH. A method for analyzing clustered interval-censored data based on Cox's model. Stat Med 2013; 32:822-832; PMID:22911905; http://dx.doi.org/10.1002/sim.5562
86. El Adlouni S, Beaulieu C, Ouarda TBMJ, Gosselin PL, Saint-Hilaire A. Effects of climate on West Nile Virus transmission risk used for public health decision-making in Quebec. Int J Health Geogr 2007; 6:40-47; PMID:17883862; http://dx.doi.org/10.1186/1476-072X-6-40
87. Anderson RM, May RM. Population biology of infectious diseases: Part I. Nature 1979; 280:361-367; PMID:460412; http://dx.doi.org/10.1038/280361a0
88. Brauder F, Castillo-Chavez C. Mathematical models in population biology and epidemiology. New York: Springer-Verlag, 2001.
89. Murray JD. Mathematical Biology II. New York: Springer-Verlag, 2002.
90. Feng Z, Dieckmann U, Levin S, eds. Disease evolution: models, concepts and data analysis. AMS 2006.
91. Keeling MJ. The effects of local spatial structure on epi-demiological invasions. Proc Biol Sci 1999; 266:859-867; PMID:10343409; http://dx.doi.org/10.1098/rspb.1999.0716
92. Greenhalgh D, Das R. Modelling epidemics with variable contact rates. Theor Popul Biol 1995; 47:129-179; PMID:7740440; http://dx.doi.org/10.1006/tpbi.1995.1006
93. Liu WM, Levin SA, Iwasa Y. Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. J Math Biol 1986; 23:187-204; PMID:3958634; http://dx.doi.org/10.1007/BF00276956
94. Hethcote HW, Zhien M, Shengbing L. Effects of quarantine in six endemic models for infectious diseases. Math Biosci 2002; 180:141-160; PMID:12387921; http://dx.doi.org/10.1016/S0025-5564(02)00111-6
95. Joo J, Lebowitz JL. Pair approximation of the stochastic susceptible-infected-recovered-susceptible epidemic model on the hypercubic lattice. Phys Rev E Stat Nonlin Soft Matter Phys 2004; 70:036114; PMID:15524594; http://dx.doi.org/10.1103/PhysRevE.70.036114
96. Reppas A, De Decker Y, Siettos CI. On the Efficiency of the Equation-Free Closure of Statistical Moments: Dynamical properties of a Stochastic Epidemic Model on Erdos-Renyi networks. J Stat Mech 2012; 8:P08020; http://dx.doi.org/10.1088/1742-5468/2012/08/P08020
97. Coburn BJ, Wagner BG, Blower S. Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1). BMC Med 2009; 7:30; PMID:19545404; http://dx.doi.org/10.1186/1741-7015-7-30
98. Nichol KL, Tummers K, Hoyer-Leitzel A, Marsh J, Moynihan M, McKelvey S. Modeling seasonal influenza outbreak in a closed college campus: impact of preseason vaccination, in-season vaccination and holidays/ breaks. PLoS One 2010; 5:e9548; PMID:20209058; http://dx.doi.org/10.1371/journal.pone.0009548
99. Correia AM, Mena FC, Soares AJ. An Application of the SIR Model to the Evolution of Epidemics in Portugal, Dynamics. Games and Science II. Springer Proceedings in Mathematics 2011; 2:247-250; http://dx.doi.org/10.1007/978-3-642-14788-3_19
100. Gaudart J, Touré O, Dessay N, Dicko AL, Ranque S, Forest L, et al. Modelling malaria incidence with environmental dependency in a locality of Sudanese savannah area, Mali. Malar J 2009; 8:61; PMID:19361335; http://dx.doi.org/10.1186/1475-2875-8-61
101. Magal P, McCluskey CC, Webb GF. Lyapunov functional and global asymptotic stability for an infection-age model. Appl Anal 2010; 89:1109-1140; http://dx.doi.org/10.1080/00036810903208122
102. Metcalf CJE, Munayco C V, Chowell G, Grenfell BT, Bjørnstad ON. Rubella metapopulation dynamics and importance of spatial coupling to the risk of congenital rubella syndrome in Peru. J R Soc Interface 2011; 8:369-376; PMID:20659931; http://dx.doi.org/10.1098/rsif.2010.0320
103. Ajelli M, Fumanelli L, Manfredi P, Merler S. Spatiotemporal dynamics of viral hepatitis A in Italy. Theor Popul Biol 2011; 79:1-11; PMID:20883708; http://dx.doi.org/10.1016/j.tpb.2010.09.003
104. Webb GF, D'Agata EM, Magal P, Ruan S. A model of antibiotic-resistant bacterial epidemics in hospitals. Proc Natl Acad Sci U S A 2005; 102:13343-13348; PMID:16141326; http://dx.doi.org/10.1073/pnas.0504053102
105. Gaudart J, Ghassani M, Mintsa J, Rachdi M, Waku J, Demongeot J. Demographic and spatial factors as causes of an epidemic spread, the copule approach. Application to the retro-prediction of the Black Death epidemy of 1346. IEEE Advanced Information Networking and Application 2010: 751-758.
106. Gaudart J, Ghassani M, Mintsa J, Rachdi M, Waku J, Demongeot J. Demography and diffusion in epidemics: malaria and black death spread. Acta Biotheor 2010; 58:277-305; PMID:20706773; http://dx.doi.org/10.1007/s10441-010-9103-z
107. Demongeot J, Gaudart J, Mintsa J, Rachdi M. Demography in epidemics modelling. Communications Pure & Appl. Analysis 2012; 11:61-82.
108. Severo N. Generalizations of some stochastic epidemic models. Math Biosci 1969; 4:395-402; http://dx.doi.org/10.1016/0025-5564(69)90019-4
109. Prosperi MCF, D'Autilia R, Incardona F, De Luca A, Zazzi M, Ulivi G. Stochastic modelling of genotypic drug-resistance for human immunodeficiency virus towards long-term combination therapy optimization. Bioinformatics 2009; 25:1040-1047; PMID:18977781; http://dx.doi.org/10.1093/bioinformatics/btn568
110. Vardavas R, Blower S. The emergence of HIV transmitted resistance in Botswana: "when will the WHO detection threshold be exceeded?" PLoS One 2007; 2:e152; PMID:17225857; http://dx.doi.org/10.1371/journal.pone.0000152
111. Allen LJ, Burgin AM. Comparison of deterministic and stochastic SIS and SIR models in discrete time. Math Biosci 2000; 163:1-33; PMID:10652843; http://dx.doi.org/10.1016/S0025-5564(99)00047-4
112. Lekone PE, Finkenstädt B F. Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study. Biometrics 2006; 62:1170-1177; PMID:17156292; http://dx.doi.org/10.1111/j.1541-0420.2006.00609.x
113. Bishai D, Johns B, Nair D, Nabyonga-Orem J, Fiona-Makmot B, Simons E, et al. The cost-effectiveness of supplementary immunization activities for measles: a stochastic model for Uganda. J Infect Dis 2011; 204(Suppl 1):S107-115; PMID:21666151; http://dx.doi.org/10.1093/infdis/jir131
114. Wang RH, Jin Z, Liu QX, van de Koppel J, Alonso D. A simple stochastic model with environmental transmission explains multi-year periodicity in outbreaks of avian flu. PLoS One 2012; 7:e28873; PMID:22363397; http://dx.doi.org/10.1371/journal.pone.0028873
115. Streftaris G, Gibson GJ. Bayesian inference for stochastic epidemics in closed populations. Stat Model 2004; 4:63-75; http://dx.doi.org/10.1191/1471082X04st065oa
116. Mintsa J, Rachdi M, Demongeot J. Stochastic approach in modelling epidemic spread. In: IEEE AINA' 11 & BLSMC' 11, IEEE Proceedings, Piscataway, 478-482 (2011).
117. Allen LJS, Burgin AM. Comparison of deterministic and stochastic SIS and SIR models in discrete time. Math Biosci 2000; 163:1-33; PMID:10652843; http://dx.doi.org/10.1016/S0025-5564(99)00047-4
118. Newman MEJ. The structure and function of networks. SIAM Rev 2003; 45:167-256; http://dx.doi.org/10.1137/S003614450342480
119. Barabasi AL. Statistical mechanics of complex networks. Rev Mod Phys 2002; 74:47-97; http://dx.doi.org/10.1103/RevModPhys.74.47
120. Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU. Complex networks: Structure and dynamics. Phys Rep 2006; 424:175-308; http://dx.doi.org/10.1016/j.physrep.2005.10.009
121. Keeling MJ, Danon L, Vernon MC, House TA. Individual identity and movement networks for disease metapopulations. Proc Natl Acad Sci U S A 2010; 107:8866-8870; PMID:20421468; http://dx.doi.org/10.1073/pnas.1000416107
122. Keeling MJ, Eames KT. Networks and epidemic models. J R Soc Interface 2005; 2:295-307; PMID:16849187; http://dx.doi.org/10.1098/rsif.2005.0051
123. Read JM, Eames KTF, Edmunds WJ. Dynamic social networks and the implications for the spread of infectious disease. J R Soc Interface 2008; 5:1001-1007; PMID:18319209; http://dx.doi.org/10.1098/rsif.2008.0013
124. Kuperman M, Abramson G. Small world effect in an epidemiological model. Phys Rev Lett 2001; 86:2909-2912; PMID:11290070; http://dx.doi.org/10.1103/PhysRevLett.86.2909
125. Hwang DU, Boccaletti S, Moreno Y, López-Ruiz R. Thresholds for epidemic outbreaks in finite scale-free networks. Math Biosci Eng 2005; 2:317-327; PMID:20369925; http://dx.doi.org/10.3934/mbe.2005.2.317
126. Shirley MDF, Rushton S P. The impacts of network topology on disease spread. Ecol Complex 2005; 2:287-299; http://dx.doi.org/10.1016/j.ecocom.2005.04.005
127. Reppas AI, Spiliotis KG, Siettos CI. On the effect of the path length of small-world networks on epidemic dynamics. Virulence 2012; 3:146-153; PMID:22460641; http://dx.doi.org/10.4161/viru.19131
128. Gross T, Sayama H. Adaptive Networks: Theory, Models, and Data. Springer, Heidelberg, 2009.
129. Christakis NA, Fowler JH. Social network sensors for early detection of contagious outbreaks. PLoS One 2010; 5:e12948; PMID:20856792; http://dx.doi.org/10.1371/journal.pone.0012948
130. Salathé M, Kazandjieva M, Lee JW, Levis P, Feldman M W, Jones JH. A high-resolution human contact network for infectious disease transmission. Proc Natl Acad Sci U S A 2010; 107:22020-22025; PMID:21149721; http://dx.doi.org/10.1073/pnas.1009094108
131. Rocha LEC, Liljeros F, Holme P. Simulated epidemics in an empirical spatiotemporal network of 50,185 sexual contacts. PLoS Comput Biol 2011; 7:e1001109; PMID:21445228; http://dx.doi.org/10.1371/journal.pcbi.1001109
132. Eubank S, Guclu H, Kumar VS, Marathe MV, Srinivasan A, Toroczkai Z, et al. Modelling disease outbreaks in realistic urban social networks. Nature 2004; 429:180-184; PMID:15141212; http://dx.doi.org/10.1038/nature02541
133. Ferguson NM, Cummings DA, Cauchemez S, Fraser C, Riley S, Meeyai A, et al. Strategies for containing an emerging influenza pandemic in Southeast Asia. Nature 2005; 437:209-214; PMID:16079797; http://dx.doi.org/10.1038/nature04017
134. Burke DS, Epstein JM, Cummings DA, Parker JI, Cline KC, Singa RM, et al. Individual-based computational modeling of smallpox epidemic control strategies. Acad Emerg Med 2006; 13:1142-1149; PMID:17085740; http://dx.doi.org/10.1111/j.1553-2712.2006.tb01638.x
135. Balcan D, Colizza V, Gonçalves B, Hu H, Ramasco JJ, Vespignani A. Multiscale mobility networks and the spatial spreading of infectious diseases. Proc Natl Acad Sci U S A 2009; 106:21484-21489; PMID:20018697; http://dx.doi.org/10.1073/pnas.0906910106
136. Ginsberg J, Mohebbi MH, Patel RS, Brammer L, Smolinski MS, Brilliant L. Detecting influenza epidemics using search engine query data. Nature 2009; 457:1012-1014; PMID:19020500; http://dx.doi.org/10.1038/nature07634
137. Hulth A, Rydevik G, Linde A. Web queries as a source for syndromic surveillance. PLoS One 2009; 4:e4378; PMID:19197389; http://dx.doi.org/10.1371/journal.pone.0004378
138. Chan EH, Sahai V, Conrad C, Brownstein JS. Using web search query data to monitor dengue epidemics: a new model for neglected tropical disease surveillance. PLoS Negl Trop Dis 2011; 5:e1206; PMID:21647308; http://dx.doi.org/10.1371/journal.pntd.0001206
139. Kevrekidis IG, Gear CW, Hyman JM, Kevrekidis PG, Runborg O, Theodoropoulos C. Equation-free coarsegrained multiscale computation: enabling microscopic simulators to perform system-level analysis. Comm Math Sciences 2003; 1:715-762.
140. Cisternas J, Gear CW, Levin S, Kevrekidis IG. Equation-free modelling of evolving diseases: coarsegrained computations with individual-based models. Proc R Soc Lond A 2004; 460:1-19.
141. Reppas AI, Spiliotis KG, Siettos CI. Epidemionics: from the host-host interactions to the systematic analysis of the emergent macroscopic dynamics of epidemic networks. Virulence 2010; 1:338-349; PMID:21178467; http://dx.doi.org/10.4161/viru.1.4.12196
142. Siettos CI. Equation-Free multiscale computational analysis of individual-based epidemic dynamics on networks. Appl Math Comput 2011; 218:324-336; http://dx.doi.org/10.1016/j.amc.2011.05.067