Mathematical modeling of infectious disease dynamics

References

• Trevisanato SI. The biblical plague of the Philistines now has a name, tularemia. Med Hypotheses 2007; 69:1144 - 6; http://dx.doi.org/10.1016/j.mehy.2007.02.036; PMID: 17467189
   PubMed Web of Science ®Google Scholar
• 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 - 9; http://dx.doi.org/10.1016/j.mehy.2005.02.025; PMID: 15922121
   PubMed Web of Science ®Google Scholar
• World Health Organization, UNAIDS, Global Report 2011.
   Google Scholar
• World Health Organization. “Avian influenza: assessing the pandemic threat.” January, 2005. WHO/CDS/2005.29.
   Google Scholar
• Stöhr K, Esveld M. Public health. Will vaccines be available for the next influenza pandemic?. Science 2004; 306:2195 - 6; http://dx.doi.org/10.1126/science.1108165; PMID: 15618505
   PubMed Web of Science ®Google Scholar
• Bernoulli D. Essai d'une nouvelle analyse de la mortalité causée par la petite vérole. Mém. Math Phys Acad Roy Sci Paris 1766; 1:1 - 45
   Google Scholar
• 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 - 88; http://dx.doi.org/10.1002/rmv.443; PMID: 15334536
   PubMed Web of Science ®Google Scholar
• Dietz K, Heesterbeek JAP. Daniel Bernoulli’s epidemiological model revisited. Math Biosci 2002; 180:1 - 21; http://dx.doi.org/10.1016/S0025-5564(02)00122-0; PMID: 12387913
   PubMed Web of Science ®Google Scholar
• Lambert JH. Die Toedlichkeit der Kinderblattern. Beytrage zum Gebrauche der Mathematik und deren Anwendung. Buchhandlung der Realschule 1772; 3:568
   Google Scholar
• Laplace PS. Th’eorie analytique des probabilit’es. Courcier, Paris, 1812.
   Google Scholar
• Ross R. The prevention of malaria. London: John Murray, 1911: 651–686.
   Google Scholar
• 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; http://dx.doi.org/10.1371/journal.ppat.1002588; PMID: 22496640
   PubMed Web of Science ®Google Scholar
• Kermack WO, McKendrick AG. Contribution to the mathematical theory of epidemics. Proc R Soc Lond, A Contain Pap Math Phys Character 1927; 115:700 - 21; http://dx.doi.org/10.1098/rspa.1927.0118
   Google Scholar
• 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
   Google Scholar
• 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
   Google Scholar
• Guldberg CM, Waage P. Studies Concerning Affinity. C. M. Forhandlinger: Videnskabs-Selskabet i Christiana 1864; 111.
   Google Scholar
• En'ko PD. On the course of epidemics of some infectious diseases. Vrach. St. Petersburg 1889; 1008-1010. 1039-1042, 1061-1063.
   Google Scholar
• En’ko PD. On the course of epidemics of some infectious diseases. Int J Epidemiol 1989; 18:749 - 55; http://dx.doi.org/10.1093/ije/18.4.749; PMID: 2695472
   PubMed Web of Science ®Google Scholar
• 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
   Google Scholar
• Frost WH. Some conceptions of epidemics in general by Wade Hampton Frost. Am J Epidemiol 1976; 103:141 - 51; PMID: 766618
   PubMed Web of Science ®Google Scholar
• McLeod KS. Our sense of Snow: the myth of John Snow in medical geography. Soc Sci Med 2000; 50:923 - 35; http://dx.doi.org/10.1016/S0277-9536(99)00345-7; PMID: 10714917
   PubMed Web of Science ®Google Scholar
• Greenwood M. The application of mathematics to epidemiology. Nature 1916; xcvii:243 - 4; http://dx.doi.org/10.1038/097243a0
   Google Scholar
• 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
   Web of Science ®Google Scholar
• Serfling RE. Methods for current statistical analysis of excess pneumonia-influenza deaths. Public Health Rep 1963; 78:494 - 506; http://dx.doi.org/10.2307/4591848; PMID: 19316455
   PubMed Web of Science ®Google Scholar
• Stroup DF, 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 - 59; http://dx.doi.org/10.1002/sim.4780071006; PMID: 3264612
   PubMed Web of Science ®Google Scholar
• Costagliola D, Flahault A, Galinec D, Garnerin P, Menares J, Valleron A-J. When is the epidemic warning cut-off point exceeded?. Eur J Epidemiol 1994; 10:475 - 6; http://dx.doi.org/10.1007/BF01719680; PMID: 7843360
   PubMed Web of Science ®Google Scholar
• Greenland S. Regression Methods for Epidemiologic Analysis. Handbook of Epidemiology. Part II, 2005, 625-691, DOI: 10.1007/978-3-540-26577-1_17.
   Google Scholar
• Pelat C, Boëlle P-Y, Cowling BJ, Carrat F, Flahault A, Ansart S, et al. Online detection and quantification of epidemics. BMC Med Inform Decis Mak 2007; 7:29; http://dx.doi.org/10.1186/1472-6947-7-29; PMID: 17937786
   PubMed Web of Science ®Google Scholar
• 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
   Google Scholar
• 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 - 26; PMID: 6258426
   PubMed Web of Science ®Google Scholar
• 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 - 7; http://dx.doi.org/10.1046/j.1365-3156.2002.00924.x; PMID: 12358620
   PubMed Web of Science ®Google Scholar
• Soebiyanto RP, Adimi F, Kiang RK. Modeling and predicting seasonal influenza transmission in warm regions using climatological parameters. PLoS One 2010; 5:e9450; http://dx.doi.org/10.1371/journal.pone.0009450; PMID: 20209164
   PubMed Web of Science ®Google Scholar
• 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; http://dx.doi.org/10.1371/journal.pone.0020661; PMID: 21713040
   PubMed Web of Science ®Google Scholar
• Bai Y, Jin Z. Prediction of SARS epidemic by BP neural networks with online prediction strategy. Chaos Solitons Fractals 2005; 26:559 - 69; http://dx.doi.org/10.1016/j.chaos.2005.01.064
   Web of Science ®Google Scholar
• Akaike H. A new look at the statistical model identification. IEEE Trans Automat Contr 1974; 19:716 - 23; http://dx.doi.org/10.1109/TAC.1974.1100705
   Web of Science ®Google Scholar
• Page ES. Continuous inspection scheme. Biometrika 1954; 41:100 - 15
   Web of Science ®Google Scholar
• Raubertas RF. An analysis of disease surveillance data that uses the geographic locations of the reporting units. Stat Med 1989; 8:267 - 71, discussion 279-81; http://dx.doi.org/10.1002/sim.4780080306; PMID: 2711060
   PubMed Web of Science ®Google Scholar
• Cowling BJ, Wong IOL, Ho L-M, Riley S, Leung GM. Methods for monitoring influenza surveillance data. Int J Epidemiol 2006; 35:1314 - 21; http://dx.doi.org/10.1093/ije/dyl162; PMID: 16926216
   PubMed Web of Science ®Google Scholar
• Höhle M, Paul M. Count data regression charts for the monitoring of surveillance time series. Comput Stat Data Anal 2008; 52:4357 - 68; http://dx.doi.org/10.1016/j.csda.2008.02.015
   Web of Science ®Google Scholar
• 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; http://dx.doi.org/10.1186/1472-6947-8-37; PMID: 18700044
   PubMed Web of Science ®Google Scholar
• 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; http://dx.doi.org/10.1371/journal.pone.0040310; PMID: 22905091
   PubMed Web of Science ®Google Scholar
• Roberts SW. Control chart tests based on geometric moving averages. Technomearics 1959; 1:239 - 50; http://dx.doi.org/10.1080/00401706.1959.10489860
   Google Scholar
• Elbert Y, Burkom HS. Development and evaluation of a data-adaptive alerting algorithm for univariate temporal biosurveillance data. Stat Med 2009; 28:3226 - 48; http://dx.doi.org/10.1002/sim.3708; PMID: 19725023
   PubMed Web of Science ®Google Scholar
• Shiryaev AN. On optimum methods in quickest detection problems. Theory Probab Appl 1963; 8:22 - 46; http://dx.doi.org/10.1137/1108002
   Google Scholar
• Frisen M, de Mare J. Optimal surveillance. Biometrika 1991; 78:271 - 80
   Web of Science ®Google Scholar
• 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
   Web of Science ®Google Scholar
• Bock D, Andersson E, Frisén M. Statistical surveillance of epidemics: peak detection of influenza in Sweden. Biom J 2008; 50:71 - 85; http://dx.doi.org/10.1002/bimj.200610362; PMID: 17849383
   PubMed Web of Science ®Google Scholar
• 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 - 45; http://dx.doi.org/10.1016/j.csda.2010.01.020
   Web of Science ®Google Scholar
• Frisén M, Andersson E, Schiöler L. Sufficient reduction in multivariate surveillance. Comm Statist Theory Methods 2011; 40:1821 - 38; http://dx.doi.org/10.1080/03610921003714162
   Web of Science ®Google Scholar
• Naus JI. Clustering of random points in two dimensions. Biometrika 1965; 52:263 - 7
   Web of Science ®Google Scholar
• 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; http://dx.doi.org/10.1371/journal.pmed.0020059; PMID: 15719066
   PubMed Web of Science ®Google Scholar
• Le Strat Y, Carrat F. Monitoring epidemiologic surveillance data using hidden Markov models. Stat Med 1999; 18:3463 - 78; http://dx.doi.org/10.1002/(SICI)1097-0258(19991230)18:24<3463::AID-SIM409>3.0.CO;2-I; PMID: 10611619
   PubMed Web of Science ®Google Scholar
• 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.
   Google Scholar
• Cooper B, Lipsitch M. The analysis of hospital infection data using hidden Markov models. Biostatistics 2004; 5:223 - 37; http://dx.doi.org/10.1093/biostatistics/5.2.223; PMID: 15054027
   PubMed Web of Science ®Google Scholar
• 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
   Google Scholar
• Viterbi AJ. Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Trans Inf Theory 1967; 13:260 - 9; http://dx.doi.org/10.1109/TIT.1967.1054010
   Web of Science ®Google Scholar
• Dempster AP, Laird NM, Rubin DB. Maximum likelihood from incomplete data via the EM Algorithm. J R Stat Soc, B 1977; 39:1 - 38
   Google Scholar
• Best N, Richardson S, Thomson A. A comparison of Bayesian spatial models for disease mapping. Stat Methods Med Res 2005; 14:35 - 59; http://dx.doi.org/10.1191/0962280205sm388oa; PMID: 15690999
   PubMed Web of Science ®Google Scholar
• Knorr-Held L, Rasser G. Bayesian detection of clusters and discontinuities in disease maps. Biometrics 2000; 56:13 - 21; http://dx.doi.org/10.1111/j.0006-341X.2000.00013.x; PMID: 10783772
   PubMed Web of Science ®Google Scholar
• Gangnon RE, Clayton MK. Bayesian detection and modeling of spatial disease clustering. Biometrics 2000; 56:922 - 35; http://dx.doi.org/10.1111/j.0006-341X.2000.00922.x; PMID: 10985238
   PubMed Web of Science ®Google Scholar
• Denison DGT, Holmes CC. Bayesian partitioning for estimating disease risk. Biometrics 2001; 57:143 - 9; http://dx.doi.org/10.1111/j.0006-341X.2001.00143.x; PMID: 11252589
   PubMed Web of Science ®Google Scholar
• MacNab YC. Hierarchical Bayesian modeling of spatially correlated health service outcome and utilization rates. Biometrics 2003; 59:305 - 16; http://dx.doi.org/10.1111/1541-0420.00037; PMID: 12926715
   PubMed Web of Science ®Google Scholar
• Frisèn M. Spatial outbreak detection based on inference principles for multivariate surveillance. Research Report 2012; 1: ISSN 0349-8034.
   Google Scholar
• Robertson C, Nelson TA, MacNab YC, Lawson AB, Lawson AB. Review of methods for space-time disease surveillance. Spat Spatiotemporal Epidemiol 2010; 1:105 - 16; http://dx.doi.org/10.1016/j.sste.2009.12.001; PMID: 22749467
   PubMedGoogle Scholar
• Lawson AB, Kleinman K, eds. Spatial and Syndromic Surveillance for Public Health. Chichester: Wiley, 2005.
   Google Scholar
• Rencher AC. Methods of Multivariate Analysis. John Wiley and Sons, 2002.
   Google Scholar
• Kleinschmidt I, Bagayoko M, Clarke GPY, Craig M, Le Sueur D. A spatial statistical approach to malaria mapping. Int J Epidemiol 2000; 29:355 - 61; http://dx.doi.org/10.1093/ije/29.2.355; PMID: 10817136
   PubMed Web of Science ®Google Scholar
• 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 - 300; PMID: 1626546
   PubMed Web of Science ®Google Scholar
• Cohen AA, Dhingra N, Jotkar RM, Rodriguez PS, Sharma VP, Jha P. The Summary Index of Malaria Surveillance (SIMS): a stable index of malaria within India. Popul Health Metr 2010; 8:1; http://dx.doi.org/10.1186/1478-7954-8-1; PMID: 20181218
   PubMed Web of Science ®Google Scholar
• 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; http://dx.doi.org/10.1186/1475-2875-8-68; PMID: 19374738
   PubMed Web of Science ®Google Scholar
• 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
   Web of Science ®Google Scholar
• Kulldorff M, Nagarwalla N. Spatial disease clusters: detection and inference. Stat Med 1995; 14:799 - 810; http://dx.doi.org/10.1002/sim.4780140809; PMID: 7644860
   PubMed Web of Science ®Google Scholar
• 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; http://dx.doi.org/10.1371/journal.pmed.0020059; PMID: 15719066
   PubMed Web of Science ®Google Scholar
• 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; http://dx.doi.org/10.1186/1471-2458-6-286; PMID: 17118176
   PubMed Web of Science ®Google Scholar
• Sklar A. Random variables, joint distributions, and copulas. Kybernetica 1973; 9:449 - 60
   Google Scholar
• Nelsen RB. An Introduction to Copulas. 2nd edition. NewYork: Springer, 2006.
   Google Scholar
• Cox DR. Regression Models and Life Tables (with Discussion). J R Stat Soc, B 1972; 34:187 - 220
   Google Scholar
• Cox DR, Oakes D. Analysis of Survival Data. London: Chapman and Hall. 1984.
   Google Scholar
• Molenberghs G, Lessafre E. Marginal modeling of correlated ordina data using a multivariate Plackett distribution. J Am Stat Assoc 1994; 89:633 - 44; http://dx.doi.org/10.1080/01621459.1994.10476788
   Web of Science ®Google Scholar
• 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 - 97; http://dx.doi.org/10.1097/QAD.0b013e3283471deb; PMID: 21505309
   PubMed Web of Science ®Google Scholar
• 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 - 35
   Google Scholar
• 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; http://dx.doi.org/10.1136/sextrans-2012-050636; PMID: 23172342
   PubMed Web of Science ®Google Scholar
• 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; http://dx.doi.org/10.1371/journal.pmed.1001304; PMID: 22973181
   PubMed Web of Science ®Google Scholar
• Tibaldi F, Molenberghs G, Burzykowski T, Geys H. Pseudo-likelihood estimation for a marginal multivariate survival model. Stat Med 2004; 23:947 - 63; http://dx.doi.org/10.1002/sim.1664; PMID: 15027082
   PubMed Web of Science ®Google Scholar
• Kor CT, Cheng KF, Chen YH. A method for analyzing clustered interval-censored data based on Cox’s model. Stat Med 2013; 32:822 - 32; http://dx.doi.org/10.1002/sim.5562; PMID: 22911905
   PubMed Web of Science ®Google Scholar
• 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 - 7; http://dx.doi.org/10.1186/1476-072X-6-40; PMID: 17883862
   PubMed Web of Science ®Google Scholar
• Anderson RM, May RM. Population biology of infectious diseases: Part I. Nature 1979; 280:361 - 7; http://dx.doi.org/10.1038/280361a0; PMID: 460412
   PubMed Web of Science ®Google Scholar
• Brauder F, Castillo-Chavez C. Mathematical models in population biology and epidemiology. New York: Springer-Verlag, 2001.
   Google Scholar
• Murray JD. Mathematical Biology II. New York: Springer-Verlag, 2002.
   Google Scholar
• Feng Z, Dieckmann U, Levin S, eds. Disease evolution: models, concepts and data analysis. AMS 2006.
   Google Scholar
• Keeling MJ. The effects of local spatial structure on epidemiological invasions. Proc Biol Sci 1999; 266:859 - 67; http://dx.doi.org/10.1098/rspb.1999.0716; PMID: 10343409
   PubMed Web of Science ®Google Scholar
• Greenhalgh D, Das R. Modelling epidemics with variable contact rates. Theor Popul Biol 1995; 47:129 - 79; http://dx.doi.org/10.1006/tpbi.1995.1006; PMID: 7740440
   PubMed Web of Science ®Google Scholar
• 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; http://dx.doi.org/10.1007/BF00276956; PMID: 3958634
   PubMed Web of Science ®Google Scholar
• Hethcote HW, Zhien M, Shengbing L. Effects of quarantine in six endemic models for infectious diseases. Math Biosci 2002; 180:141 - 60; http://dx.doi.org/10.1016/S0025-5564(02)00111-6; PMID: 12387921
   PubMed Web of Science ®Google Scholar
• 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; http://dx.doi.org/10.1103/PhysRevE.70.036114; PMID: 15524594
   PubMed Web of Science ®Google Scholar
• 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
   Google Scholar
• Coburn BJ, Wagner BG, Blower S. Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1). BMC Med 2009; 7:30; http://dx.doi.org/10.1186/1741-7015-7-30; PMID: 19545404
   PubMed Web of Science ®Google Scholar
• Nichol KL, Tummers K, Hoyer-Leitzel A, Marsh J, Moynihan M, McKelvey S. Modeling seasonal influenza outbreak in a closed college campus: impact of pre-season vaccination, in-season vaccination and holidays/breaks. PLoS One 2010; 5:e9548; http://dx.doi.org/10.1371/journal.pone.0009548; PMID: 20209058
   PubMed Web of Science ®Google Scholar
• 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 - 50; http://dx.doi.org/10.1007/978-3-642-14788-3_19
   Google Scholar
• 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; http://dx.doi.org/10.1186/1475-2875-8-61; PMID: 19361335
   PubMed Web of Science ®Google Scholar
• Magal P, McCluskey CC, Webb GF. Lyapunov functional and global asymptotic stability for an infection-age model. Appl Anal 2010; 89:1109 - 40; http://dx.doi.org/10.1080/00036810903208122
   Web of Science ®Google Scholar
• Metcalf CJE, Munayco CV, 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 - 76; http://dx.doi.org/10.1098/rsif.2010.0320; PMID: 20659931
   PubMed Web of Science ®Google Scholar
• Ajelli M, Fumanelli L, Manfredi P, Merler S. Spatiotemporal dynamics of viral hepatitis A in Italy. Theor Popul Biol 2011; 79:1 - 11; http://dx.doi.org/10.1016/j.tpb.2010.09.003; PMID: 20883708
   PubMed Web of Science ®Google Scholar
• 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 - 8; http://dx.doi.org/10.1073/pnas.0504053102; PMID: 16141326
   PubMed Web of Science ®Google Scholar
• 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
   Google Scholar
• 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; http://dx.doi.org/10.1007/s10441-010-9103-z; PMID: 20706773
   PubMed Web of Science ®Google Scholar
• Demongeot J, Gaudart J, Mintsa J, Rachdi M. Demography in epidemics modelling. . Communications Pure & Appl. Analysis 2012; 11:61 - 82
   Web of Science ®Google Scholar
• 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
   Google Scholar
• 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 - 7; http://dx.doi.org/10.1093/bioinformatics/btn568; PMID: 18977781
   PubMed Web of Science ®Google Scholar
• 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; http://dx.doi.org/10.1371/journal.pone.0000152; PMID: 17225857
   PubMed Web of Science ®Google Scholar
• Allen LJ, Burgin AM. Comparison of deterministic and stochastic SIS and SIR models in discrete time. Math Biosci 2000; 163:1 - 33; http://dx.doi.org/10.1016/S0025-5564(99)00047-4; PMID: 10652843
   PubMed Web of Science ®Google Scholar
• Lekone PE, Finkenstädt BF. Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study. Biometrics 2006; 62:1170 - 7; http://dx.doi.org/10.1111/j.1541-0420.2006.00609.x; PMID: 17156292
   PubMed Web of Science ®Google Scholar
• 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 - 15; http://dx.doi.org/10.1093/infdis/jir131; PMID: 21666151
   PubMed Web of Science ®Google Scholar
• Wang R-H, Jin Z, Liu Q-X, 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; http://dx.doi.org/10.1371/journal.pone.0028873; PMID: 22363397
   PubMed Web of Science ®Google Scholar
• 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
   Web of Science ®Google Scholar
• Mintsa J, Rachdi M, Demongeot J. Stochastic approach in modelling epidemic spread. In: IEEE AINA' 11 & BLSMC' 11, IEEE Proceedings, Piscataway, 478-482 (2011).
   Google Scholar
• Allen LJS, Burgin AM. Comparison of deterministic and stochastic SIS and SIR models in discrete time. Math Biosci 2000; 163:1 - 33; http://dx.doi.org/10.1016/S0025-5564(99)00047-4; PMID: 10652843
   PubMed Web of Science ®Google Scholar
• Newman MEJ. The structure and function of networks. SIAM Rev 2003; 45:167 - 256; http://dx.doi.org/10.1137/S003614450342480
   Web of Science ®Google Scholar
• Barabasi AL. Statistical mechanics of complex networks. Rev Mod Phys 2002; 74:47 - 97; http://dx.doi.org/10.1103/RevModPhys.74.47
   Web of Science ®Google Scholar
• 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
   Web of Science ®Google Scholar
• 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 - 70; http://dx.doi.org/10.1073/pnas.1000416107; PMID: 20421468
   PubMed Web of Science ®Google Scholar
• Keeling MJ, Eames KT. Networks and epidemic models. J R Soc Interface 2005; 2:295 - 307; http://dx.doi.org/10.1098/rsif.2005.0051; PMID: 16849187
   PubMed Web of Science ®Google Scholar
• 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 - 7; http://dx.doi.org/10.1098/rsif.2008.0013; PMID: 18319209
   PubMed Web of Science ®Google Scholar
• Kuperman M, Abramson G. Small world effect in an epidemiological model. Phys Rev Lett 2001; 86:2909 - 12; http://dx.doi.org/10.1103/PhysRevLett.86.2909; PMID: 11290070
   PubMed Web of Science ®Google Scholar
• Hwang DU, Boccaletti S, Moreno Y, López-Ruiz R. Thresholds for epidemic outbreaks in finite scale-free networks. Math Biosci Eng 2005; 2:317 - 27; http://dx.doi.org/10.3934/mbe.2005.2.317; PMID: 20369925
   PubMed Web of Science ®Google Scholar
• Shirley MDF, Rushton SP. The impacts of network topology on disease spread. Ecol Complex 2005; 2:287 - 99; http://dx.doi.org/10.1016/j.ecocom.2005.04.005
   Web of Science ®Google Scholar
• Reppas AI, Spiliotis KG, Siettos CI. On the effect of the path length of small-world networks on epidemic dynamics. Virulence 2012; 3:146 - 53; http://dx.doi.org/10.4161/viru.19131; PMID: 22460641
   PubMed Web of Science ®Google Scholar
• Gross T, Sayama H. Adaptive Networks: Theory, Models, and Data. Springer, Heidelberg, 2009.
   Google Scholar
• Christakis NA, Fowler JH. Social network sensors for early detection of contagious outbreaks. PLoS One 2010; 5:e12948; http://dx.doi.org/10.1371/journal.pone.0012948; PMID: 20856792
   PubMed Web of Science ®Google Scholar
• Salathé M, Kazandjieva M, Lee JW, Levis P, Feldman MW, Jones JH. A high-resolution human contact network for infectious disease transmission. Proc Natl Acad Sci U S A 2010; 107:22020 - 5; http://dx.doi.org/10.1073/pnas.1009094108; PMID: 21149721
   PubMed Web of Science ®Google Scholar
• Rocha LEC, Liljeros F, Holme P. Simulated epidemics in an empirical spatiotemporal network of 50,185 sexual contacts. PLoS Comput Biol 2011; 7:e1001109; http://dx.doi.org/10.1371/journal.pcbi.1001109; PMID: 21445228
   PubMed Web of Science ®Google Scholar
• 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 - 4; http://dx.doi.org/10.1038/nature02541; PMID: 15141212
   PubMed Web of Science ®Google Scholar
• 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 - 14; http://dx.doi.org/10.1038/nature04017; PMID: 16079797
   PubMed Web of Science ®Google Scholar
• 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 - 9; http://dx.doi.org/10.1111/j.1553-2712.2006.tb01638.x; PMID: 17085740
   PubMed Web of Science ®Google Scholar
• 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 - 9; http://dx.doi.org/10.1073/pnas.0906910106; PMID: 20018697
   PubMed Web of Science ®Google Scholar
• Ginsberg J, Mohebbi MH, Patel RS, Brammer L, Smolinski MS, Brilliant L. Detecting influenza epidemics using search engine query data. Nature 2009; 457:1012 - 4; http://dx.doi.org/10.1038/nature07634; PMID: 19020500
   PubMed Web of Science ®Google Scholar
• Hulth A, Rydevik G, Linde A. Web queries as a source for syndromic surveillance. PLoS One 2009; 4:e4378; http://dx.doi.org/10.1371/journal.pone.0004378; PMID: 19197389
   PubMed Web of Science ®Google Scholar
• 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; http://dx.doi.org/10.1371/journal.pntd.0001206; PMID: 21647308
   PubMed Web of Science ®Google Scholar
• 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 - 62
   Google Scholar
• 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
   Web of Science ®Google Scholar
• 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 - 49; http://dx.doi.org/10.4161/viru.1.4.12196; PMID: 21178467
   PubMed Web of Science ®Google Scholar
• Siettos CI. Equation-Free multiscale computational analysis of individual-based epidemic dynamics on networks. Appl Math Comput 2011; 218:324 - 36; http://dx.doi.org/10.1016/j.amc.2011.05.067
   Web of Science ®Google Scholar