메뉴 건너뛰기




Volumn 3, Issue , 2018, Pages 192-248

A primer on the use of probability generating functions in infectious disease modeling

Author keywords

[No Author keywords available]

Indexed keywords

PRIMER DNA;

EID: 85059290751     PISSN: 24680427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.idm.2018.08.001     Document Type: Article
Times cited : (35)

References (53)
  • 1
    • 42249098829 scopus 로고    scopus 로고
    • An introduction to stochastic epidemic models
    • Springer
    • Allen, L.J.S., An introduction to stochastic epidemic models. Mathematical epidemiology, 2008, Springer, 81–130.
    • (2008) Mathematical epidemiology , pp. 81-130
    • Allen, L.J.S.1
  • 2
    • 85054699475 scopus 로고    scopus 로고
    • An introduction to stochastic processes with applications to biology
    • CRC Press
    • Allen, L.J.S., An introduction to stochastic processes with applications to biology. 2010, CRC Press.
    • (2010)
    • Allen, L.J.S.1
  • 3
    • 85037830416 scopus 로고    scopus 로고
    • A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis
    • Allen, L.J.S., A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis. Infectious Disease Modelling 2:2 (2017), 128–142.
    • (2017) Infectious Disease Modelling , vol.2 , Issue.2 , pp. 128-142
    • Allen, L.J.S.1
  • 5
    • 0000814780 scopus 로고
    • The total size of a general stochastic epidemic
    • Bailey, N.T.J., The total size of a general stochastic epidemic. Biometrika, 1953, 177–185.
    • (1953) Biometrika , pp. 177-185
    • Bailey, N.T.J.1
  • 6
    • 0003812093 scopus 로고
    • The elements of stochastic processes with applications to the natural sciences
    • John Wiley & Sons
    • Bailey, N.T.J., The elements of stochastic processes with applications to the natural sciences. 1964, John Wiley & Sons.
    • (1964)
    • Bailey, N.T.J.1
  • 8
    • 84878503913 scopus 로고    scopus 로고
    • 0 and transmission heterogeneity from the size distribution of stuttering chains
    • 0 and transmission heterogeneity from the size distribution of stuttering chains. PLoS Computational Biology, 9(5), 2013, e1002993.
    • (2013) PLoS Computational Biology , vol.9 , Issue.5
    • Blumberg, S.1    Lloyd-Smith, J.O.2
  • 9
    • 78651414561 scopus 로고    scopus 로고
    • Accuracy and stability of computing high-order derivatives of analytic functions by Cauchy integrals
    • Bornemann, F., Accuracy and stability of computing high-order derivatives of analytic functions by Cauchy integrals. Foundations of Computational Mathematics 11:1 (2011), 1–63.
    • (2011) Foundations of Computational Mathematics , vol.11 , Issue.1 , pp. 1-63
    • Bornemann, F.1
  • 11
    • 79955550951 scopus 로고    scopus 로고
    • A stochastic model of latently infected cell reactivation and viral blip generation in treated HIV patients
    • Conway, J.M., Coombs, D., A stochastic model of latently infected cell reactivation and viral blip generation in treated HIV patients. PLoS Computational Biology, 7(4), 2011, e1002033.
    • (2011) PLoS Computational Biology , vol.7 , Issue.4
    • Conway, J.M.1    Coombs, D.2
  • 12
    • 0003426971 scopus 로고    scopus 로고
    • Mathematical epidemiology of infectious diseases
    • Wiley Chichester
    • Diekmann, O., Heesterbeek, J.A.P., Mathematical epidemiology of infectious diseases. 2000, Wiley Chichester.
    • (2000)
    • Diekmann, O.1    Heesterbeek, J.A.P.2
  • 13
  • 14
  • 15
    • 0001477232 scopus 로고
    • The total progeny in a branching process and a related random walk
    • Dwass, M., The total progeny in a branching process and a related random walk. Journal of Applied Probability 6:3 (1969), 682–686.
    • (1969) Journal of Applied Probability , vol.6 , Issue.3 , pp. 682-686
    • Dwass, M.1
  • 16
    • 77954812738 scopus 로고    scopus 로고
    • Networks, crowds, and markets: Reasoning about a highly connected world
    • Cambridge University Press
    • Easley, D., Kleinberg, J., Networks, crowds, and markets: Reasoning about a highly connected world. 2010, Cambridge University Press.
    • (2010)
    • Easley, D.1    Kleinberg, J.2
  • 17
    • 49249141558 scopus 로고
    • Cyclotomic polynomials and nonstandard dice
    • Gallian, J.A., Rusin, D.J., Cyclotomic polynomials and nonstandard dice. Discrete Mathematics 27:3 (1979), 245–259.
    • (1979) Discrete Mathematics , vol.27 , Issue.3 , pp. 245-259
    • Gallian, J.A.1    Rusin, D.J.2
  • 18
    • 0002764624 scopus 로고
    • Mathematical games
    • Gardner, M., Mathematical games. Scientific American 238 (1978), 19–32.
    • (1978) Scientific American , vol.238 , pp. 19-32
    • Gardner, M.1
  • 20
    • 84898077414 scopus 로고    scopus 로고
    • Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates
    • Harko, T., Lobo, F.S.N., Mak, M.K., Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates. Applied Mathematics and Computation 236 (2014), 184–194.
    • (2014) Applied Mathematics and Computation , vol.236 , pp. 184-194
    • Harko, T.1    Lobo, F.S.N.2    Mak, M.K.3
  • 21
    • 73549085327 scopus 로고    scopus 로고
    • A first course in Bayesian statistical methods
    • Springer Science & Business Media
    • Hoff, P.D., A first course in Bayesian statistical methods. 2009, Springer Science & Business Media.
    • (2009)
    • Hoff, P.D.1
  • 23
    • 84872358666 scopus 로고    scopus 로고
    • How big is an outbreak likely to be? methods for epidemic final-size calculation
    • House, T., Ross, J.V., Sirl, D., How big is an outbreak likely to be? methods for epidemic final-size calculation. Proceedings of the Royal Society A, 469(2150), 2013, 20120436.
    • (2013) Proceedings of the Royal Society A , vol.469 , Issue.2150
    • House, T.1    Ross, J.V.2    Sirl, D.3
  • 27
    • 85007290724 scopus 로고    scopus 로고
    • Mathematics of epidemics on networks: From exact to approximate models
    • Springer
    • Kiss, I.Z., Miller, J.C., Simon, P.L., Mathematics of epidemics on networks: From exact to approximate models. 2017, Springer.
    • (2017)
    • Kiss, I.Z.1    Miller, J.C.2    Simon, P.L.3
  • 28
    • 84929484464 scopus 로고    scopus 로고
    • Characterizing the transmission potential of zoonotic infections from minor outbreaks
    • Kucharski, A.J., Edmunds, W.J., Characterizing the transmission potential of zoonotic infections from minor outbreaks. PLoS Computational Biology, 11(4), 2015, e1004154.
    • (2015) PLoS Computational Biology , vol.11 , Issue.4
    • Kucharski, A.J.1    Edmunds, W.J.2
  • 30
    • 27844455994 scopus 로고    scopus 로고
    • Superspreading and the effect of individual variation on disease emergence
    • Lloyd-Smith, J.O., Schreiber, S.J., Kopp, P.E., Getz, W.M., Superspreading and the effect of individual variation on disease emergence. Nature, 438(7066), 2005, 355.
    • (2005) Nature , vol.438 , Issue.7066 , pp. 355
    • Lloyd-Smith, J.O.1    Schreiber, S.J.2    Kopp, P.E.3    Getz, W.M.4
  • 31
    • 0016636706 scopus 로고
    • Final size distributions for epidemics
    • Ludwig, D., Final size distributions for epidemics. Mathematical Biosciences 23 (1975), 33–46.
    • (1975) Mathematical Biosciences , vol.23 , pp. 33-46
    • Ludwig, D.1
  • 32
    • 33746581986 scopus 로고    scopus 로고
    • Generality of the final size formula for an epidemic of a newly invading infectious disease
    • Ma, J.J., Earn, D.J.D., Generality of the final size formula for an epidemic of a newly invading infectious disease. Bulletin of Mathematical Biology 68:3 (2006), 679–702.
    • (2006) Bulletin of Mathematical Biology , vol.68 , Issue.3 , pp. 679-702
    • Ma, J.J.1    Earn, D.J.D.2
  • 33
    • 0017185443 scopus 로고
    • Simple mathematical models with very complicated dynamics
    • May, R.M., Simple mathematical models with very complicated dynamics. Nature 261:5560 (1976), 459–467.
    • (1976) Nature , vol.261 , Issue.5560 , pp. 459-467
    • May, R.M.1
  • 34
    • 79951515510 scopus 로고    scopus 로고
    • A note on a paper by Erik Volz: SIR dynamics in random networks
    • Miller, J.C., A note on a paper by Erik Volz: SIR dynamics in random networks. Journal of Mathematical Biology 62:3 (2011), 349–358.
    • (2011) Journal of Mathematical Biology , vol.62 , Issue.3 , pp. 349-358
    • Miller, J.C.1
  • 35
    • 84864775325 scopus 로고    scopus 로고
    • A note on the derivation of epidemic final sizes
    • Miller, J.C., A note on the derivation of epidemic final sizes. Bulletin of Mathematical Biology 74:9 (2012), 2125–2141.
    • (2012) Bulletin of Mathematical Biology , vol.74 , Issue.9 , pp. 2125-2141
    • Miller, J.C.1
  • 37
    • 84859089658 scopus 로고    scopus 로고
    • Edge-based compartmental modelling for infectious disease spread
    • Miller, J.C., Slim, A.C., Volz, E.M., Edge-based compartmental modelling for infectious disease spread. Journal of The Royal Society Interface 9:70 (2012), 890–906.
    • (2012) Journal of The Royal Society Interface , vol.9 , Issue.70 , pp. 890-906
    • Miller, J.C.1    Slim, A.C.2    Volz, E.M.3
  • 38
    • 0034310659 scopus 로고    scopus 로고
    • Exact solution of site and bond percolation on small-world networks
    • Moore, C., Newman, M.E.J., Exact solution of site and bond percolation on small-world networks. Physical Review E, 62(5), 2000, 7059.
    • (2000) Physical Review E , vol.62 , Issue.5 , pp. 7059
    • Moore, C.1    Newman, M.E.J.2
  • 40
    • 81055137611 scopus 로고    scopus 로고
    • Estimating the transmission potential of supercritical processes based on the final size distribution of minor outbreaks
    • Nishiura, H., Yan, P., Sleeman, C.K., Mode, C.J., Estimating the transmission potential of supercritical processes based on the final size distribution of minor outbreaks. Journal of Theoretical Biology 294 (2012), 48–55.
    • (2012) Journal of Theoretical Biology , vol.294 , pp. 48-55
    • Nishiura, H.1    Yan, P.2    Sleeman, C.K.3    Mode, C.J.4
  • 41
    • 0003627794 scopus 로고    scopus 로고
    • Chaos and fractals: New frontiers of science
    • Springer Science & Business Media
    • Peitgen, H.-O., Jürgens, H., Saupe, D., Chaos and fractals: New frontiers of science. 2006, Springer Science & Business Media.
    • (2006)
    • Peitgen, H.-O.1    Jürgens, H.2    Saupe, D.3
  • 43
    • 84938369951 scopus 로고    scopus 로고
    • Pythontex: Reproducible documents with LaTeX, Python, and more
    • Poore, G.M., Pythontex: Reproducible documents with LaTeX, Python, and more. Computational Science & Discovery, 8(1), 2015, 014010.
    • (2015) Computational Science & Discovery , vol.8 , Issue.1
    • Poore, G.M.1
  • 46
    • 84866409556 scopus 로고    scopus 로고
    • Temporal percolation of the susceptible network in an epidemic spreading
    • Valdez, L.D., Macri, P.A., Braunstein, L.A., Temporal percolation of the susceptible network in an epidemic spreading. PLoS One, 7(9), 2012, e44188.
    • (2012) PLoS One , vol.7 , Issue.9
    • Valdez, L.D.1    Macri, P.A.2    Braunstein, L.A.3
  • 47
    • 36749049140 scopus 로고    scopus 로고
    • SIR dynamics in random networks with heterogeneous connectivity
    • Volz, E.M., SIR dynamics in random networks with heterogeneous connectivity. Journal of Mathematical Biology 56:3 (2008), 293–310.
    • (2008) Journal of Mathematical Biology , vol.56 , Issue.3 , pp. 293-310
    • Volz, E.M.1
  • 50
    • 85070424175 scopus 로고    scopus 로고
    • odeintw. “”.
    • W. Weckesser odeintw. “ https://github.com/WarrenWeckesser/odeintw”.
    • Weckesser, W.1
  • 51
    • 0007173298 scopus 로고
    • Left-continuous random walk and the Lagrange expansion
    • Wendel, J.G., Left-continuous random walk and the Lagrange expansion. American Mathematical Monthly, 1975, 494–499.
    • (1975) American Mathematical Monthly , pp. 494-499
    • Wendel, J.G.1
  • 52
    • 0004251247 scopus 로고    scopus 로고
    • generatingfunctionology
    • 3rd ed. A K Peters, Ltd
    • Wilf, H.S., generatingfunctionology. 3rd ed., 2005, A K Peters, Ltd.
    • (2005)
    • Wilf, H.S.1
  • 53
    • 42249091479 scopus 로고    scopus 로고
    • Distribution theory, stochastic processes and infectious disease modelling
    • Yan, P., Distribution theory, stochastic processes and infectious disease modelling. Mathematical Epidemiology, 2008, 229–293.
    • (2008) Mathematical Epidemiology , pp. 229-293
    • Yan, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.