Open Access
Issue |
Math. Model. Nat. Phenom.
Volume 16, 2021
Mathematical Models and Methods in Epidemiology
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|
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Article Number | 34 | |
Number of page(s) | 20 | |
DOI | https://doi.org/10.1051/mmnp/2021028 | |
Published online | 04 June 2021 |
- C.L. Althaus, Estimating the reproduction number of Ebola virus (EBOV) duringthe 2014 outbreak in West Africa. PLOS Curr. Outbreaks (2014). [Google Scholar]
- O.M. Araz, A. Galvani and L.A. Meyers, Geographic prioritization of distributing pandemic influenza vaccines. Health Care Manag. Sci. 15 (2012) 175–187. [Google Scholar]
- N.T. Bailey, Mathematical Theory of Epidemics, Charles Griffin (1957). [Google Scholar]
- E. Bakare, A. Nwagwo and E. Danso-addo, Optimal control analysis of an SIR epidemic model with constant recruitment. Int. J. Appl. Math. Res. 3 (2014). [CrossRef] [Google Scholar]
- A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences. Society for Industrial and Applied Mathematics (1994). [Google Scholar]
- D. Bernoulli, Essai d’une nouvelle analyse de la mortalité causée par la petite vérole et des avantages de l’inoculation pour la prévenir. Mémoires de mathématique et de physique, presentés à l’Académie royale des sciences, par divers sçavans & lûs dans ses assemblées (1760) 1–45. [Google Scholar]
- B. Bolker and B.T. Grenfel, Space, persistence and dynamics of measles epidemics. Philos. Trans. Royal Soc. London B 348 (1995) 309–320. [Google Scholar]
- J. Burton, L. Billings, D.A. Cummings and I.B. Schwartz, Disease persistence in epidemiological models: the interplay between vaccination and migration. Math. Biosci. 239 (2012) 91–96. [Google Scholar]
- A.A. Chernov, M.Y. Kelbert and A.A. Shemendyuk, Optimal vaccine allocation during the mumps outbreak in two SIR centres. Math. Med. Biol. 37 (2019) 303–312. [Google Scholar]
- D.J. Daley and J. Gani, Epidemic Modelling: An Introduction. Cambridge Studies in Mathematical Biology, Cambridge University Press (1999). [Google Scholar]
- O. Diekmann, J.A.P. Heesterbeek and J.A.J. Metz, On the definition and the computation of the basic reproduction ratio r0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28 (1990) 365–382. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- L.E. Duijzer, W.L. van Jaarsveld, J. Wallinga and R. Dekker, Dose-optimal vaccine allocation over multiple populations. Prod. Oper. Manag. 27 (2018) 143–159. [Google Scholar]
- R. Feng and J. Garrido, Actuarial applications of epidemiological models. North Am. Actuarial J. 15 (2011). [Google Scholar]
- N. Ferguson, D. Laydon, G. Nedjati Gilani, N. Imai, K. Ainslie, M. Baguelin, S. Bhatia, A. Boonyasiri, Z. Cucunuba Perez, G. Cuomo-Dannenburg, A. Dighe, I. Dorigatti, H. Fu, K. Gaythorpe, W. Green, A. Hamlet, W. Hinsley, L. Okell, S. Van Elsland, H. Thompson, R. Verity, E. Volz, H. Wang, Y. Wang, P. Walker, P. Winskill, C. Whittaker, C. Donnelly, S. Riley and A. Ghani, Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand, report, Imperial College London, March 2020. [Google Scholar]
- P.E.M. Fine, Herd immunity: history, theory, practice. Epidemiolog. Rev. 15 (1993) 265–302. [Google Scholar]
- W. Gleißner, The spread of epidemics. Appl. Math. Comput. 27 (1988) 167–171. [Google Scholar]
- E. Goldstein, A. Apolloni, B. Lewis, J.C. Miller, M. Macauley, S. Eubank, M. Lipsitch and J. Wallinga, Distribution of vaccine/antivirals and the ’least spread line’ in a stratified population. J. Roy. Soc. Interface 7 (2010) 755–764. [Google Scholar]
- H.W. Hethcote, An immunization model for a heterogeneous population. Theor. Popul. Biol. 14 (1978) 338–349. [Google Scholar]
- W.O. Kermack and A.G. McKendrick, A contribution to the mathematical theory of epidemics. Proc. Roy. Soc. A 115 (1927) 700–721. [Google Scholar]
- M. Kretzschmar, P.F.M. Teunis and R.G. Pebody, Incidence and reproduction numbers of pertussis: estimates from serological and social contact data in five European countries. PLOS Med. 7 (2010) 1–10. [Google Scholar]
- S. Lee, M. Golinski and G. Chowell, Modeling optimal age-specific vaccination strategies against pandemic influenza. Bull. Math. Biol. 74 (2012) 958–980. [Google Scholar]
- C. Lefèvre, P. Picard and M. Simon, Epidemic risk and insurance coverage. J. Appl. Probab. 54 (2017) 286–303. [Google Scholar]
- Y. Liu, A.A. Gayle, A. Wilder-Smith and J. Rocklöv, The reproductive number of COVID-19 is higher compared to SARS coronavirus. J. Travel Med. 27 (2020) taaa021. [Google Scholar]
- I.M. Longini, E. Ackerman and L.R. Elveback, An optimization model for influenza a epidemics. Math. Biosci. 38 (1978) 141–157. [Google Scholar]
- G. Macdonald, The epidemiology and control of malaria. Oxford University Press, London (1957). [Google Scholar]
- M. Martcheva, An Introduction to Mathematical Epidemiology. Springer US (2015). [Google Scholar]
- L. Matrajt, M.E. Halloran and I.M. Longini, Jr, Optimal vaccine allocation for the early mitigation of pandemic influenza. PLOS Comput. Biol. 9 (2013) 1–15. [Google Scholar]
- L. Matrajt and I.M. Longini, Jr, Optimizing vaccine allocation at different points in time during an epidemic. PLOS ONE 5 (2010) 1–11. [Google Scholar]
- S.D. Mylius, T.J. Hagenaars, A.K. Lugnér and J. Wallinga, Optimal allocation of pandemic influenza vaccine depends on age, risk and timing. Vaccine 26 (2008) 3742–3749. [Google Scholar]
- A. Reich, Properties of premium calculation principles. Insurance 5 (1986) 97–101. [Google Scholar]
- J. Riou and C.L. Althaus, Pattern of early human-to-human transmission of Wuhan 2019 novel coronavirus (2019-nCoV), December 2019 to January 2020. Eurosurveillance 25 (2020). [CrossRef] [Google Scholar]
- R. Ross, The Prevention of Malaria, John Murray Publishing House, London (1910). [Google Scholar]
- I. Sazonov, M. Kelbert and M.B. Gravenor, A two-stage model for the SIR outbreak: Accounting for the discrete and stochastic nature of the epidemic at the initial contamination stage. Math. Biosci. 234 (2011) 108–117. [Google Scholar]
- I. Sazonov, M. Kelbert and M.B. Gravenor, A new view on migration processes between SIR centra: an account of the different dynamics of host and guest. J. Infect. Non Infect. Dis. 1 (2015). [Google Scholar]
- P. van den Driessche, Reproduction numbers of infectious disease models. Infect. Disease Model. 2 (2017) 288–303. [Google Scholar]
- P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180 (2002) 29–48. [Google Scholar]
- E.C. Yuan, D.L. Alderson, S. Stromberg and J.M. Carlson, Optimal vaccination in a stochastic epidemic model of two non-interacting populations. PLOS ONE 10 (2015) 1–25. [CrossRef] [Google Scholar]
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