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All issues Volume 27 (2023) ESAIM: PS, 27 (2023) 345-401 References
Open Access
Issue
ESAIM: PS
Volume 27, 2023
Page(s) 345 - 401
DOI https://doi.org/10.1051/ps/2023003
Published online 27 February 2023
  1. A. Abakuks, An optimal isolation policy for an epidemic. J. Appi. Probab. 10 (1973) 247–262. [CrossRef] [Google Scholar]
  2. H. Andersson and T. Britton, Stochastic epidemic models and their statistical analysis. Springer Science & Business Media (2012), lecture Notes in Statistics (LNS, Volume 151). [Google Scholar]
  3. F. Ball, A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models. Adv. Appi. Probab. 18 (1986) 289–310. [CrossRef] [Google Scholar]
  4. F. Ball and D. Clancy, The final size and severity of a generalised stochastic multitype epidemic model. Adv. Appi. Probab. 25 (1993) 721–736. [CrossRef] [Google Scholar]
  5. D. Bichara and A. Iggidr, Multi-patch and multi-group epidemic models: a new framework. J. Math. Biol. 77 (2018) 107–134. [Google Scholar]
  6. P. Billingsley, Convergence of Probability Measures. John Wiley & Sons (1999). [Google Scholar]
  7. L. Bolzoni, E. Bonacini, R. Della Marca and M. Groppi, Optimal control of epidemic size and duration with limited resources. Math. Biosci. 315 (2019) 108232. [CrossRef] [MathSciNet] [Google Scholar]
  8. F. Brauer, Ona nonlinear integral equation for population growth problems. SIAM J. Math. Anal. 6 (1975) 312–317. [Google Scholar]
  9. F. Brauer, C. Castillo-Chavez and Z. Feng, Mathematical Models in Epidemiology. Springer (2019). [Google Scholar]
  10. T. Britton and E. Pardoux, Stochastic epidemics in a homogeneous community, Stochastic Epidemic Models with Inference (T. Britton and E. Pardoux eds). Part I. Lecture Notes in Math. 2255 (2019) 1–120. [Google Scholar]
  11. E. Çınlar, Probability and Stochastics, Springer Science & Business Media (2011). [Google Scholar]
  12. D. Clancy, SIR epidemic models with general infectious period distribution. Stat. Probab. Lett. 85 (2014) 1–5. [Google Scholar]
  13. K.L. Cooke, An epidemic equation with immigration. Math. Biosci. 29 (1976) 135–158. [CrossRef] [MathSciNet] [Google Scholar]
  14. O. Diekmann, Limiting behaviour in an epidemic model. Noniinear Anai.: Theory Methods Appi. 1 (1977) 459–470. [Google Scholar]
  15. S.N. Ethier and T.G. Kurtz, Markov Processes: Characterization and Convergence. John Wiley & Sons, 2nd edition (2009). [Google Scholar]
  16. R. Forien, G. Pang and E. Pardoux, Epidemic models with varying infectivity. SIAM J. Appi. Math. 81 (2021) 1893–1930. [Google Scholar]
  17. R. Forien, G. Pang and E. Pardoux, Estimating the state of the Covid-19 epidemic in France using a model with memory. Royal Soc. Open Sci. 8 (2021) 202327. [Google Scholar]
  18. A. Gomez-Corral and M. Lopez-García, On SIR epidemic models with generally distributed infectious periods: number of secondary cases and probability of infection. Int. J. Biomath. 10 (2017) 1750024. [CrossRef] [MathSciNet] [Google Scholar]
  19. M.G. Hahn, Central limit theorems in D[0,1], Zeitsch. Wahrscheinlichkeitstheorie und verwandte Gebiete 44 (1978) 89–101. [Google Scholar]
  20. E. Hansen and T. Day, Optimal control of epidemics with limited resources. J. Math. Biol. 62 (2011) 423–451. [Google Scholar]
  21. H.W. Hethcote and P. van den Driessche, An SIS epidemic model with variable population size and a delay. J. Math. Biol. 34 (1995) 177–194. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  22. W. Huang, K.L. Cooke and C. Castillo-Chavez, Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission. SIAM J. Appi. Math. 52 (1992) 835–854. [Google Scholar]
  23. A. Iggidr, G. Sallet and M.O. Souza, On the dynamics of a class of multi-group models for vector-borne diseases. J. Math. Anal. Appi. 441 (2016) 723–743. [Google Scholar]
  24. P. Magal and C. McCluskey, Two-group infection age model including an application to nosocomial infection. SIAM J. Appl. Math. 73 (2013) 1058–1095. [Google Scholar]
  25. P. Magal, O. Seydi and G. Webb, Final size of an epidemic for a two-group SIR model. SIAM J. Appi. Math. 76 (2016) 2042–2059. [Google Scholar]
  26. P. Magal, O. Seydi and G. Webb, Final size of a multi-group SIR epidemic model: irreducible and non-irreducible modes of transmission. Math. Biosci. 301 (2018) 59–67. [CrossRef] [MathSciNet] [Google Scholar]
  27. P. Massart, The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality. Ann. Probab. 18 (1990) 1269–1283. [CrossRef] [MathSciNet] [Google Scholar]
  28. R.K. Miller, Nolinear Volterra Integral Equations. Benjiamin Press, Menlo Park, Cal. (1971). [Google Scholar]
  29. G. Pang and E. Pardoux, Functional central limit theorems for epidemic models with varying infectivity. Stochastics (2022). DOI: 10.1080/17442508.2022.2124870. [Google Scholar]
  30. G. Pang and E. Pardoux, Functional limit theorems for non-Markovian epidemic models. Ann. Appi. Probab. 32 (2022) 1615–1665. [Google Scholar]
  31. G. Pang and E. Pardoux, Functional law of large numbers and PDEs for epidemic models with infection-age dependent infectivity. To appear Appi. Math. Optim. (2023), arXiv:2106.03758. [Google Scholar]
  32. M. Prague, L. Wittkop, Q. Clairon, D. Dutartre, R. Thiebaut and B.P. Hejblum, Population modeling of early COVID-19 epidemic dynamics in French regions and estimation of the lockdown impact on infection rate. https://doi.org/10.1101/2020.04.21.20073536 (2020). [Google Scholar]
  33. G. Reinert, The asymptotic evolution of the general stochastic epidemic. Ann. Appi. Probab. 5 (1995) 1061–1086. [Google Scholar]
  34. N.H. Shah, N. Sheoran, E. Jayswal, D. Shukla, N. Shukla, J. Shukla and Y. Shah, Modelling COVID-19 transmission in the United States through interstate and foreign travels and evaluating impact of governmental public health interventions. J. Math. Anai. Appi. 514 (2022) 124896. [Google Scholar]
  35. P. van den Driessche and J. Watmough, A simple SIS epidemic model with a backward bifurcation. J. Math. Bioi. 40 (2000) 525–540. [Google Scholar]
  36. F.J. Wang, Limit theorems for age and density dependent stochastic population models. J. Math. Bioi. 2 (1975) 373–400. [Google Scholar]
  37. F.J. Wang, A central limit theorem for age-and density-dependent population processes. Stoch. Process. Appi. 5 (1977) 173–193. [Google Scholar]
  38. F.J. Wang, Gaussian approximation of some closed stochastic epidemic models. J. Appi. Probab. 14 (1977) 221–231. [CrossRef] [Google Scholar]
  39. K.H. Wickwire, Optimal isolation policies for deterministic and stochastic epidemics. Math. Biosci. 26 (1975) 325–346. [CrossRef] [MathSciNet] [Google Scholar]

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