Open Access
Issue |
ESAIM: PS
Volume 29, 2025
|
|
---|---|---|
Page(s) | 45 - 112 | |
DOI | https://doi.org/10.1051/ps/2024015 | |
Published online | 15 January 2025 |
- H.W. Hethcote, Qualitative analyses of communicable disease models. Math. Biosci. 28 (1976) 335–356. [CrossRef] [MathSciNet] [Google Scholar]
- H.W. Hethcote, Simulations of pertussis epidemiology in the United States: effects of adult booster vaccinations. Math. Biosci. 158 (1999) 47–73. [CrossRef] [Google Scholar]
- H.R. Thieme and J. Yang, An endemic model with variable re-infection rate and applications to influenza. Math. Biosci. 180 (2002) 207–235. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- M.V. Barbarossa and G. Röst, Mathematical models for vaccination, waning immunity and immune system boosting: a general framework, in BIOMAT 2014: International Symposium on Mathematical and Computational Biology. World Scientific (2015) 185–205. [Google Scholar]
- M. Ehrhardt, J. Gašper and S. Kilianová, Sir-based mathematical modeling of infectious diseases with vaccination and waning immunity. J. Computat. Sci. 37 (2019) 101027. [CrossRef] [Google Scholar]
- R.-M. Carlsson, L.M. Childs, Z. Feng, J.W. Glasser, J.M. Heffernan, J. Li and G. Röst, Modeling the waning and boosting of immunity from infection or vaccination. J. Theoret. Biol. 497 (2020) 110265. [CrossRef] [MathSciNet] [Google Scholar]
- L.F Strube, M. Walton and L.M. Childs, Role of repeat infection in the dynamics of a simple model of waning and boosting immunity. J. Biol. Syst. 29 (2021) 303–324. [CrossRef] [Google Scholar]
- L. Childs, D.W. Dick, Z. Feng, J.M. Heffernan, J. Li and G. Röst, Modeling waning and boosting of COVID-19 in Canada with vaccination. Epidemics 39 (2022) 100583. [CrossRef] [PubMed] [Google Scholar]
- M. Safan, K. Barley, M.M. Elhaddad, M.A. Darwish and S.H. Saker, Mathematical analysis of an SIVRWS model for pertussis with waning and naturally boosted immunity. Symmetry 14 (2022) 2288. [CrossRef] [Google Scholar]
- M.E. Khalifi and T. Britton, Extending susceptible-infectious-recovered-susceptible epidemics to allow for gradual waning of immunity. J. R. Soc. Interface. 20 (2023) 20230042. [CrossRef] [Google Scholar]
- F. Foutel-Rodier, A. Charpentier and H. Guérin, Optimal vaccination policy to prevent endemicity: a stochastic model. J. Math. Biol. 90 (2025) 1–55. [CrossRef] [Google Scholar]
- S. Elgart, A perturbative approach to the analysis of many-compartment models characterized by the presence of waning immunity. J. Math. Biol. 87 (2023) 61. [CrossRef] [PubMed] [Google Scholar]
- R. Forien, G. Pang, E. Pardoux and A.-B Zotsa-Ngoufack, Stochastic epidemic models with varying infectivity and waning immunity. Preprint arXiv:2311.02260 v1 (2024). [Google Scholar]
- R. Forien, G. Pang and É. Pardoux, Epidemic models with varying infectivity. SIAM J. Appl. Math. 81 (2021) 1893–1930. [CrossRef] [MathSciNet] [Google Scholar]
- W.O. Kermack and A.G. McKendrick, Contributions to the mathematical theory of epidemics. II.—The problem of endemicity. Proc. Roy. Soc. Lond. Ser. A 138 (1932) 55–83. [CrossRef] [Google Scholar]
- W.O. Kermack and A.G. McKendrick, Contributions to the mathematical theory of epidemics—III. Further studies of the problem of endemicity. 1933. Proc. Roy. Soc. Lond. Ser. A 141 (1933) 89–118. [Google Scholar]
- H. Inaba, Kermack and McKendrick revisited: the variable susceptibility model for infectious diseases. Jpn. J. Ind. Appl. Math. 18 (2021) 273–292. [Google Scholar]
- G. Pang and É. Pardoux, Functional central limit theorems for epidemic models with varying infectivity. Stochastics (2022) 1–48. [Google Scholar]
- G. Pang and É. Pardoux, Functional limit theorems for non-Markovian epidemic models. Ann. Appl. Probab. 32 (2022) 1615–1665. [CrossRef] [MathSciNet] [Google Scholar]
- T. Britton and E. Pardoux eds, Stochastic Epidemic Models with Inference. Springer (2019). [CrossRef] [Google Scholar]
- T.G. Kurtz, Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. J. Appl. Probab. 8 (1971) 344–356. [CrossRef] [Google Scholar]
- M.G. Hahn, Central limit theorems in D[0, 1]. Z. Wahrsch. verwandte Gebiete 44 (1978) 89–101. [CrossRef] [MathSciNet] [Google Scholar]
- E. Çinlar, Probability and Stochastics, Vol. 261. Springer Science & Business Media (2011). [Google Scholar]
- J. Chevallier, Mean-field limit of generalized Hawkes processes. Stochast. Processes Appl. 127 (2017) 3870–3912. [CrossRef] [Google Scholar]
- J. Chevallier, Fluctuations for mean-field interacting age-dependent Hawkes processes. Electron. J. Probab. 22 (2017). [CrossRef] [Google Scholar]
- V.C. Tran, Modèles particulaires stochastiques pour des problèmes d’évolution adaptative et pour l’approximation de solutions statistiques. PhD thesis, Université de Nanterre-Paris X (2006). [Google Scholar]
- M. Riedler, M. Thieullen and G. Wainrib, Limit theorems for infinite-dimensional piecewise deterministic Markov processes. Applications to stochastic excitable membrane models. Electron. J. Probab. 17 (2012) 1–48. [CrossRef] [Google Scholar]
- A.-S. Sznitman, Topics in propagation of chaos, in Ecole d’été de probabilités de Saint-Flour XIX’1989. Springer (1991) 165–251. [Google Scholar]
- P. Billingsley, Convergence of Probability Measures. John Wiley & Sons (1999). [CrossRef] [Google Scholar]
- G. Pang, R. Talreja and W. Whitt, Martingale proofs of many-server heavy-traffic limits for markovian queues. Probab. Surv. 4 (2007) 193–267. [CrossRef] [MathSciNet] [Google Scholar]
- H. Guérin and A.-B. Zotsa-Ngoufack, Stochastic epidemic model with memory of previous infection and waning immunity. In press, 2025. [Google Scholar]
- J. Jacod and A. Shiryaev, Limit Theorems for Stochastic Processes, Vol. 288. Springer Science & Business Media (2013). [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.