Open Access
Issue
Math. Model. Nat. Phenom.
Volume 16, 2021
Article Number 57
Number of page(s) 32
DOI https://doi.org/10.1051/mmnp/2021049
Published online 03 November 2021
  1. B. Ainseba, Z. Feng, M. Iannelli and F.A. Milner, Control strategies for TB epidemics. Siam J. Appl. Math. 77 (2017) 82–107. [Google Scholar]
  2. B. Ainseba and M. Iannelli, Optimal screening in structured SIR epidemics. MMNP 7 (2012) 12–27. [Google Scholar]
  3. T.T. Ashezua, N.I. Akinwande, S. Abdulrahman, R.O. Dayiwola and F. Kuta, Local stability analysis of an infection age mathematical model for tuberculosis disease dynamics. J. Appl. Sci. Environ. Manag. 19 (2015) 665–669. [Google Scholar]
  4. S. Bentout, Y. Chen and S. Djilali, Global dynamics of an SEIR model with two age structures and a nonlinear incidence. Acta Appl. Math. 171 (2021) 1–27. [Google Scholar]
  5. Soufiane S. Bentout and T.M. Touaoula, Global analysis of an infection age model with a class of nonlinear incidence rates. J. Math. Anal. Appl. 434 (2016) 1211–1239. [Google Scholar]
  6. D. Bernouilli, Essai d’une nouvelle analyse de la mortalité causée par la petite vérole et des avantages de l’inoculation pour la prévenir. Mém. Math. Phys. Acad. Roy. Sci., Paris 1760 (1766) 1–45. [Google Scholar]
  7. D. Bernouilli, Reflexions sur les avantages de l’inoculation. Mercure de France (1760) 173–190. [Google Scholar]
  8. I. Boudjema and T.M. Touaoula, Global stability of an infection and vaccination age-structured model with general nonlinear incidence. J. Nonlinear Funct. Anal. 33 (2018) 1–21. [Google Scholar]
  9. F. Brauer, Age infection in epidemiology models. Electr. J. Differ. Equ. Conf . 12 (2005) 29–37. [Google Scholar]
  10. C. Castillo-Chavez and Z. Feng, Mathematical models for the disease dynamics of the tuberculosis, Fourth International Conference on Mathematical Population Dynamics (1995). [Google Scholar]
  11. A. Chekroun, M.N. Frioui, T. Kuniya and T.M. Touaoula, Global stability of an age structured epidemic model with general Lyapunov functional. Math. Biosci. Eng. 16 (2019) 1525–1553. [Google Scholar]
  12. A. Chekroun, M.N. Frioui, T. Kuniya and T.M. Touaoula, Mathematical analysis of an age structured heroin-cocaine epidemic model. Discr. Continu. Dyn. Syst. B 25 (2020) 444–4477. [Google Scholar]
  13. Y. Chen, J. Yang and F. Zhang, The global stability for an SIRS model with infection age. Math. Biosci. Eng. 11 (2014) 449–469. [Google Scholar]
  14. O. Diekmann; J.A.P. Heesterbeek and J.AJ. 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. [Google Scholar]
  15. S. Djilali, T.M. Touaoula and S.E. Miri, A Heroin epidemic model: very general non linear incidence, treat-age, and global stability. Acta Appl. Math. Math. Appl. 52 (2017) 171–194. [Google Scholar]
  16. M. Erdem, M. Safan and C. Castillo-Chavez, Mathematical Analysis of an SIQR influenza model with imperfect quarantine. Bull. Math. Biol. 79 (2017) doi: 10.1007/s11538-017-0301-6. [Google Scholar]
  17. M.N. Frioui, T.M. Touaoula and B. Ainseba, Global dynamics of an age structured model with relapse. Discrete Contin. Dyn. Syst. Ser. B (2020) doi: 10.3934/dcdsb.2019226. [Google Scholar]
  18. M. Iannelli, Mathematical Theory of Age- Structured Population Dynamics. Giardini Editori E Stampatori In Pisa (1994). [Google Scholar]
  19. M. Iannelli and F. Milner, The basic Approach to age structured population Dynamics: Models, Methods and Numerics. Lecture Notes on Mathematical Modelling in the Life Science (2017). [Google Scholar]
  20. W.O. Kermack and A.G. McKendrick, Contributions to the mathematical theory of epidemics 1. Proc. R. Soc. 115 (1927) 700–721. [Google Scholar]
  21. T. Kuniya, Stability Analysis of an Age structured SIR model with a reduction method to EDOs. Mathematics 6 (2018) 147. [Google Scholar]
  22. J.P. LaSalle, The stability of dynamical systems. Regional conference series in applied mathematics, 25. SIAM (1976). [Google Scholar]
  23. P. Magal and S. Ruan, Theory and Applications of Abstract semilinear Cauchy problems. Appl. Math. Sci. (2018). [Google Scholar]
  24. P. Magal, McCluskey and G.F. Webb, Lyapunov functional and global asymptotic stability for infection age model. Appl. Anal 89 (2010) 1109–1140. [Google Scholar]
  25. B. Miller, Preventive therapy for tuberculosis. Med. Clin. N. Am. 77 (1993) 1263–1275. [Google Scholar]
  26. K. Mischaikow, H. Smith and H. Thieme, Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions. Trans. Am. Math. Soc. 347 (1995) 1669–1685. [Google Scholar]
  27. A. Perasso, Global stability and uniform persistence for an infection Load structured SI model with Exponential growth velocity. Commun. Pure Appl. Anal. 18 (2019) 15–32. [Google Scholar]
  28. H.l. Smith and H.R. Thieme, Dynamical Systems and population persistence. In Vol. 118 of Graduate Studies in Mathematics (2011). [Google Scholar]
  29. H.R. Thieme and C. Castillo-Chavez, How may infection age dependent infectivity affects the dynamics of HIV/AIDS. Siam J. Appl. Math. 53 (1993) 1447–1479. [Google Scholar]
  30. G.F. Webb, Theory of Nonlinear age Dependent Population Dynamics. Marcel Dekker, New York (1985). [Google Scholar]
  31. R. Xu, X. Tian and F. Zhang, Global dynamics of tuberculosis transmission model with age of infection and incomplete treatment. Adv. Differ. Equ. 2017 (2017) 242. [Google Scholar]
  32. Y. Yang, S. Ruan and D. Xia, Global stability of an age structured virus Dynamics Model with Beddington–Deangelis infection function. Math. Biosci. Eng. 12 (2015) 859–877. [Google Scholar]
  33. Z. Yui, Y. Yougguang and Z. Lu, Stability analysis of an age structured SEIRS model with time delay (2020). [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.