Open Access
Issue |
Math. Model. Nat. Phenom.
Volume 20, 2025
|
|
---|---|---|
Article Number | 17 | |
Number of page(s) | 36 | |
Section | Mathematical methods | |
DOI | https://doi.org/10.1051/mmnp/2025015 | |
Published online | 24 June 2025 |
- L.J.S. Allen, B.M. Bolker, Y. Lou and A.L. Nevai, Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model. Discrete Contin. Dyn. Syst. Ser. A, 21 (2008) 1-20. [CrossRef] [Google Scholar]
- S. Bentout and S. Djilali, Asymptotic profiles of a generalized reaction-diffusion SIS epidemic model with spatial heterogeneity. Z. Angew. Math. Phys. 75 (2024) 1-31. [Google Scholar]
- S.K. Hu and R. Yuan, Asymptotic profiles of a nonlocal dispersal SIS epidemic model with Neumann boundary condition. J. Math. Anal. Appl. 580 (2024) 127710. [Google Scholar]
- X. Sun and R. Cui, Analysis on a diffusive SIS epidemic model with saturated incidence rate and linear source in a heterogeneous environment. J. Math. Anal. Appl. 490 (2020) 124212. [CrossRef] [MathSciNet] [Google Scholar]
- F.Y. Yang, W.T. Li and S. Ruan, Dynamics of a nonlocal dispersal SIS epidemic model with Neumann boundary conditions. J. Differ. Equ. 267 (2019) 2011-2051. [CrossRef] [Google Scholar]
- Z. Linhua and M. Fan, Dynamics of an SIR epidemic model with limited medical resources revisited. Nonlinear Anal. Real World Appl. 13 (2012) 312-324. [Google Scholar]
- W.O. Kermack and A.G. McKendrick, A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. Ser. A 115 (1927) 700-721. [Google Scholar]
- T. Kuniya and J. Wang, Global dynamics of an SIR epidemic model with nonlocal diffusion. Nonlinear Anal. Real World Appl. 43 (2018) 262-282. [Google Scholar]
- Y. Luo, S. Tang, Z. Teng and L. Zhang, Global dynamics in a reaction-diffusion multi-group SIR epidemic model with nonlinear incidence. Nonlinear Anal. Real World Appl. 50 (2019) 365-385. [Google Scholar]
- J. Wang and B. Dai, Dynamical analysis of a multi-group SIR epidemic model with nonlocal diffusion and nonlinear incidence rate. Nonlinear Anal. Real World Appl. 68 (2022) 103661. [Google Scholar]
- S. Qiao, F. Yang and W. Li, Traveling waves of a nonlocal dispersal SEIR model with standard incidence. Nonlinear-Anal. Real World Appl. 49 (2019) 196-216. [Google Scholar]
- J. Gao, C. Zhang and J. Wang, Analysis of a reaction-diffusion SVIR model with a fixed latent period and non-local infections. Appl. Anal. 101 (2022) 497-518. [CrossRef] [MathSciNet] [Google Scholar]
- S. Han, C. Lei and X. Zhang, Qualitative analysis on a diffusive SIRS epidemic model with standard incidence infection mechanism. Z. Angew. Math. Phys. 71 (2020) 190. [Google Scholar]
- T. Li, F. Zhang, H. Liu and Y. Chen, Threshold dynamics of an SIRS model with nonlinear incidence rate and transfer from infectious to susceptible. J. Math. Anal. Appl. 470 (2017) 52-57. [Google Scholar]
- Y. Pan, S. Zhu and J. Wang, Asymptotic profiles of a diffusive SIRS epidemic model with standard incidence mechanism and a logistic source. Z. Angew. Math. Phys. 73 (2022) 1-26. [Google Scholar]
- 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. [CrossRef] [MathSciNet] [Google Scholar]
- W. Li, Y. Zhang, J. Ji and L. Huang, Dynamics of a diffusion epidemic SIRI system in heterogeneous environment. Z. Angew. Math. Phys. 74 (2023) 104. [Google Scholar]
- B. Li and Q. Bie, Long-time dynamics of an SIRS reaction-diffusion epidemic model. J. Math. Anal. Appl. 475 (2019) 1910-1926. [CrossRef] [MathSciNet] [Google Scholar]
- J. Wang, R. Zhang, T. Kuniya, A reaction-diffusion susceptible-vaccinated-infected-recovered model in a spatially heterogeneous environment with Dirichlet boundary condition. Math. Comput. Simul. 190 (2021) 848-865. [Google Scholar]
- C. Huang and Y. Tan, Global behavior of a reaction-diffusion model with time delay and Dirichlet condition. J. Differ. Equ. 271 (2021) 186-215. [CrossRef] [Google Scholar]
- H. Berestycki, J. Coville and H.-H. Vo, On the definition and the properties of the principal eigenvalue of some nonlocal operators. J. Funct. Anal. 271 (2016) 2701-2751. [CrossRef] [MathSciNet] [Google Scholar]
- H. Berestycki, J. Coville and H.-H. Vo, Persistence criteria for populations with non-local dispersion. J. Math. Biol. 72 (2016) 1693-1745. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- A. El Hassani, B. Bettioui, K. Hattaf and N. Achtaich, Global dynamics of a diffusive SARS-CoV-2 model with antiviral treatment and fractional Laplacian operator. Math. Model. Comput. 11 (2024) 1-15. [Google Scholar]
- L. Lili, R. Xu and Z. Jin, Global dynamics of a spatial heterogeneous viral infection model with intracellular delay and nonlocal diffusion. Appl. Math. Model. 82 (2020) 150-167. [CrossRef] [MathSciNet] [Google Scholar]
- G. Zhao and S. Ruan, Spatial and temporal dynamics of a nonlocal viral infection model. SIAM J. Appl. Math. 78 (2018) 1954-1980. [Google Scholar]
- Z. Qiu, M.Y. Li and Z. Shen, Global dynamics of an infinite-dimensional epidemic model with nonlocal state structures. J. Differ. Equ. 265 (2018) 5262-5296. [CrossRef] [Google Scholar]
- X. Wang, Y. Chen and J. Yang, Spatial and temporal dynamics of a viral infection model with two nonlocal effects. Complexity 2019 (2019) 5842942. [CrossRef] [Google Scholar]
- F.B. Wang, J. Shi and X. Zou, Dynamics of a host-pathogen system on a bounded spatial domain. Commun. Pure Appl. Anal. 14 (2015) 2535-2560. [CrossRef] [MathSciNet] [Google Scholar]
- W. Wang and Z. Feng, Global dynamics of a diffusive viral infection model with spatial heterogeneity. Nonlinear Anal. Real World Appl. 72 (2023) 103763. [Google Scholar]
- K. Hattaf and N. Yousfi, A class of delayed viral infection models with general incidence rate and adaptive immune response. Int. J. Dyn. Control 3 (2015) 123-131. [Google Scholar]
- H. El Mamouni and K. Hattaf, Existence of traveling waves by means of fixed point theory for an epidemic model with Hattaf-Yousfi incidence rate and temporary immunity acquired by vaccination. Adv. Fixed Point Theory 13 (2023) 123-137. [Google Scholar]
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York (1983). [Google Scholar]
- H.L. Smith and H.R. Thieme, Dynamical Systems and Population Persistence. Graduate Studies in Mathematics, vol. 118. American Mathematical Society, Providence, RI (2011). [Google Scholar]
- X.Y. Wang , Y.M. Chen and J.Y. Yang, Spatial and temporal dynamics of a virus infection model with twononlocal effects. Complexity (2019). [PubMed] [Google Scholar]
- J.K. Hale and P. Waltman, Persistence in infinite-dimensional systems. SIAM J. Math. Anal. 20 (1989) 388-395. [Google Scholar]
- H.R. Thieme, Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity. SIAM J. Appl. Math. 70 (2009) 188-211. [CrossRef] [MathSciNet] [Google Scholar]
- J. Garcia-Melian and J.D. Rossi, On the principal eigenvalue of some nonlocal diffusion problems. J. Differ. Equ. 246 (2006) 21-36. [Google Scholar]
- F. Yang and W. Li, Dynamics of a nonlocal dispersal SIS epidemic model. Commun. Pure Appl. Anal., 16 (2017) 781-798. [CrossRef] [MathSciNet] [Google Scholar]
- H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext, Springer, New York (2010). [Google Scholar]
- F. Andreu-Vaillo, J.M. Mazon, J.D. Rossi and J.J. Toledo-Melero, Nonlocal Diffusion Problems. Math. Surveys Monogr., Vol. 165. American Mathematical Society, Providence, RI (2010). [Google Scholar]
- H.L. Smith and X.-Q. Zhao, Robust persistence for semi-dynamical systems. Nonlinear Anal. 47 (2001) 6169-6179. [Google Scholar]
- P. Magal and X.-Q. Zhao, Global attractors and steady states for uniformly persistent dynamical systems. SIAM J. Math. Anal. 37 (2005) 251-275. [Google Scholar]
- A.C. Ponce, An estimate in the spirit of Poincare's inequality. J. Eur. Math. Soc. 6 (2004) 1-15. [CrossRef] [MathSciNet] [Google Scholar]
- S. Bentout, Analysis of global behavior in an age-structured epidemic model with nonlocal dispersal and distributed delay. Math. Methods Appl. Sci. 47 (2024) 7398-7416. [Google Scholar]
- M.J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals. Princeton University Press (2008). [Google Scholar]
- F. Mahroug and S. Bentout, Dynamics of a diffusion dispersal viral epidemic model with age infection in a spatially heterogeneous environment with general nonlinear function. Math. Methods Appl. Sci. 46 (2023) 14983-15010. [Google Scholar]
- K. Hattaf, A new mixed fractional derivative with applications in computational biology. Computation 12 (2024) 7. [CrossRef] [Google Scholar]
- K. Hattaf, A new class of generalized fractal and fractal-fractional derivatives with non-singular kernels. Fractal Fract. 7 (2023) 395. [CrossRef] [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.