1. bookVolume 32 (2022): Issue 2 (June 2022)
    Towards Self-Healing Systems through Diagnostics, Fault-Tolerance and Design (Special section, pp. 171-269), Marcin Witczak and Ralf Stetter (Eds.)
Journal Details
License
Format
Journal
eISSN
2083-8492
First Published
05 Apr 2007
Publication timeframe
4 times per year
Languages
English
Open Access

Global Behavior of a Multi–Group Seir Epidemic Model with Spatial Diffusion in a Heterogeneous Environment

Published Online: 04 Jul 2022
Volume & Issue: Volume 32 (2022) - Issue 2 (June 2022) - Towards Self-Healing Systems through Diagnostics, Fault-Tolerance and Design (Special section, pp. 171-269), Marcin Witczak and Ralf Stetter (Eds.)
Page range: 271 - 283
Received: 14 Nov 2021
Accepted: 18 Mar 2022
Journal Details
License
Format
Journal
eISSN
2083-8492
First Published
05 Apr 2007
Publication timeframe
4 times per year
Languages
English

Allen, L.J.S., Bolker, B.M., Lou, Y. and Nevai, A.L. (2008). Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model, Discrete and Continuous Dynamical Systems B 21(1): 1–20.10.3934/dcds.2008.21.1 Search in Google Scholar

Chaturantabut, S. (2020). Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework, International Journal of Applied Mathematics and Computer Science 30(4): 615–628, DOI: 10.34768/amcs-2020-0045. Open DOISearch in Google Scholar

Chen, T., Xu, J. and Wu, B. (2016). Stability of multi-group coupled systems on networks with multi-diffusion based on the graph-theoretic approach, Mathematical Methods in the Applied Sciences 39(18): 5744–5756.10.1002/mma.3975 Search in Google Scholar

Du, Y. (2006). Order Structure and Topological Methods in Nonlinear Partial Differential Equations. Vol. 1: Maximum Principles and Applications, World Scientific, Singapore.10.1142/5999 Search in Google Scholar

El-Douh, A.A.-R., Lu, S.F., Elkouny, A.A. and Amein, A.S. (2022). Hybrid cryptography with a one-time stamp to secure contact tracing for COVID-19 infection, International Journal of Applied Mathematics and Computer Science 32(1): 139–146, DOI: 10.34768/amcs-2022-0011. Open DOISearch in Google Scholar

Grabowski, P. (2021). Comparison of direct and perturbation approaches to analysis of infinite-dimensional feedback control systems, International Journal of Applied Mathematics and Computer Science 31(2): 195–218, DOI: 10.34768/amcs-2021-0014. Open DOISearch in Google Scholar

Guo, Z., Wang, F.-B. and Zou, X. (2012). Threshold dynamics of an infective disease model with a fixed latent period and non-local infections, Journal of Mathematical Biology 65(6–7): 1387–1410.10.1007/s00285-011-0500-y Search in Google Scholar

Hale, J.K. (1969). Dynamical systems and stability, Journal of Mathematical Analysis and Applications 26(1): 39–59.10.1016/0022-247X(69)90175-9 Search in Google Scholar

Hale, J.K. (1988). Asymptotic Behavior of Dissipative Systems, American Mathematical Society, Providence. Search in Google Scholar

Li, H., Peng, R. and Wang, F.-B. (2017). Varying total population enhances disease persistence: Qualitative analysis on a diffusive SIS epidemic model, Journal of Differential Equations 262(2): 885–913.10.1016/j.jde.2016.09.044 Search in Google Scholar

Liu, P. and Li, H.-X. (2020a). Global behavior of a multi-group SEIR epidemic model with age structure and spatial diffusion, Mathematical Biosciences and Engineering 17(6): 7248–7273.10.3934/mbe.202037233378896 Search in Google Scholar

Liu, P. and Li, H.-X. (2020b). Global stability of autonomous and nonautonomous hepatitis B virus models in patchy environment, Journal of Applied Analysis and Computation 10(5): 1771–1799.10.11948/20190191 Search in Google Scholar

Luo, Y., Tang, S., Teng, Z. and Zhang, L. (2019). Global dynamics in a reaction-diffusion multi-group SIR epidemic model with nonlinear incidence, Nonlinear Analysis: Real World Applications 50: 365–385.10.1016/j.nonrwa.2019.05.008 Search in Google Scholar

Martin, R.H. and Smith, H.L. (1990). Abstract functional differential equations and reaction-diffusion systems, Transactions of the American Mathematical Society 321(1): 1–44.10.1090/S0002-9947-1990-0967316-X Search in Google Scholar

Smith, H.L. (1995). Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, American Mathematical Society, Providence. Search in Google Scholar

Song, P., Lou, Y. and Xiao, Y. (2019). A spatial SEIRS reaction-diffusion model in heterogeneous environment, Journal of Differential Equations 267(9): 5084–5114.10.1016/j.jde.2019.05.022 Search in Google Scholar

Wang, W. and Zhao, X.-Q. (2012). Basic reproduction numbers for reaction-diffusion epidemic models, SIAM Journal on Applied Dynamical Systems 11(4): 1652–1673.10.1137/120872942 Search in Google Scholar

Wu, J. (1996). Theory and Applications of Partial Functional Differential Equations, Springer, New York.10.1007/978-1-4612-4050-1 Search in Google Scholar

Xing, Y. and Li, H.-X. (2021). Almost periodic solutions for a SVIR epidemic model with relapse, Mathematical Biosciences and Engineering 18(6): 7191–7217.10.3934/mbe.202135634814245 Search in Google Scholar

Yang, J. and Wang, X. (2019). Dynamics and asymptotical profiles of an age-structured viral infection model with spatial diffusion, Applied Mathematics and Computation 360(11): 236–254.10.1016/j.amc.2019.05.007 Search in Google Scholar

Yang, Y., Zou, L., Zhang, T. and Xu, Y. (2020). Dynamical analysis of a diffusive SIRS model with general incidence rate, Discrete and Continuous Dynamical Systems B 25(7): 2433–2451.10.3934/dcdsb.2020017 Search in Google Scholar

Zhao, L., Wang, Z.-C. and Ruan, S. (2018). Traveling wave solutions in a two-group SIR epidemic model with constant recruitment, Journal of Mathematical Biology 77(6–7, SI): 1871–1915.10.1007/s00285-018-1227-929564532 Search in Google Scholar

Zhao, X.-Q. (2003). Dynamical Systems in Population Biology, Springer, New York.10.1007/978-0-387-21761-1 Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo