Abstract
Richard Levins [111] used the term “metapopulation” to describe a population of populations. Metapopulations naturally occur in fragmented habitats where each component of the habitat is occupied by one population and the populations are connected by migration. Levins proposed a very simple equation model to investigate the dynamics of the metapopulation in a temporally varying environment. Later, Hanski and Gilpin [67] gave more details from ecological view of point.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
J. Arino, Diseases in Metapopulations (World Scientific, Singapore, 2009)
J. Arino, Modeling and Dynamics of Infectious Diseases, vol. 11 (World Scientific, Singapore, 2009)
M. Bartlett, Deterministic and Stochastic Models for Recurrent Epidemics, vol. IV (University of California Press, Berkeley, 1956)
S. Busenberg, M. Iannelli, H. Thieme, Global behavior of an age-structured epidemic model. SIAM J. Math. Anal. 22, 1065–1080 (1991)
O. Diekmann, J. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation (Wiley, Chichester, 2000)
O. Diekmann, J.A.P. Heesterbeek, J.A.J. Metz, On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 365–382 (1990)
F. Faddy, A note on the behavior of deterministic spatial epidemics. Math.Biosci. 80, 19–22 (1986)
Z. Feng, W. Huang, C. Castillo-Chavez, Global behavior of a multi-group sis epidemic model with age structure. J. Differ. Equ. 218, 292–324 (2005)
E. Fromont, D. Pontier, M. Langlais, Disease propagation in connected host populations with density-dependent dynamics: the case of feline leukemia virus. J. Theor. Biol. 223, 465–475 (2003)
M. Gilpin, I. Hanski, Metapopulation Dynamics: Empirical and Theoretical Investigations (Harcourt Brace Jovanovich, London, 1991)
H. Guo, M.Y. Li, Z. Shuai, Global stability of the endemic equilibrium of multigroup sir epidemic models. Can. Appl. Math. Q. 14, 259–284 (2006)
H. Inaba, A semigroup approach to the strong ergodic theorem of the multistate stable population process. Math. Popul. Studies 1, 49–77 (1988)
H. Inaba, Threshold and stability results for an age-structured epidemic model. J. Math. Biol. 28, 411–434 (1990)
H. Inaba, On a new perspective of the basic reproduction number in heterogeneous environments. J. Math. Biol. 65, 309–348 (2012)
H. Inaba, Age-Structured Population Dynamics in Demography and Epidemiology (Springer, Singapore, 2017)
A. Korobeinikov, Global properties of sir and seir epidemi models with multiple parallel infectious stages. Bull. Math. Biol. 71, 75–83 (2009)
T. Kuniya, Global stability analysis with a discretization approach for an age-structured multigroup sir epidemic model. Nonlinear Anal. RWA 12, 2640–2655 (2011)
T. Kuniya, J. Wang, H. Inaba, A multi-group sir epidemic model with age structure. Discrete Cont. Dyn. Syst. Ser. B 21, 3515–3550 (2016)
T. Kuniya, H. Inaba, J. Yang, Global behavior of SIS epidemic models with age structure and spatial heterogeneity. Jpn. J. Ind. Appl. Math. 35, 669–706 (2018)
A. Lajmanovich, J. Yorke, A deterministic model for gonorrhea in a nonhomogeneous population. Math. Biosci. 28, 221–236 (1976)
R. Levins, Extinction, in Some Mathematical Problems in Biology, ed. by M. Gerstenhaber (American Mathematical Society, Providence, 1970)
L. Ravachev, I.M.Longini, A mathematical model for the global spread of influenza. Math. Biosci. 75, 22 (1985)
D.J. Rodriguez, L.Torres-Sorando, Models of infectious diseases in spatially heterogeneous environments. Bull. Math. Biol. 63, 547–571 (2001)
R. Sun, Global stability of the endemic equilibrium of multigroup sir models with nonlinear incidence. Comput. Math. Appl. 60, 2286–2291 (2010)
H. Thieme, Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity. SIAM J. Appl. Math. 70, 188–211 (2009)
W. Wang, X. Zhao, An epidemic model in a patchy environment. Math. Biosci. 190, 97–112 (2004)
G. Webb, Theory of Nonlinear Age-Dependent Population Dynamics. Monographs and Textbooks in Pure and Applied Mathematics, vol. 89 (Marcel Dekker, New York, 1985)
K. Yosida, Functional Analysis, 2nd edn. (Springer, Berlin/Heidelberg/New York, 1968)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Li, XZ., Yang, J., Martcheva, M. (2020). Metapopulation and Multigroup Age-Structured Models. In: Age Structured Epidemic Modeling. Interdisciplinary Applied Mathematics, vol 52. Springer, Cham. https://doi.org/10.1007/978-3-030-42496-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-42496-1_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-42495-4
Online ISBN: 978-3-030-42496-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)