Abstract
In this section we present some basic and advanced analysis of age-structured epidemic models. In the next subsection, we discuss well posedness.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
O. Angulo, J.C. López-Marcos, F.A. Milner, The application of an age-structured model with unbounded mortality to demography. Math. Biosci. 208, 495–520 (2007)
T. Arbogast, F.A. Milner, A finite difference method for a two-sex model of population dynamics. SIAM J. Numer. Anal. 26, 1474–1486 (1989)
V. Barbu, M. Iannelli, Optimal control of population dynamics. J. Optim. Theory Appl. 102, 1–14 (1999)
C. Castillo-Chavez, B. Song, Dynamical models of tuberculosis and their applications. Math. Biosci. Eng. 1, 361–404 (2004)
C. Castillo-Chavez, Z. Feng, To treat or not to treat: the case of tuberculosis. J. Math. Biol. 35, 629–656 (1997)
Z. Feng, C. Castillo-Chavez, A. Capurro, A model for tuberculosis with exogenous reinfection. Theor. Pop. Biol. 57, 235–247 (2000)
K.R. Fister, S. Lenhart, Optimal control of a competitive system with age-structure. J. Math. Anal. Appl. 291, 526–537 (2004)
K.R. Fister, S. Lenhart, Optimal harvesting in an age-structured predator-prey model. Appl. Math. Optim. 54, 1–15 (2006)
K.R. Fister, H. Gaff, S. Lenhart, E. Numfor, E. Schaefer, J. Wang, Optimal control of vaccination in an age-structured cholera model, in Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases, ed. by G. Chowell, J.M. Hyman (Springer, New York, 2016)
M.G.M. Gomes, L.J. White, G.F. Medley, The reinfection threshold. J. Theor. Biol. 236, 111–113 (2005)
D.M. Gordon, S.E. Stern, P.J. Collignon, Influence of the age and sex of human hosts on the distribution of escherichia coli ecor groups and virulence traits. Microbiology 151, 15–23 (2005)
K. Hadeler, J. Müller, Vaccination in age structured populations ii: Optimal strategies, in Models for Infectious Diseases, Their Structure and Relation to Data, ed. by G.M.V. Isham, (Cambridge University Press, Cambridge, 1996), pp. 102–114
M. Iannelli, F. Milner, The Basic Approach to Age-Structured Population Dynamics (Springer, New York, 2017)
M. Iannelli, F.A. Milner, A. Pugliese, Analytical and numerical results for the age-structured S-I-S epidemic model with mixed inter-intracohort transmission. SIAM J. Math. Anal. 23, 662–688 (1992)
H. Inaba, Backward bifurcation in a HIV/AIDS epidemic model with age structure. I. The case of proportionate mixing, Sūrikaisekikenkyūsho Kōkyūroku, pp. 189–196 (2003). Functional equations in mathematical models (Japanese) (Kyoto, 2002)
H. Inaba, Age-Structured Population Dynamics in Demography and Epidemiology (Springer, Singapore, 2017)
S. Lenhart, J.T. Workman, Optimal Control Applied to Biological Models. Chapman & Hall/CRC Mathematical and Computational Biology Series, (Chapman & Hall/CRC, Boca Raton, FL, 2007)
M. Martcheva, S.S. Pilyugin, R.D. Holt, Subthreshold and superthreshold coexistence of pathogen variants: the impact of host age-structure. Math. Biosci. 207, 58–77 (2007)
F.A. Milner, G. Rabbiolo, Rapidly converging numerical algorithms for models of population dynamics. J. Math. Biol. 30, 733–753 (1992)
E. Numfor, S. Bhattacharya, S. Lenhart, M. Martcheva, Optimal control in coupled within-host and between-host models. Math. Model. Nat. Phenom. 9, 171–203 (2014)
G. Rahav, Y. Toledano, D. Engelhard, A. Simhon, A.E. Moses, T. Sacks, M. Shapiro, Invasive pneumococcal infections: a comparison between adults and children. Medicine 76, 295–303 (1997)
G. Webb, Theory of Nonlinear Age-Dependent Population Dynamics. Monographs and Textbooks in Pure and Applied Mathematics, vol. 89 (Marcel Dekker, New York, 1985)
Acknowledgements
The authors thank Suzanne Lenhart for valuable comments and Eric Numfor and Necibe Tuncer for help with the code.
Author information
Authors and Affiliations
Appendix
Appendix
In this appendix we include the MATLAB code that executes the numerical method in the section.
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Li, XZ., Yang, J., Martcheva, M. (2020). Age-Structured Epidemic Models. In: Age Structured Epidemic Modeling. Interdisciplinary Applied Mathematics, vol 52. Springer, Cham. https://doi.org/10.1007/978-3-030-42496-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-42496-1_2
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)