1. bookVolume 19 (2009): Issue 3 (September 2009)
    Verified Methods: Applications in Medicine and Engineering (special issue), Andreas Rauh, Ekaterina Auer, Eberhard P. Hofer and Wolfram Luther (Eds.)
Journal Details
License
Format
Journal
eISSN
2083-8492
ISSN
1641-876X
First Published
05 Apr 2007
Publication timeframe
4 times per year
Languages
English
Open Access

Verified Solution Method for Population Epidemiology Models with Uncertainty

Published Online: 24 Sep 2009
Volume & Issue: Volume 19 (2009) - Issue 3 (September 2009) - Verified Methods: Applications in Medicine and Engineering (special issue), Andreas Rauh, Ekaterina Auer, Eberhard P. Hofer and Wolfram Luther (Eds.)
Page range: 501 - 512
Journal Details
License
Format
Journal
eISSN
2083-8492
ISSN
1641-876X
First Published
05 Apr 2007
Publication timeframe
4 times per year
Languages
English

Allen, L. J. S. and Burgin, A. M. (2000). Comparison of deterministic and stochastic SIS and SIR models in discrete time, Mathematical Biosciences 163(1): 1-33.10.1016/S0025-5564(99)00047-4Search in Google Scholar

Anderson, R. M. and May, R. M. (1979). Population biology of infectious diseases: Part 1, Nature 280(5721): 361-367.10.1038/280361a0Search in Google Scholar

Berz, M. and Makino, K. (1998). Verified integration of ODEs and flows using differential algebraic methods on highorder Taylor models, Reliable Computing 4(4): 361-369.10.1023/A:1024467732637Search in Google Scholar

Corliss, G. F. and Rihm, R. (1996). Validating an a priori enclosure using high-order Taylor series, in G. Alefeld, A. Frommer and B. Lang (Eds.), Scientific Computing and Validated Numerics, Akademie Verlag, Berlin, pp. 228-238.Search in Google Scholar

de Jong, M. C. M., Diekmann, O. and Heesterbeek, H. (1995). How does transmission of infection depend on population size?, in D. Mollison (Ed.), Epidemic Models: Their Structure and Relation to Data, Cambridge University Press, Cambridge, pp. 84-94.Search in Google Scholar

Dushoff, J., Plotkin, J. B., Levin, S. A. and Earn, D. J. D. (2004). Dynamical resonance can account for seasonality of influenza epidemics, Proceedings of the National Academy of Sciences 101(48): 16915-16916.10.1073/pnas.0407293101Search in Google Scholar

Edelstein-Keshet, L. (2005). Mathematical Models in Biology, SIAM, Philadelphia, PA.10.1137/1.9780898719147Search in Google Scholar

Fan, M., Li, M. Y. and Wang, K. (2001). Global stability of an SEIS epidemic model with recruitment and a varying total population size, Mathematical Biosciences 170(2): 199-208.10.1016/S0025-5564(00)00067-5Search in Google Scholar

Greenhalgh, D. (1997). Hopf bifurcation in epidemic models with a latent period and nonpermanent immunity, Mathematical and Computer Modelling 25(2): 85-107.10.1016/S0895-7177(97)00009-5Search in Google Scholar

Hansen, E. R. and Walster, G. W. (2004). Global Optimization Using Interval Analysis, Marcel Dekker, New York, NY.10.1201/9780203026922Search in Google Scholar

Hethcote, H. W. (1976). Qualitative analysis of communicable disease models, Mathematical Biosciences 28(4): 335-356.10.1016/0025-5564(76)90132-2Search in Google Scholar

Jaulin, L., Kieffer, M., Didrit, O. and Walter, É. (2001). Applied Interval Analysis, Springer-Verlag, London.10.1007/978-1-4471-0249-6Search in Google Scholar

Kearfott, R. B. (1996). Rigorous Global Search: Continuous Problems, Kluwer, Dordrecht.10.1007/978-1-4757-2495-0Search in Google Scholar

Kermack, W. O. and McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society of London, Part A 115(772): 700-721.10.1098/rspa.1927.0118Search in Google Scholar

Li, M. Y., Graef, J. R., Wand, L. and Karsai, J. (1999). Global dynamics of a SEIR model with varying total population size, Mathematical Biosciences 160(2): 191-215.10.1016/S0025-5564(99)00030-9Search in Google Scholar

Lin, Y. and Stadtherr, M. A. (2007). Validated solutions of initial value problems for parametric ODEs, Applied Numerical Mathematics 57(10): 1145-1162.10.1016/j.apnum.2006.10.006Search in Google Scholar

Liu, W., Levin, S. A. and Iwasa, Y. (1986). Influence of non-linear incidence rates upon the behavior of SIRS epidemiological models, Journal of Mathematical Biology 23(2): 187-204.10.1007/BF00276956Search in Google Scholar

Lohner, R. J. (1992). Computations of guaranteed enclosures for the solutions of ordinary initial and boundary value problems, in J. Cash and I. Gladwell (Eds.), Computational Ordinary Differential Equations, Clarendon Press, Oxford, pp. 425-435.Search in Google Scholar

Makino, K. and Berz, M. (1996). Remainder differential algebras and their applications, in M. Berz, C. Bishof, G. Corliss and A. Griewank (Eds.), Computational Differentiation: Techniques, Applications, and Tools, SIAM, Philadelphia, PA, pp. 63-74.Search in Google Scholar

Makino, K. and Berz, M. (1999). Efficient control of the dependency problem based on Taylor model methods, Reliable Computing 5(1): 3-12.Search in Google Scholar

Makino, K. and Berz, M. (2003). Taylor models and other validated functional inclusion methods, International Journal of Pure and Applied Mathematics 4(4): 379-456.Search in Google Scholar

Nedialkov, N. S., Jackson, K. R. and Corliss, G. F. (1999). Validated solutions of initial value problems for ordinary differential equations, Applied Mathematics and Computation 105:(1): 21-68.10.1016/S0096-3003(98)10083-8Search in Google Scholar

Nedialkov, N. S., Jackson, K. R. and Pryce, J. D. (2001). An effective high-order interval method for validating existence and uniqueness of the solution of an IVP for an ODE, Reliable Computing 7(6): 449-465.10.1023/A:1014798618404Search in Google Scholar

Neher, M., Jackson, K. R. and Nedialkov, N. S. (2007). On Taylor model based integration of ODEs, SIAM Journal on Numerical Analysis 45(1): 236-262.10.1137/050638448Search in Google Scholar

Neumaier, A. (1990). Interval Methods for Systems of Equations, Cambridge University Press, Cambridge.10.1017/CBO9780511526473Search in Google Scholar

Neumaier, A. (2003). Taylor forms—Use and limits, Reliable Computing 9(1): 43-79.10.1023/A:1023061927787Search in Google Scholar

Pugliese, A. (1990). An SEI epidemic model with varying population size, in S. Busenberg and M. Martelli (Eds.), Differential Equations Models in Biology, Epidemiology and Ecology, Lecture Notes in Computer Science, Vol. 92, Springer, Berlin, pp. 121-138.Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo