[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)00047-4]Search in Google Scholar
[Anderson, R. M. and May, R. M. (1979). Population biology of infectious diseases: Part 1, Nature 280(5721): 361-367.10.1038/280361a0]Search 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:1024467732637]Search 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.0407293101]Search in Google Scholar
[Edelstein-Keshet, L. (2005). Mathematical Models in Biology, SIAM, Philadelphia, PA.10.1137/1.9780898719147]Search 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)00067-5]Search 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)00009-5]Search in Google Scholar
[Hansen, E. R. and Walster, G. W. (2004). Global Optimization Using Interval Analysis, Marcel Dekker, New York, NY.10.1201/9780203026922]Search in Google Scholar
[Hethcote, H. W. (1976). Qualitative analysis of communicable disease models, Mathematical Biosciences 28(4): 335-356.10.1016/0025-5564(76)90132-2]Search in Google Scholar
[Jaulin, L., Kieffer, M., Didrit, O. and Walter, É. (2001). Applied Interval Analysis, Springer-Verlag, London.10.1007/978-1-4471-0249-6]Search in Google Scholar
[Kearfott, R. B. (1996). Rigorous Global Search: Continuous Problems, Kluwer, Dordrecht.10.1007/978-1-4757-2495-0]Search 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.1927.0118]Search 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)00030-9]Search 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.2006.10.006]Search 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/BF00276956]Search 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)10083-8]Search 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:1014798618404]Search 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): 236-262.10.1137/050638448]Search in Google Scholar
[Neumaier, A. (1990). Interval Methods for Systems of Equations, Cambridge University Press, Cambridge.10.1017/CBO9780511526473]Search in Google Scholar
[Neumaier, A. (2003). Taylor forms—Use and limits, Reliable Computing 9(1): 43-79.10.1023/A:1023061927787]Search 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