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On the existence of a nontrivial equilibrium in relation to the basic reproductive number Cover

On the existence of a nontrivial equilibrium in relation to the basic reproductive number

Open Access
|Sep 2017

References

  1. Aguiar, M., Kooi, B.W., Rocha, F., Ghaffari, P. and Stollenwerk, N. (2013). How much complexity is needed to describe the fluctuations observed in dengue hemorrhagic fever incidence data?, Ecological Complexity16: 31–40.10.1016/j.ecocom.2012.09.001
  2. Arino, J., Miller, J.M. and van den Driessche, P. (2005). A multi-species epidemic model with spatial dynamics, Mathematical Medicine and Biology: A Journal of the IMA22(2): 3140.10.1093/imammb/dqi003
  3. Cushing, J.M. (1998). An Introduction to Structured Population Dynamics, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, PA.10.1137/1.9781611970005
  4. Gelfand, I. (1941). Normierte Ringe, Mathematiceskii Sbornik9(51)(1): 3–24.
  5. Golubitsky, M. and Schaeffer, D.G. (1985). Singularities and Groups in Bifurcation Theory, Vol. I, Springer, New York, NY.10.1007/978-1-4612-5034-0
  6. Horn, R.A. and Johnson, C.R. (2013). Matrix Analysis, 2nd Ed., Cambridge University Press, New York, NY.
  7. Krasnoselskii, M. and Zabreiko, P. (1984). GeometricalMethods of Nonlinear Analysis, Springer, New York, NY.
  8. Ma, T. and Wang, S. (2005). Bifurcation Theory and Applications, World Scientific Series on Nonlinear Science A, Vol. 53, World Scientific Publishing, Singapore.
  9. Nirenberg, L. (2001). Topics in Nonlinear Functional Analysis, Courant Lecture Notes in Mathematics 6, New York University Courant Institute of Mathematical Sciences, New York, NY.10.1090/cln/006
  10. Ortega, J.M. (1932). Numerical Analysis: A Second Course, SIAM, Philadelphia, PA.
  11. Rabinowitz, P.H. (1971). Some global results for nonlinear eigenvalue problems, Journal of Functional Analysis7(3): 487–513.10.1016/0022-1236(71)90030-9
  12. Rabinowitz, P.H. (1977). A bifurcation theorem for potential operators, Journal of Functional Analysis25(4): 412–424.10.1016/0022-1236(77)90047-7
  13. van den Driessche, P. and Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences180(1): 29–48.10.1016/S0025-5564(02)00108-6
  14. Wijaya, K.P., Goetz, T. and Soewono, E. (2014). An optimal control model of mosquito reduction management in a dengue endemic region, International Journal of Biomathematics7(5): 1450056–22.10.1142/S1793524514500569
  15. Wijaya, K.P., Goetz, T. and Soewono, E. (2016). Advances in mosquito dynamics modeling, Mathematical Methods in the Applied Sciences39(16): 4750–4763.10.1002/mma.3517
  16. Zadeh, L.A. and Desoer, C.A. (1963). Linear System Theory: The State Approach, McGraw-Hill, New York, NY.
DOI: https://doi.org/10.1515/amcs-2017-0044 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 623 - 636
Submitted on: Aug 2, 2016
Accepted on: Apr 18, 2017
Published on: Sep 23, 2017
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2017 Karunia Putra Wijaya, Sutimin, Edy Soewono, Thomas Götz, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.