ON VACCINATION CONTROLS FOR THE SEIR EPIDEMIC MODEL WITH SUSCEPTIBLE PLUS IMMUNE POPULATIONS TRACKING THE WHOLE POPULATION

M. De la Sen, S. Alonso-Quesada, A. Ibeas

2011

Abstract

This paper presents a simple continuous-time linear vaccination-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes more difficult contacts among susceptible and infected. The control objective is the asymptotically tracking the joint susceptible plus the removed-by-immunity population to the total population while achieving simultaneously the remaining population (i.e. infected plus infectious) to asymptotically tend to zero.

References

  1. De la Sen, M., 2008. About the properties of a modified generalized Beveron-Holt equation in ecology models. Discrete Dynamics in Nature and Society 2008, Article ID 592950, 23 pages, doi: 10.1155/2008/592950.
  2. De la Sen, M., 2008. The generalized Beverton-Holt equation and the control of populations. Applied Mathematical Modelling 32, pp. 2312-2328.
  3. De la Sen, M., Alonso-Quesada, S., 2008. A control theory point of view on Beverton-Holt equation in population dynamics and some of its generalizations. Applied Mathematics and Computation 199, pp. 464-481.
  4. De la Sen, M., Alonso-Quesada, S., 2008. Modelmatching-based control of the Beverton-Holt equation in Ecology. Discrete Dynamics in Nature and Society 2008, Article ID 793512, 21 pages, doi: 10.1155/2008/793512.
  5. De la Sen, M., Alonso-Quesada, S., 2009. Control issues for the Beverton-Holt equation in ecology by locally monitoring the environment carrying capacity: Nonadaptive and adaptive cases. Applied Mathematics and Computation 215, pp. 2616-2633.
  6. Erturk, V. S., Momani, S., 2008. Solutions to the problem of prey and predator and the epidemic model via differential transform method, Kybernetes 37, pp. 1180-1188.
  7. Keeling, M. J., Rohani, P., 2008. Modeling Infectious Diseases in Humans and Animals, Princeton University Press, Princeton and Oxford.
  8. Khan, H., Mohapatra, R. N., Varajvelu, K., Liao, S. J., 2009. The explicit series solution of SIR and SIS epidemic models. Applied Mathematics and Computation 215, pp. 653-669.
  9. Mollison, D., 2003. Epidemic Models: Their Structure and Relation to Data, Publications of the Newton Institute. Cambridge University Press.
  10. Mukhopadhyay, B., Battacharyya, R., 2007. Existence of epidemic waves in a disease transmission model with two-habitat population. International Journal of Systems Science 38, pp. 699-707.
  11. Ortega, N., Barros, L. C., Massad, E., 2003. Fuzzy gradual rules in epidemiology. Kybernetes, 32, pp. 460-477.
  12. Song, X. Y., Jiang, Y., Wei, H. M., 2009. Analysis of a saturation incidence SVEIRS epidemic model with pulse and two time delays. Applied Mathematics and Computation 214, pp. 381-390.
  13. White, P. J., Trout, R. C., Moss, S. R., Desai, A., Armesto, M., Forrester N. L., Gould, E. A., Hudson, P. J., 2004. Epidemiology of rabbit haemorrhagic disease virus in the United Kingdom: evidence for seasonal transmission by both virulent and avirulent modes of infection. Epidemiology and Infection 132, pp. 555- 567.
  14. Yildirim, A., Cherruault, Y., 2009. Anaytical approximate solution of a SIR epidemic model with constant vaccination strategy by homotopy perturbation method. Kybernetes 38, pp. 1566-1575.
  15. Zhang, T. L., Liu, J. L., Teng, Z. D., 2009. Dynamic behaviour for a nonautonomous SIRS epidemic model with distributed delays. Applied Mathematics and Computation 214, pp. 624-631.
Download


Paper Citation


in Harvard Style

De la Sen M., Alonso-Quesada S. and Ibeas A. (2011). ON VACCINATION CONTROLS FOR THE SEIR EPIDEMIC MODEL WITH SUSCEPTIBLE PLUS IMMUNE POPULATIONS TRACKING THE WHOLE POPULATION . In Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms - Volume 1: BIOINFORMATICS, (BIOSTEC 2011) ISBN 978-989-8425-36-2, pages 165-172. DOI: 10.5220/0003152901650172


in Bibtex Style

@conference{bioinformatics11,
author={M. De la Sen and S. Alonso-Quesada and A. Ibeas},
title={ON VACCINATION CONTROLS FOR THE SEIR EPIDEMIC MODEL WITH SUSCEPTIBLE PLUS IMMUNE POPULATIONS TRACKING THE WHOLE POPULATION },
booktitle={Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms - Volume 1: BIOINFORMATICS, (BIOSTEC 2011)},
year={2011},
pages={165-172},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003152901650172},
isbn={978-989-8425-36-2},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms - Volume 1: BIOINFORMATICS, (BIOSTEC 2011)
TI - ON VACCINATION CONTROLS FOR THE SEIR EPIDEMIC MODEL WITH SUSCEPTIBLE PLUS IMMUNE POPULATIONS TRACKING THE WHOLE POPULATION
SN - 978-989-8425-36-2
AU - De la Sen M.
AU - Alonso-Quesada S.
AU - Ibeas A.
PY - 2011
SP - 165
EP - 172
DO - 10.5220/0003152901650172