On a generalized time-varying SEIR epidemic model with mixed point and distributed time-varying delays and combined regular and impulsive vaccination controls

Advances in Difference Equations

Volumn 2010, Issue , 2010, Pages

  Agarwal, Ravi P ^b,c   De La Sen, M ^a   Ibeas, A ^d   Alonso Quesada, S ^a  

^a UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^b Florida Institute of Technology ^*  (United States)

^c KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

^d UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79953280211     PISSN: 16871839     EISSN: 16871847     Source Type: Journal    
DOI: 10.1155/2010/281612     Document Type: Article

References (29)

1. De La Sen M., Alonso-Quesada S., A control theory point of view on Beverton-Holt equation in population dynamics and some of its generalizations Applied Mathematics and Computation 2008 199 2 464 481 (Pubitemid 351618336)
2. De La Sen M., Alonso-Quesada S., Control issues for the Beverton-Holt equation in ecology by locally monitoring the environment carrying capacity: Non-adaptive and adaptive cases Applied Mathematics and Computation 2009 215 7 2616 2633
3. De La Sen M., Alonso-Quesada S., Model-matching-based control of the Beverton-Holt equation in ecology Discrete Dynamics in Nature and Society 2008 21
4. De La Sen M., About the properties of a modified generalized Beverton-Holt equation in ecology models Discrete Dynamics in Nature and Society 2008 23
5. De La Sen M., The generalized Beverton-Holt equation and the control of populations Applied Mathematical Modelling 2008 32 11 2312 2328
6. Mollison D., Epidemic Models: Their Structure and Relation to Data 1995 New York, NY, USA Newton Institute, Cambridge University Press
7. Keeling M. J., Rohani P., Modeling Infectious Diseases in Humans and Animals 2008 Princeton, NJ, USA Princeton University Press xvi+368
8. Yildirim A., Cherruault Y., Anaytical approximate solution of a SIR epidemic model with constant vaccination strategy by homotopy perturbation method Kybernetes 2009 38 9 1566 1575
9. Erturk V. S., Momani S., Solutions to the problem of prey and predator and the epidemic model via differential transform method Kybernetes 2008 37 8 1180 1188
10. Ortega N., Barros L. C., Massad E., Fuzzy gradual rules in epidemiology Kybernetes 2003 32 3-4 460 477 (Pubitemid 36467892)
11. Khan H., Mohapatra R. N., Vajravelu K., Liao S. J., The explicit series solution of SIR and SIS epidemic models Applied Mathematics and Computation 2009 215 2 653 669
12. Song X., Jiang Y., Wei H.g, Analysis of a saturation incidence SVEIRS epidemic model with pulse and two time delays Applied Mathematics and Computation 2009 214 2 381 390
13. Zhang T., Liu J., Teng Z., Dynamic behavior for a nonautonomous SIRS epidemic model with distributed delays Applied Mathematics and Computation 2009 214 2 624 631
14. Mukhopadhyay B., Bhattacharyya R., Existence of epidemic waves in a disease transmission model with two-habitat population International Journal of Systems Science 2007 38 9 699 707 (Pubitemid 47497524)
15. Barreiro A., Baos A., Delay-dependent stability of reset systems Automatica 2010 46 1 216 221
16. De La Sen M., On positivity of singular regular linear time-delay time-invariant systems subject to multiple internal and external incommensurate point delays Applied Mathematics and Computation 2007 190 1 382 401
17. De La Sen M., Quadratic stability and stabilization of switched dynamic systems with uncommensurate internal point delays Applied Mathematics and Computation 2007 185 1 508 526
18. Daley D. J., Gani J., Epidemic Modelling: An Introduction 1999 15 Cambridge, UK Cambridge University Press xii+213 Cambridge Studies in Mathematical Biology
19. Piccardi C., Lazzaris S., Vaccination policies for chaos reduction in childhood epidemics IEEE Transactions on Biomedical Engineering 1998 45 5 591 595 (Pubitemid 28212771)
20. Zhang T., Liu J., Teng Z., Dynamic behavior for a nonautonomous SIRS epidemic model with distributed delays Applied Mathematics and Computation 2009 214 2 624 631
21. Gao S., Teng Z., Xie Dehui, The effects of pulse vaccination on SEIR model with two time delays Applied Mathematics and Computation 2008 201 1-2 282 292
22. Khan Q. J. A., Krishnan E. V., An epidemic model with a time delay in transmission Applications of Mathematics 2003 48 3 193 203
23. Boichuk A., Langerov M., korkov J., Solutions of linear impulsive differential systems bounded on the entire real axis Advances in Difference Equations 2010 10
24. Nieto J. J., Tisdell C. C., On exact controllability of first-order impulsive differential equations Advances in Difference Equations 2010 9
25. Yu H. G., Zhong S. M., Agarwal R. P., Xiong L. L., Species permanence and dynamical behavior analysis of an impulsively controlled ecological system with distributed time delay Computers Mathematics with Applications 2010 59 12 3824 3835
26. Marchenko V. M., Zachkevich Z., Representation of solutions of control hybrid differential-difference impulse systems Differential Equations 2009 45 12 1811 1822
27. Marchenko V. M., Luazo Z. Z., On the stability of hybrid differential-difference systems Differential Equations 2009 45 12 1811 1822
28. De La Sen M., A method for general design of positive real functions IEEE Transactions on Circuits and Systems. I. Fundamental Theory and Applications 1998 45 7 764 769 (Pubitemid 128745121)
29. De La Sen M., Alonso-Quesada S., On vaccination control tools for a general SEIR-epidemic model 1 Proceedings of the 18th Mediterranean Conference on Control and Automation (MED '10) 2010 1322 1328