Abstract
A vaccination strategy for fighting against the propagation of epidemic diseases within a host population is purposed. A SEIR epidemic model is used to describe the propagation of the illness. This compartmental model divides the population in four classes by taking into account their status related to the infection. In this way, susceptible, exposed, infectious and recovered populations are included in the model. The vaccination strategy is based on a continuous-time nonlinear control law synthesized via an exact feedback input-output linearization approach. The asymptotic eradication of the infection from the host population under such a vaccination is proved. Moreover, the positivity and stability properties of the controlled system are investigated.
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References
De la Sen, M., Alonso-Quesada, S.: On Vaccination Control Tools for a General SEIR-Epidemic Model. In: 18th Mediterranean Conference on Control & Automation, MED 2010, pp. 1322–1328 (2010), doi:10.1109/MED.2010.5547865
Keeling, M.J., Rohani, P.: Modeling Infectious Diseases in Humans and Animals. Princeton University Press, Princeton and Oxford (2008)
Li, M.Y., Graef, J.R., Wang, L., Karsai, J.: Global Dynamics of a SEIR Model with Varying Total Population Size. Mathematical Biosciences 160, 191–213 (1999)
Makinde, O.D.: Adomian Decomposition Approach to a SIR Epidemic Model with Constant Vaccination Strategy. Applied Mathematics and Computation 184, 842–848 (2007)
Mollison, D.: Epidemic Models: Their Structure and Relation to Data. Publications of the Newton Institute, Cambridge University Press (2003)
De la Sen, M., Agarwal, R. P., Ibeas, A., Alonso-Quesada, S.: On the Existence of Equilibrium Points, Boundedness, Oscillating Behavior and Positivity of a SVEIRS Epidemic Model Under Constant and Impulsive Vaccination. Advances in Difference Equations 2011, Article ID 748608, 32 pages (2011), doi:10.1155/2011/748608
Song, X.Y., Jiang, Y., Wei, H.M.: Analysis of a Saturation Incidence SVEIRS Epidemic Model with Pulse and Two Time Delays. Applied Mathematics and Computation 214, 381–390 (2009)
Jumpen, W., Orankitjaroen, S., Boonkrong, P., Wiwatanapataphee, B.: SEIQR-SIS Epidemic Network Model and Its Stability. International Journal of Mathematics and Computers in Simulation 5, 326–333 (2011)
Safi, M.A., Gumel, A.B.: Mathematical Analysis of a Disease Transmission Model with Quarantine, Isolation and an Imperfect Vaccine. Computers and Mathematics with Applications 61, 3044–3070 (2011)
De la Sen, M., Agarwal, R.P., Ibeas, A., Alonso-Quesada, S.: 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 2010, Article ID 281612, 42 pages (2010), doi:10.1155/2010/281612
Zhang, T.L., Liu, J.L., Teng, Z.D.: Dynamic Behaviour for a Nonautonomous SIRS Epidemic Model with Distributed Delays. Applied Mathematics and Computation 214, 624–631 (2009)
Xu, R., Ma, Z., Wang, Z.: Global Stability of a Delayed SIRS Epidemic Model with Saturation Incidence and Temporary Immunity. Computers and Mathematics with Applications 59, 3211–3221 (2010)
Mukhopadhyay, B., Bhattacharyya, R.: Existence of Epidemic Waves in a Disease Transmission Model with Two-Habitat Population. International Journal of Systems Science 38, 699–707 (2007)
Isidori, A.: Nonlinear Control Systems. Springer, London (1995)
Fulton, W., Harris, J.D.: Representation Theory. Springer, New York (1991)
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Alonso-Quesada, S., De la Sen, M., Ibeas, A. (2013). A Vaccination Strategy Based on a State Feedback Control Law for Linearizing SEIR Epidemic Models. In: Gabriel, J., et al. Biomedical Engineering Systems and Technologies. BIOSTEC 2012. Communications in Computer and Information Science, vol 357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38256-7_13
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DOI: https://doi.org/10.1007/978-3-642-38256-7_13
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