Vaccination strategies based on feedback control techniques for a general SEIR-epidemic model

Abstract This paper presents several simple linear vaccination-based control strategies 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 vaccination control objective is the asymptotically tracking of the removed-by-immunity population to the total population while achieving simultaneously that the remaining populations (i.e. susceptible plus infected plus infectious) tend asymptotically to zero.

[1]  Ram N. Mohapatra,et al.  The explicit series solution of SIR and SIS epidemic models , 2009, Appl. Math. Comput..

[2]  Eduardo Massad,et al.  Fuzzy gradual rules in epidemiology , 2003 .

[3]  B. Mukhopadhyay,et al.  Existence of epidemic waves in a disease transmission model with two-habitat population , 2007, Int. J. Syst. Sci..

[4]  Shaher Momani,et al.  Solutions to the problem of prey and predator and the epidemic model via differential transform method , 2008, Kybernetes.

[5]  Manuel de la Sen,et al.  A Control Theory point of view on Beverton-Holt equation in population dynamics and some of its generalizations , 2008, Appl. Math. Comput..

[6]  Stevo Stević,et al.  On a generalized max-type difference equation from automatic control theory , 2010 .

[7]  T. Kaczorek.  Positive 1D and 2D Systems , 2001 .

[8]  J. Grasman,et al.  Reconstruction of the seasonally varying contact rate for measles. , 1994, Mathematical biosciences.

[9]  M. Keeling,et al.  Modeling Infectious Diseases in Humans and Animals , 2007 .

[10]  Ahmet Yildirim,et al.  Analytical approximate solution of a SIR epidemic model with constant vaccination strategy by homotopy perturbation method , 2009, Kybernetes.

[11]  M. De la Sen,et al.  The generalized Beverton–Holt equation and the control of populations , 2008 .

[12]  Manuel de la Sen,et al.  Control issues for the Beverton-Holt equation in ecology by locally monitoring the environment carrying capacity: Non-adaptive and adaptive cases , 2009, Appl. Math. Comput..

[13]  Zhidong Teng,et al.  Dynamic behavior for a nonautonomous SIRS epidemic model with distributed delays , 2009, Appl. Math. Comput..

[14]  Xinyu Song,et al.  Analysis of a saturation incidence SVEIRS epidemic model with pulse and two time delays , 2009, Appl. Math. Comput..

[15]  Graham C. Goodwin,et al.  Control System Design , 2000 .

[16]  Stevo Stević,et al.  A short proof of the Cushing-Henson conjecture , 2006 .

[17]  M. De la Sen,et al.  Model-Matching-Based Control of the Beverton-Holt Equation in Ecology , 2008 .