This paper presents a feedback linearization-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The modeltakes into account the total population amounts as a refrain for the illness transmission sinceits increase makes more difficult contacts among susceptible and infected. The control objectiveis novel in the sense that the asymptotically tracking of the removed-by-immunity populationto the total population while achieving simultaneously the remaining population (i.e. susceptibleplus infected plus infectious) to asymptotically converge to zero. The vaccination policy is firstlydesigned on the above proposed tracking objective. Then, it is proven that identical vaccinationrules might be found based on a general feedback linearization technique. Such a formal techniqueis very useful in control theory which provides a general method to generate families of vaccinationpolicies with sound technical background which include those proposed in the former sectionsof the paper. The output zero dynamics of the normal canonical form in the theoretical feedbacklinearization analysis is identified with that of the removed-by-immunity population. The variousproposed vaccination feedback rules involved one of more of the partial populations and there isa certain flexibility in their designs since some control parameters being multiplicative coefficientsof the various populations may be zeroed. The basic properties of stability and positivity of thesolutions are investigated in a joint way. The equilibrium points and their stability properties aswell as the positivity of the solutions are also investigated.
Feedback linearization-based vaccination control strategies for true-mass action type SEIR epidemic models
25.07.2011
doi:10.15388/NA.16.3.14094
Nonlinear Analysis: Modelling and Control; Vol 16 No 3 (2011): Nonlinear Analysis: Modelling and Control; 283-314 ; Nonlinear Analysis: Modelling and Control; T. 16 Nr. 3 (2011): Nonlinear Analysis: Modelling and Control; 283-314 ; 2335-8963 ; 1392-5113
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
DDC: | 629 |
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