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Proceedings ArticleDOI

On vaccination control tools for a general SEIR-epidemic model

23 Jun 2010-pp 1322-1328
TL;DR: 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 that takes into account the total population amounts as a refrain for the illness transmission.
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 of the removed-by-immunity population to the total population while achieving simultaneously that the remaining populations tend asymptotically to zero.
Citations
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Journal ArticleDOI
TL;DR: In this article, a generalized time-varying SEIR propagation disease model subject to delays is discussed, which potentially involves mixed regular and impulsive vaccination rules, and the proposed regular vaccination control objective is the tracking of a prescribed suited infectious trajectory for a set of given initial conditions.
Abstract: This paper discusses a generalized time-varying SEIR propagation disease model subject to delays which potentially involves mixed regular and impulsive vaccination rules. The model takes also into account the natural population growing and the mortality associated to the disease, and the potential presence of disease endemic thresholds for both the infected and infectious population dynamics as well as the lost of immunity of newborns. The presence of outsider infectious is also considered. It is assumed that there is a finite number of time-varying distributed delays in the susceptible-infected coupling dynamics influencing the susceptible and infected differential equations. It is also assumed that there are time-varying point delays for the susceptible-infected coupled dynamics influencing the infected, infectious, and removed-by-immunity differential equations. The proposed regular vaccination control objective is the tracking of a prescribed suited infectious trajectory for a set of given initial conditions. The impulsive vaccination can be used to improve discrepancies between the SEIR model and its suitable reference one.

89 citations

Journal ArticleDOI
TL;DR: A simple continuous-time linear vaccination-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) disease propagation model that takes into account the total population amounts as a refrain for the illness transmission.

56 citations

Journal ArticleDOI
TL;DR: In this paper, a continuous-time nonlinear control law synthesized via an exact feedback input-output linearization approach is proposed to fight against the propagation of epidemic diseases in an SEIR (susceptible plus infected plus infectious plus removed populations).
Abstract: This paper presents a vaccination strategy for fighting against the propagation of epidemic diseases. The disease propagation is described by an SEIR (susceptible plus infected plus infectious plus removed populations) epidemic model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes the contacts among susceptible and infected more difficult. The vaccination strategy is based on a continuous-time nonlinear control law synthesised via an exact feedback input-output linearization approach. An observer is incorporated into the control scheme to provide online estimates for the susceptible and infected populations in the case when their values are not available from online measurement but they are necessary to implement the control law. The vaccination control is generated based on the information provided by the observer. The control objective is to asymptotically eradicate the infection from the population so that the removed-by-immunity population asymptotically tracks the whole one without precise knowledge of the partial populations. The model positivity, the eradication of the infection under feedback vaccination laws and the stability properties as well as the asymptotic convergence of the estimation errors to zero as time tends to infinity are investigated.

36 citations

Journal ArticleDOI
TL;DR: In this paper, a feedback linearization-based control strategy for a SEIR (suscep- tible plus infected plus infectious plus removed populations) propagation disease model is presented.
Abstract: This paper presents a feedback linearization-based control strategy for a SEIR (suscep- tible 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 novel in the sense that the asymptotically tracking of the removed-by-immunity population to the total population while achieving simultaneously the remaining population (i.e. susceptible plus infected plus infectious) to asymptotically converge to zero. The vaccination policy is firstly designed on the above proposed tracking objective. Then, it is proven that identical vaccination rules might be found based on a general feedback linearization technique. Such a formal technique is very useful in control theory which provides a general method to generate families of vaccination policies with sound technical background which include those proposed in the former sections of the paper. The output zero dynamics of the normal canonical form in the theoretical feedback linearization analysis is identified with that of the removed-by-immunity population. The various proposed vaccination feedback rules involved one of more of the partial populations and there is a certain flexibility in their designs since some control parameters being multiplicative coefficients of the various populations may be zeroed. The basic properties of stability and positivity of the solutions are investigated in a joint way. The equilibrium points and their stability properties as well as the positivity of the solutions are also investigated.

27 citations

Journal ArticleDOI
TL;DR: In this paper, the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays were investigated and the obtained results are independent of the sizes of the delays.
Abstract: This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays. The obtained results are independent of the sizes of the delays.

26 citations

References
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Journal ArticleDOI
TL;DR: The SIR and SIS epidemic models in biology are solved by means of an analytic technique for nonlinear problems, namely the homotopy analysis method (HAM), and a one-parameter family of explicit series solutions are obtained.

97 citations

Journal ArticleDOI
TL;DR: A new SVEIRS infectious disease model with pulse and two time delays is studied and the pulse vaccination strategy is used as an effective strategy for the elimination of infectious disease.

71 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigated the positivity, stability and control of the solutions of a generalized Beverton-Holt equation arising in population dynamics which is potentially subject to bounded discontinuities at sampling instants due to the harvesting (i.e. fishing/hunting) quota and eventual independent consumption.

69 citations

Journal ArticleDOI
TL;DR: HPM is introduced to solve differential system which describes SIR epidemic model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine and reveals the vaccination reproductive number for disease control and eradication.
Abstract: Purpose – The purpose of this paper is to introduce an efficient method for solving susceptible‐infected‐removed (SIR) epidemic model. A SIR model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine. The qualitative analysis reveals the vaccination reproductive number for disease control and eradication. It introduces homotopy perturbation method (HPM) to overcome these problems.Design/methodology/approach – The paper considers HPM to solve differential system which describes SIR epidemic model. The essential idea of this method is to introduce a homotopy parameter, say p, which takes values from 0 to 1. When p=0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p is gradually increased to 1, the system goes through a sequence of deformations, the solution for each of which is close to that at the previous stage of deformation. One of the most remarkable features of the HPM is that usu...

56 citations

Journal ArticleDOI
TL;DR: The properties of the dynamic system associated with the Beverton–Holt inverse equation allow extrapolate in a simple dual way the above properties to the standard Beverton-Holt equation.

55 citations