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This paper discusses some relevant properties of a nonlinear integral equation such as the positivity and boundedness of its solution as well as its controllability under impulsive controls. The model can describe an infection evolution and the acting impulsive controls can be interpreted in particular as either vaccination actions or as variations of the infected population due to infected immigration...
In this paper, a feedback-based vaccination policy is designed for a SEIR epidemic model based on the concept of partial stability of the closed-loop system. The implementable vaccination rule is designed by only taking into account the subpopulations of exposed and infectious in contrast to previous approaches where the immune and susceptible subpopulations were also considered. Therefore, the current...
A mathematical model describing a generic disease is introduced and the dynamics of the subpopulations are studied. Through linearization of the continuous-time model, the stability of the equilibrium points and the characteristics of the disease are defined properly. Due to the nature of the disease, the model is discretized in order to apply some adaptive vaccination strategies involving feedback...
The periodic regime in a SEIR model with a delay is studied in this paper. The model is studied first under a simple set of constant parameters and then a more complex solution is proposed, depending on a set of periodic parameters related to the variable risk of contracting the disease and the different vaccination strategies applied in order to prevent it. Both the periodic parameters and the subpopulations...
This paper proposes to use the concept of partial stability instead of that of global stability to analyze the dynamic behavior of epidemic models. The rationale behind this is that it is only needed, from a practical point of view, to ensure the boundedness of the infectious and infected subpopulations in order to get the disease under control. Thus, the partial stability of a controlled SEIR epidemic...
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