Abstract
On a Generalized Time-Varying SEIR Epidemic Model with Mixed Point and Distributed Time-Varying Delays and Combined Regular and Impulsive Vaccination Controls
Highlights
Important control problems nowadays related to Life Sciences are the control of ecological models like, for instance, those of population evolution Beverton-Holt model, Hassell model, Ricker model, etc. 1–5 via the online adjustment of the species environment carrying capacity, that of the population growth or that of the regulated harvesting quota as well as the disease propagation via vaccination control
In a set of papers, several variants and generalizations of the Beverton-Holt model standard time-invariant, timevarying parameterized, generalized model, or modified generalized model have been investigated at the levels of stability, cycle-oscillatory behavior, permanence, and control through the manipulation of the carrying capacity see, e.g., 1–5
A mixed regular continuoustime/impulsive vaccination control strategy is proposed for a generalized time-varying SEIR epidemic model which is subject to point and distributed time-varying delays [12, 13, 15,16,17]
Summary
Important control problems nowadays related to Life Sciences are the control of ecological models like, for instance, those of population evolution Beverton-Holt model, Hassell model, Ricker model, etc. 1–5 via the online adjustment of the species environment carrying capacity, that of the population growth or that of the regulated harvesting quota as well as the disease propagation via vaccination control. There are other many variants of the above models, for instance, including vaccination of different kinds: constant 8 , impulsive , discrete-time, and so forth, by incorporating point or distributed delays 12, , oscillatory behaviors , and so forth. A mixed regular continuoustime/impulsive vaccination control strategy is proposed for a generalized time-varying SEIR epidemic model which is subject to point and distributed time-varying delays 12, 13, 15–. The parameters are not assumed to be constant but being defined by piecewise continuous real functions, the transmission coefficient included Another novelty of the proposed generalized SEIR model is the potential presence of unparameterized disease thresholds for both the infected and infectious populations. It is assumed that the total population as well as the infectious one can be directly known by inspecting the day-to-day disease effects by directly taking the required data Those data are injected to the vaccination rules. Either the use of the disease statistical data related to the percentages of each of the populations or the use of observers could be incorporated to the scheme to have either approximate estimations or very adjusted asymptotic estimations of each of the partial populations
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