Control issues for the Beverton–Holt equation in ecology by locally monitoring the environment carrying capacity: Non-adaptive and adaptive cases

On the equilibrium points, boundedness and positivity of a SVEIRS epidemic model under constant regular vaccination

“…On the other hand, we can use from L´Hopital rule the following limit relations in the entries (1,4) and (2,4) …”

“…[1][2][3][4][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 (namely, the so-called standard time-invariant one, the time-varying parameterized one, the generalized model and the 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, for instance, [1][2][3][4][5]). The design of related control actions has been proved to be important in those papers at the levels, for instance, of aquaculture exploitation or plague fighting.…”

On the Passivity and Positivity Properties in Dynamic Systems: Their Achievement under Control Laws and Their Maintenance under Parameterizations Switching

“…See, for instance, [16][17][18]. The above properties follow from the positivity properties of the unforced and forced output solution trajectory in externally positive systems.…”

About feedback vaccination rules for a true-mass action-type SEIR epidemic model

“…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, time-varying parameterized, generalized model or modified generalized model) have been investigated at the levels of stability, cycleoscillatory behavior, permanence and control through the manipulation of the carrying capacity (see, for instance, [1][2][3][4][5]). The design of related control actions has been proved to be important in those papers at the levels, for instance, of aquaculture exploitation or plague fighting.…”