Robust Sliding Control of SEIR Epidemic Models

This paper is aimed at designing a robust vaccination strategy capable of eradicating an infectious disease from a population regardless of the potential uncertainty in the parameters defining the disease. For this purpose, a control theoretic approach based on a sliding-mode control law is used. Initially, the controller is designed assuming certain knowledge of an upper-bound of the uncertainty signal. Afterwards, this condition is removed while an adaptive sliding control system is designed. The closed-loop properties are proved mathematically in the nonadaptive and adaptive cases. Furthermore, the usual sign function appearing in the sliding-mode control is substituted by the saturation function in order to prevent chattering. In addition, the properties achieved by the closed-loop system under this variation are also stated and proved analytically. The closed-loop system is able to attain the control objective regardless of the parametric uncertainties of the model and the lack of a priori knowledge on the system.

On the Stability and Equilibrium Points of Multistaged SI (n) R Epidemic Models

This paper relies on the concept of next generation matrix defined ad hoc for a new proposed extended SEIR model referred to as SI(n)R-model to study its stability. The model includes n successive stages of infectious subpopulations, each one acting at the exposed subpopulation of the next infectious stage in a cascade global disposal where each infectious population acts as the exposed subpopulation of the next infectious stage. The model also has internal delays which characterize the time intervals of the coupling of the susceptible dynamics with the infectious populations of the various cascade infectious stages. Since the susceptible subpopulation is common, and then unique, to all the infectious stages, its coupled dynamic action on each of those stages is modeled with an increasing delay as the infectious stage index increases from 1 to n. The physical interpretation of the model is that the dynamics of the disease exhibits different stages in which the infectivity and the mortality rates vary as the individual numbers go through the process of recovery, each stage with a characteristic average time.

Pulse vs. Optimal Stationary Fishing: The Northern Stock of Hake

Pulse fishing may be a global optimal strategy in multicohort fisheries. In this article we compare the pulse fishing solutions obtained by using global numerical methods with the analytical stationary optimal solution. This allows us to quantify the potential benefits associated with the use of periodic fishing in the Northern Stock of hake. Results show that: first, management plans based exclusively on traditional reference targets as Fmsy may drive fishery economic results far from the optimal; second, global optimal solutions would imply, in a cyclical manner, the closure of the fishery for some periods and third, second best stationary policies with stable employment only reduce optimal present value of discounted profit in a 2%.

Selectivity, pulse fishing and endogenous lifespan in Beverton-Holt models

Optimal management in a multi-cohort Beverton-Holt model with any number of age classes and imperfect selectivity is equivalent to finding the optimal fish lifespan by chosen fallow cycles. Optimal policy differs in two main ways from the optimal lifespan rule with perfect selectivity. First, weight gain is valued in terms of the whole population structure. Second, the cost of waiting is the interest rate adjusted for the increase in the pulse length. This point is especially relevant for assessing the role of selectivity. Imperfect selectivity reduces the optimal lifespan and the optimal pulse length. We illustrate our theoretical findings with a numerical example. Results obtained using global numerical methods select the optimal pulse length predicted by the optimal lifespan rule.

An observer-based vaccination control law for an SEIR epidemic model based on feedback linearization techniques for nonlinear systems

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.

On some new mathematical models for infective diseases: analysis, equilibrium, positivity and vaccination controls

196 p.