A switched multicontroller for an SEIADR epidemic model with monitored equilibrium points and supervised transients and vaccination costs

Abstract

This paper presents a multicontroller structure for an SEIADR (susceptible-exposedsymptomatic infectious-asymptomatic infectious-dead lying bodies recovered by immunity, or immune, subpopulations) epidemic model, which has three different controls involving feedback, namely, the vaccination on the susceptible subpopulation, the antiviral treatment on the symptomatic infectious subpopulation, and the impulsive removal on the infective lying bodies. The incorporation of the asymptomatic infectious and infective dead bodies to SEIR-type models allows a better modeling of diseases where the death bodies are infective as, for instance, the Ebola disease. The proposed supervised multicontroller scheme consists of a parallel disposal of several alternative controller parameterizations together with a switching scheme that chooses the active controller through consecutive time intervals via a supervisory decision scheme. The supervisory scheme decides to switch or not at testing time instants. Switching is performed to a distinct active scheme to the current active if the tentative controller minimizes the value of a loss function compared to the values of the other control schemes available in the parallel controller disposal. The supervisory loss (or cost) function incorporates several additive weighted terms including the infection loss function evolution and the vaccination, antiviral treatment, and bodies removal efforts.

On a SIR Model in a Patchy Environment Under Constant and Feedback Decentralized Controls with Asymmetric Parameterizations

“…Proposition (ii) has been proved. To prove Property (iii), assume that there is an attainable (i.e., with no negative component) endemic equilibrium point if R 0 < 1 and note, from Equations (1), (14) and (15), that…”

“…This is the case, for instance, if an additional treatment control is injected on the infectious subpopulation. See, for instance [14,15].…”

“…In [13], some useful numerical tools are given concerning the non-singularity of perturbed matrices which are used in this paper. Background literature on dynamic systems, including its role on epidemic modelling, is given in [14][15][16][17][18][19]. In this context, typical situations which need relevant attention when dealing with epidemic models, thinking of their usefulness in their practical implementation in health centers are:…”

Some Formal Results on Positivity, Stability, and Endemic Steady-State Attainability Based on Linear Algebraic Tools for a Class of Epidemic Models with Eventual Incommensurate Delays

“…A particular case of the SEIADR (susceptibleexposed-symptomatic infectious-asymptomatic infectiousinfectious corpses-recovered) proposed in [6,7] follows below for the case when the vaccination and treatment control parameters 0 , , and are constant and there is no impulsive control for the infectious corpses removal control action:̇(…”

“…The frontier between both situations typically occurs when the reproduction number is unity. See, for instance, [6][7][8][9][10][11][12] and 2 Discrete Dynamics in Nature and Society some references therein. In those studies, the first orthant of the space state is an invariant subspace as a result of the nonnegativity properties of the state trajectory solutions which is also an invoked property of other biological problems related to species evolution dynamics.…”