On a Controlled Se(Is)(Ih)(Iicu)AR Epidemic Model with Output Controllability Issues to Satisfy Hospital Constraints on Hospitalized Patients

Abstract

An epidemic model, the so-called SE(Is)(Ih)(Iicu)AR epidemic model, is proposed which splits the infectious subpopulation of the classical SEIR (Susceptible-Exposed-Infectious-Recovered) model into four subpopulations, namely asymptomatic infectious and three categories of symptomatic infectious, namely slight infectious, non-intensive care infectious, and intensive care hospitalized infectious. The exposed subpopulation has four different transitions to each one of the four kinds of infectious subpopulations governed under eventually different proportionality parameters. The performed research relies on the problem of satisfying prescribed hospitalization constraints related to the number of patients via control interventions. There are four potential available controls which can be manipulated, namely the vaccination of the susceptible individuals, the treatment of the non-intensive care unit hospitalized patients, the treatment of the hospitalized patients at the intensive care unit, and the transmission rate which can be eventually updated via public interventions such as isolation of the infectious, rules of groups meetings, use of face masks, decrees of partial or total quarantines, and others. The patients staying at the non-intensive care unit and those staying at the intensive care unit are eventually, but not necessarily, managed as two different hospitalized subpopulations. The controls are designed based on output controllability issues in the sense that the levels of hospital admissions are constrained via prescribed maximum levels and the measurable outputs are defined by the hospitalized patients either under a joint consideration of the sum of both subpopulations or separately. In this second case, it is possible to target any of the two hospitalized subpopulations only or both of them considered as two different components of the output. Different algorithms are given to design the controls which guarantee, if possible, that the prescribed hospitalization constraints hold. If this were not possible, because the levels of serious infection are too high according to the hospital availability means, then the constraints are revised and modified accordingly so that the amended ones could be satisfied by a set of controls. The algorithms are tested through numerically worked examples under disease parameterizations of COVID-19.

On a Discrete SEIR Epidemic Model with Two-Doses Delayed Feedback Vaccination Control on the Susceptible

“…Thus, an output feedback approach is adopted in this work and discussed in the sequel. However, control theory has developed many analytical tools that allows one to face this problem by using other approaches such as state feedback and feedback linearization [ 2 ], output-controllability [ 19 ], optimal control [ 21 ], impulsive control [ 22 ], sliding mode [ 23 ] and lockdown and quarantine [ 18 , 28 ], to cite just a few.…”

“…Therefore, discrete epidemic models have been found appropriate for processing such data. See, for instance, [ 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 ] and some related references therein. Studies on particular data for different countries or regions can be found in the literature related to COVID-19, sometimes related to public interventions, such as quarantines, isolation measures, lockdowns, use of masks, social distance rules, etc.…”

“…Studies on particular data for different countries or regions can be found in the literature related to COVID-19, sometimes related to public interventions, such as quarantines, isolation measures, lockdowns, use of masks, social distance rules, etc. See, for instance, those concerned with Saudi Arabia [ 16 , 17 ], Madrid capital town, metropolitan area and surrounding administrative area [ 18 , 19 ], India [ 23 , 24 ], Italy [ 25 ], United States [ 26 ], Canada and several of its provinces [ 28 ], Switzerland, [ 29 ], Brazil [ 30 ], etc. In addition, the analysis of data has been sometimes accompanied with mathematical analysis techniques on the pandemic evolution related to public interventions or mathematically founded analysis of the obtained data.…”

“…In that way, the impact of lockdowns is investigated in [ 17 ], while the effects of total or partial quarantines are investigated in [ 18 ] for a SEIAR model, which incorporates the asymptomatic subpopulation to the typical SEIR model by considering the isolated population as removed either from the infectious individuals or from the susceptible ones. In [ 19 ], a more general model of potential usefulness in the description and monitoring of COVID-19 has been proposed, discussed, and tested with recorded real data. Such a model includes three different infectious subpopulations, namely, the slightly infections, the hospitalized ones and the ones staying at the intensive care units are considered.…”

On a Discrete SEIR Epidemic Model with Exposed Infectivity, Feedback Vaccination and Partial Delayed Re-Susceptibility

“…The whole extended SEIR model under consideration includes the asymptomatic individuals as a separate subpopulation with its own transition from the exposed individuals. In addition, in [19], a general model with three different infectious subpopulations, namely, the slightly infections, the hospitalized ones and those in the intensive care unit, are considered. Each one of the above subpopulations as well as the asymptomatic ones have their own transitions from the exposed subpopulation, and vaccination and treatment controls are also considered to satisfy a priori established hospitalization constraints for the seriously infectious individuals on availability of beds and specific needed hospital means for intensive treatment.…”