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.
Highlights
For the last two decades, an important effort has been made to propose and analyze new mathematical epidemic models being based on integro-differential equations and/or difference equations
This paper proposes and investigates an extended SEIR epidemic model with seven subpopulations, namely, the so-called SE(Is)(Ih)(Icicu)AR epidemic model, under the points of view of fulfilling general suitable properties like, for instance, the positivity and stability of the solutions and its output controllability properties for appropriately defined outputs which fix the maximum levels of reasonable presence of hospitalized patients at certain checking time instants
This paper has developed a so-called SE(Is)(Ih)(Icicu)AR epidemic model which includes four infectious subpopulations which are the asymptomatic one, the slight one, the hospitalized one which does not need intensive care, that which needs intensive care
Summary
For the last two decades, an important effort has been made to propose and analyze new mathematical epidemic models being based on integro-differential equations and/or difference equations. In other circumstances they should deal with separately since intensive care needs more technical means, like respirators, for instance and sometimes more specialized sanitary staff In this way, Programme 1 is generalized as follows to consider firstly as targeting objective the sum of both hospitalized infectious requiring or not requiring intensive care at time instants t = kT for k ∈ Z+. The above general ideas, which are based on medical evidence from extensive observation of cases [47] motivate us to focus on the formulation about how to allow a maximum number of infectious-susceptible contagion contacts, the relevant factor of the transmission rate which could be controlled, so that the foreseen hospital availability for serious infectious and admission to the intensive care unit might be kept under control.
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