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  • 1
    Online Resource
    Online Resource
    On a New Discrete SEIADR Model with Mixed Controls: Study of Its Properties
    MDPI AG ; 2018
    In:  Mathematics Vol. 7, No. 1 ( 2018-12-25), p. 18-
    Details
    In: Mathematics, MDPI AG, Vol. 7, No. 1 ( 2018-12-25), p. 18-
    Abstract: A new discrete SEIADR epidemic model is built based on previous continuous models. The model considers two extra subpopulation, namely, asymptomatic and lying corpses on the usual SEIR models. It can be of potential interest for diseases where infected corpses are infectious like, for instance, Ebola. The model includes two types of vaccinations, a constant one and another proportional to the susceptible subpopulation, as well as a treatment control applied to the infected subpopulation. We study the positivity of the controlled model and the stability of the equilibrium points. Simulations are made in order to provide allocation and examples to the different possible conditions. The equilibrium point with no infection and its stability is related, via the reproduction number values, to the reachability of the endemic equilibrium point.
    Type of Medium: Online Resource
    ISSN: 2227-7390
    URL: Article
    DOI: 10.3390/math7010018
    Language: English
    Publisher: MDPI AG
    Publication Date: 2018
    detail.hit.zdb_id: 2704244-3
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  • 2
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    A Modelization of the Propagation of COVID-19 in Regions of Spain and Italy with Evaluation of the Transmission Rates Related to the Intervention Measures
    MDPI AG ; 2021
    In:  Biology Vol. 10, No. 2 ( 2021-02-05), p. 121-
    Details
    In: Biology, MDPI AG, Vol. 10, No. 2 ( 2021-02-05), p. 121-
    Abstract: Two discrete mathematical SIR models (Susceptible-Infectious-Recovered) are proposed for modelling the propagation of the SARS-CoV-2 (COVID-19) through Spain and Italy. One of the proposed models is delay-free while the other one considers a delay in the propagation of the infection. The objective is to estimate the transmission, also known as infectivity rate, through time taking into account the infection evolution data supplied by the official health care systems in both countries. Such a parameter is estimated through time at different regional levels and it is seen to be strongly dependent on the intervention measures such as the total (except essential activities) or partial levels of lockdown. Typically, the infectivity rate evolves towards a minimum value under total lockdown and it increases again when the confinement measures are partially or totally removed.
    Type of Medium: Online Resource
    ISSN: 2079-7737
    URL: Article
    DOI: 10.3390/biology10020121
    Language: English
    Publisher: MDPI AG
    Publication Date: 2021
    detail.hit.zdb_id: 2661517-4
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  • 3
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    About Partial Reachability Issues in an SEIR Epidemic Model and Related Infectious Disease Tracking in Finite Time under Vaccination and Treatment Controls
    Hindawi Limited ; 2021
    In:  Discrete Dynamics in Nature and Society Vol. 2021 ( 2021-2-26), p. 1-21
    Details
    In: Discrete Dynamics in Nature and Society, Hindawi Limited, Vol. 2021 ( 2021-2-26), p. 1-21
    Abstract: This paper studies some basic properties of an SEIR (Susceptible-Exposed-Infectious-Recovered) epidemic model subject to vaccination and treatment controls. Firstly, the basic stability, boundedness, and nonnegativity of the state trajectory solution are investigated. Then, the problem of partial state reachability from a certain state value to a targeted one in finite time is focused on since it turns out that epidemic models are, because of their nature, neither (state) controllable from a given state to the origin nor reachable from a given initial condition. The particular formal statement of the partial reachability is focused on as a problem of output-reachability by defining a measurable output or lower dimension than that of the state. A special case of interest is that when the output is defined as the infectious subpopulation to be step-to-step tracked under suitable amounts being compatible with the required constraints. As a result, and provided that the output-controllability Gramian is nonsingular on a certain time interval of interest, a feedback control effort might be designed so that a prescribed value of the output can be approximately tracked. A linearization approximation is performed to simplify and facilitate the above task which is based on a point-to-point linearization of the solution trajectory. To this end, an “ad hoc” sampled approximate output trajectory is defined as control objective to be targeted through a point-wise calculated Jacobian matrix. A supervised appropriate restatement of the targeted suited sampled output values is redefined, if necessary, to make the initial proposed sampled trajectory compatible with the various needed constraints on nonnegativity and control boundedness. The design can be optionally performed under constant or adaptive sampling rates. Finally, some numerical examples are given to test the theoretical aspects and the design efficiency of the model.
    Type of Medium: Online Resource
    ISSN: 1607-887X , 1026-0226
    URL: Article
    DOI: 10.1155/2021/5556897
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2021
    detail.hit.zdb_id: 2033014-5
    SSG: 11
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  • 4
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    Online Resource
    On the Use of Entropy Issues to Evaluate and Control the Transients in Some Epidemic Models
    MDPI AG ; 2020
    In:  Entropy Vol. 22, No. 5 ( 2020-05-09), p. 534-
    Details
    In: Entropy, MDPI AG, Vol. 22, No. 5 ( 2020-05-09), p. 534-
    Abstract: This paper studies the representation of a general epidemic model by means of a first-order differential equation with a time-varying log-normal type coefficient. Then the generalization of the first-order differential system to epidemic models with more subpopulations is focused on by introducing the inter-subpopulations dynamics couplings and the control interventions information through the mentioned time-varying coefficient which drives the basic differential equation model. It is considered a relevant tool the control intervention of the infection along its transient to fight more efficiently against a potential initial exploding transmission. The study is based on the fact that the disease-free and endemic equilibrium points and their stability properties depend on the concrete parameterization while they admit a certain design monitoring by the choice of the control and treatment gains and the use of feedback information in the corresponding control interventions. Therefore, special attention is paid to the evolution transients of the infection curve, rather than to the equilibrium points, in terms of the time instants of its first relative maximum towards its previous inflection time instant. Such relevant time instants are evaluated via the calculation of an “ad hoc” Shannon’s entropy. Analytical and numerical examples are included in the study in order to evaluate the study and its conclusions.
    Type of Medium: Online Resource
    ISSN: 1099-4300
    URL: Article
    DOI: 10.3390/e22050534
    Language: English
    Publisher: MDPI AG
    Publication Date: 2020
    detail.hit.zdb_id: 2014734-X
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  • 5
    Online Resource
    Online Resource
    On the Entropy of Events under Eventually Global Inflated or Deflated Probability Constraints. Application to the Supervision of Epidemic Models under Vaccination Controls
    MDPI AG ; 2020
    In:  Entropy Vol. 22, No. 3 ( 2020-02-29), p. 284-
    Details
    In: Entropy, MDPI AG, Vol. 22, No. 3 ( 2020-02-29), p. 284-
    Abstract: This paper extends the formulation of the Shannon entropy under probabilistic uncertainties which are basically established in terms or relative errors related to the theoretical nominal set of events. Those uncertainties can eventually translate into globally inflated or deflated probabilistic constraints. In the first case, the global probability of all the events exceeds unity while in the second one lies below unity. A simple interpretation is that the whole set of events losses completeness and that some events of negative probability might be incorporated to keep the completeness of an extended set of events. The proposed formalism is flexible enough to evaluate the need to introduce compensatory probability events or not depending on each particular application. In particular, such a design flexibility is emphasized through an application which is given related to epidemic models under vaccination and treatment controls. Switching rules are proposed to choose through time the active model, among a predefined set of models organized in a parallel structure, which better describes the registered epidemic evolution data. The supervisory monitoring is performed in the sense that the tested accumulated entropy of the absolute error of the model versus the observed data is minimized at each supervision time-interval occurring in-between each two consecutive switching time instants. The active model generates the (vaccination/treatment) controls to be injected to the monitored population. In this application, it is not proposed to introduce a compensatory event to complete the global probability to unity but instead, the estimated probabilities are re-adjusted to design the control gains.
    Type of Medium: Online Resource
    ISSN: 1099-4300
    URL: Article
    DOI: 10.3390/e22030284
    Language: English
    Publisher: MDPI AG
    Publication Date: 2020
    detail.hit.zdb_id: 2014734-X
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  • 6
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    Online Resource
    On a SIR Model in a Patchy Environment Under Constant and Feedback Decentralized Controls with Asymmetric Parameterizations
    MDPI AG ; 2019
    In:  Symmetry Vol. 11, No. 3 ( 2019-03-22), p. 430-
    Details
    In: Symmetry, MDPI AG, Vol. 11, No. 3 ( 2019-03-22), p. 430-
    Abstract: : This paper presents a formal description and analysis of an SIR (involving susceptible- infectious-recovered subpopulations) epidemic model in a patchy environment with vaccination controls being constant and proportional to the susceptible subpopulations. The patchy environment is due to the fact that there is a partial interchange of all the subpopulations considered in the model between the various patches what is modelled through the so-called travel matrices. It is assumed that the vaccination controls are administered at each community health centre of a particular patch while either the total information or a partial information of the total subpopulations, including the interchanging ones, is shared by all the set of health centres of the whole environment under study. In the case that not all the information of the subpopulations distributions at other patches are known by the health centre of each particular patch, the feedback vaccination rule would have a decentralized nature. The paper investigates the existence, allocation (depending on the vaccination control gains) and uniqueness of the disease-free equilibrium point as well as the existence of at least a stable endemic equilibrium point. Such a point coincides with the disease-free equilibrium point if the reproduction number is unity. The stability and instability of the disease-free equilibrium point are ensured under the values of the disease reproduction number guaranteeing, respectively, the un-attainability (the reproduction number being less than unity) and stability (the reproduction number being more than unity) of the endemic equilibrium point. The whole set of the potential endemic equilibrium points is characterized and a particular case is also described related to its uniqueness in the case when the patchy model reduces to a unique patch. Vaccination control laws including feedback are proposed which can take into account shared information between the various patches. It is not assumed that there are in the most general case, symmetry-type constrains on the population fluxes between the various patches or in the associated control gains parameterizations.
    Type of Medium: Online Resource
    ISSN: 2073-8994
    URL: Article
    DOI: 10.3390/sym11030430
    Language: English
    Publisher: MDPI AG
    Publication Date: 2019
    detail.hit.zdb_id: 2518382-5
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  • 7
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    Supervision of the Infection in an SI (SI-RC) Epidemic Model by Using a Test Loss Function to Update the Vaccination and Treatment Controls
    MDPI AG ; 2020
    In:  Applied Sciences Vol. 10, No. 20 ( 2020-10-15), p. 7183-
    Details
    In: Applied Sciences, MDPI AG, Vol. 10, No. 20 ( 2020-10-15), p. 7183-
    Abstract: This paper studies and proposes some supervisory techniques to update the vaccination and control gains through time in a modified SI (susceptible-infectious) epidemic model involving the susceptible and subpopulations. Since the presence of linear feedback controls are admitted, a compensatory recovered (or immune) extra subpopulation is added to the model under zero initial conditions to deal with the recovered subpopulations transferred from the vaccination and antiviral/antibiotic treatment on the susceptible and the infectious, respectively. Therefore, the modified model is referred to as an SI(RC) epidemic model since it integrates the susceptible, infectious and compensatory recovered subpopulations. The defined time-integral supervisory loss function can evaluate weighted losses involving, in general, both the susceptible and the infectious subpopulations. It is admitted, as a valid supervisory loss function, that which involves only either the infectious or the susceptible subpopulations. Its concrete definition involving only the infectious is related to the Shannon information entropy. The supervision problem is basically based on the implementation of a parallel control structure with different potential control gains to be judiciously selected and updated through time. A higher decision level structure of the supervisory scheme updates the appropriate active controller (i.e., that with the control gain values to be used along the next time window), as well as the switching time instants. In this way, the active controller is that which provides the best associated supervisory loss function along the next inter-switching time interval. Basically, a switching action from one active controller to another one is decided as a better value of the supervisory loss function is detected for distinct controller gain values to the current ones.
    Type of Medium: Online Resource
    ISSN: 2076-3417
    URL: Article
    DOI: 10.3390/app10207183
    Language: English
    Publisher: MDPI AG
    Publication Date: 2020
    detail.hit.zdb_id: 2704225-X
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  • 8
    Online Resource
    Online Resource
    On a Discrete SEIR Epidemic Model with Two-Doses Delayed Feedback Vaccination Control on the Susceptible
    MDPI AG ; 2021
    In:  Vaccines Vol. 9, No. 4 ( 2021-04-18), p. 398-
    Details
    In: Vaccines, MDPI AG, Vol. 9, No. 4 ( 2021-04-18), p. 398-
    Abstract: A new discrete susceptible-exposed-infectious-recovered (SEIR) epidemic model is presented subject to a feedback vaccination effort involving two doses. Both vaccination doses, which are subject to a non-necessarily identical effectiveness, are administrated by respecting a certain mutual delay interval, and their immunity effect is registered after a certain delay since the second dose. The delays and the efficacies of the doses are parameters, which can be fixed in the model for each concrete experimentation. The disease-free equilibrium point is characterized as well as its stability properties, while it is seen that no endemic equilibrium point exists. The exposed subpopulation is supposed to be infective eventually, under a distinct transmission rate of that of the infectious subpopulation. Some simulation examples are presented by using disease parameterizations of the COVID-19 pandemic under vaccination efforts requiring two doses.
    Type of Medium: Online Resource
    ISSN: 2076-393X
    URL: Article
    DOI: 10.3390/vaccines9040398
    Language: English
    Publisher: MDPI AG
    Publication Date: 2021
    detail.hit.zdb_id: 2703319-3
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  • 9
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    On a generalized SVEIR epidemic model under regular and adaptive impulsive vaccination
    Vilnius University Press ; 2014
    In:  Nonlinear Analysis: Modelling and Control Vol. 19, No. 1 ( 2014-01-20), p. 83-108
    Details
    In: Nonlinear Analysis: Modelling and Control, Vilnius University Press, Vol. 19, No. 1 ( 2014-01-20), p. 83-108
    Abstract: A model for a generic disease with incubation and recovered stages is proposed. It incorporates a vaccinated subpopulation which presents a partial immunity to the disease. We study the stability, periodic solutions and impulsive vaccination design in the generalized modeled system for the dynamics and spreading of the disease under impulsive and non-impulsive vaccination. First, the effect of a regular impulsive vaccination on the evolution of the subpopulations is studied. Later a non-regular impulsive vaccination strategy is introduced based on an adaptive control law for the frequency and quantity of applied vaccines. We show the later strategy improves drastically the efficiency of the vaccines and reduce the infectious subpopulation more rapidly over time compared to a regular impulsive vaccination with constant values for both the frequency and vaccines quantity.
    Type of Medium: Online Resource
    ISSN: 2335-8963 , 1392-5113
    URL: Article
    DOI: 10.15388/NA.2014.1.6
    Language: Unknown
    Publisher: Vilnius University Press
    Publication Date: 2014
    detail.hit.zdb_id: 2604540-0
    SSG: 11
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  • 10
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    On the Equilibrium Points, Boundedness and Positivity of a Sveirs Epidemic Model under Constant Regular Constrained Vaccination
    Vilnius University Press ; 2011
    In:  Informatica Vol. 22, No. 3 ( 2011-1-1), p. 339-370
    Details
    In: Informatica, Vilnius University Press, Vol. 22, No. 3 ( 2011-1-1), p. 339-370
    Type of Medium: Online Resource
    ISSN: 0868-4952 , 1822-8844
    URL: Article
    DOI: 10.15388/Informatica.2011.330
    Language: English
    Publisher: Vilnius University Press
    Publication Date: 2011
    detail.hit.zdb_id: 2187811-0
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