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Open accessJournal ArticleDOI: 10.3390/MATH9050520

On a discrete seir epidemic model with exposed infectivity, feedback vaccination and partial delayed re-susceptibility

02 Mar 2021-Vol. 9, Iss: 5, pp 1-35
Abstract: A new discrete Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model is proposed, and its properties of non-negativity and (both local and global) asymptotic stability of the solution sequence vector on the first orthant of the state-space are discussed. The calculation of the disease-free and the endemic equilibrium points is also performed. The model has the following main characteristics: (a) the exposed subpopulation is infective, as it is the infectious one, but their respective transmission rates may be distinct; (b) a feedback vaccination control law on the Susceptible is incorporated; and (c) the model is subject to delayed partial re-susceptibility in the sense that a partial immunity loss in the recovered individuals happens after a certain delay. In this way, a portion of formerly recovered individuals along a range of previous samples is incorporated again to the susceptible subpopulation. The rate of loss of partial immunity of the considered range of previous samples may be, in general, distinct for the various samples. It is found that the endemic equilibrium point is not reachable in the transmission rate range of values, which makes the disease-free one to be globally asymptotically stable. The critical transmission rate which confers to only one of the equilibrium points the property of being asymptotically stable (respectively below or beyond its value) is linked to the unity basic reproduction number and makes both equilibrium points to be coincident. In parallel, the endemic equilibrium point is reachable and globally asymptotically stable in the range for which the disease-free equilibrium point is unstable. It is also discussed the relevance of both the vaccination effort and the re-susceptibility level in the modification of the disease-free equilibrium point compared to its reached component values in their absence. The influences of the limit control gain and equilibrium re-susceptibility level in the reached endemic state are also explicitly made viewable for their interpretation from the endemic equilibrium components. Some simulation examples are tested and discussed by using disease parameterizations of COVID-19.

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Topics: Equilibrium point (55%), Epidemic model (52%)
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7 results found


Open accessJournal ArticleDOI: 10.3390/VACCINES9040398
18 Apr 2021-Vaccine
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.

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Topics: Epidemic model (52%)

3 Citations


Open accessJournal ArticleDOI: 10.1080/10652469.2021.1913138
Thomas Simon1Institutions (1)
Abstract: We give some necessary and some sufficient conditions for the complete monotonicity on the negative half-line of a Mittag–Leffler function of Le Roy type. It is conjectured that the underlying posi...

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Topics: Mittag-Leffler function (58%), Infinite divisibility (57%), Gamma function (55%) ... show more

2 Citations


Journal ArticleDOI: 10.1007/S40808-021-01220-6
Drashti Kapadia1, Namrata D. Jariwala1Institutions (1)
Abstract: Tropospheric ozone (O3), as an air pollutant is increasing at an alarming rate in urban areas. The concentration of ozone is affected by precursor pollutants, such as particulate matter (PM10, PM2.5), carbon monoxide (CO), nitrogen dioxide (NO2), sulfur dioxide (SO2), carbon dioxide (CO2), and nitric oxide (NO), and meteorological parameters, such as air temperature (AT), relative humidity (RH), global solar radiation (SR), wind direction (WD), and wind speed (WS) of the area. Ozone is a secondary pollutant and strong oxidizing agent injurious to human health. The present study aimed to identify the most crucial factors that influence ozone formation and to develop an ozone prediction model using artificial neural network with optimal inputs. The data obtained from Limbayat, real-time air pollutants monitoring station of Surat city, have been used to evolve the model, followed by feature selection techniques, namely, sensitivity analysis, Boruta algorithm, and recursive feature elimination algorithm (RFE). Finally, 6/14 influencing parameters have been identified using an attribute selection approach. Interestingly, “hour of the day” was found the most prominent and governing parameter among the 14 parameters after applying various feature selection techniques in the experiments. The result showed that the efficiency of the prediction model was 79.4% when six parameters were used in the machine learning algorithms.

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Topics: Tropospheric ozone (60%), Ozone (53%), Nitrogen dioxide (52%) ... show more

1 Citations


Open accessJournal ArticleDOI: 10.3390/APP11146266
06 Jul 2021-Applied Sciences
Abstract: The authors are grateful to the institute Carlos III for grant COV20/01213, to the Spanish Government for Grants RTI2018-094336-B-I00 and RTI2018-094902-BC22 (MCIU/AEI/FEDER, UE) and to the Basque Government for Grant IT1207-19.

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1 Citations


Open accessPosted ContentDOI: 10.1007/S11071-021-07036-4
08 Nov 2021-Nonlinear Dynamics
Abstract: In this research, the challenging problem of Covid-19 mitigation is looked at from an engineering point of view. At first, the behavior of coronavirus in the Iranian and Russian societies is expressed by a set of ordinary differential equations. In the proposed model, the control input signals are vaccination, social distance and facial masks, and medical treatment. The unknown parameters of the system are estimated by long short-term memory (LSTM) algorithm. In the LSTM algorithm, the problem of long-term dependency is prevented. The uncertainty and measurement noises are inherent characteristics of epidemiological models. For this reason, an extended Kalman filter (EKF) is developed to estimate the state variables of the proposed model. In continuation, a robust sliding mode controller is designed to control the spread of coronavirus under vaccination, social distance and facial masks, and medical treatment. The stability of the closed-loop system is guaranteed by the Lyapunov theorems. The official confirmed data provided by the Iranian and Russian ministries of health are employed to simulate the proposed algorithms. It is understood from simulation results that global vaccination has the potential to create herd immunity in long term. Under the proposed controller, daily Covid-19 infections and deaths become less than 500 and 10 people, respectively.

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Topics: Sliding mode control (55%), Extended Kalman filter (53%), Control theory (52%) ... show more

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36 results found


Journal ArticleDOI: 10.1137/S0036144500371907
01 Dec 2000-Siam Review
Abstract: Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\sigma$, and the replacement number $R$ are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of $R_{0}$ and $\sigma$ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.

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5,074 Citations


Open accessJournal ArticleDOI: 10.1016/J.JTBI.2004.09.006
Abstract: We present a model of contagion that unifies and generalizes existing models of the spread of social influences and microorganismal infections Our model incorporates individual memory of exposure to a contagious entity (eg a rumor or disease), variable magnitudes of exposure (dose sizes), and heterogeneity in the susceptibility of individuals Through analysis and simulation, we examine in detail the case where individuals may recover from an infection and then immediately become susceptible again (analogous to the so-called SIS model) We identify three basic classes of contagion models which we call epidemic threshold, vanishing critical mass, and critical mass classes, where each class of models corresponds to different strategies for prevention or facilitation We find that the conditions for a particular contagion model to belong to one of the these three classes depend only on memory length and the probabilities of being infected by one and two exposures, respectively These parameters are in principle measurable for real contagious influences or entities, thus yielding empirical implications for our model We also study the case where individuals attain permanent immunity once recovered, finding that epidemics inevitably die out but may be surprisingly persistent when individuals possess memory

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348 Citations


Open accessJournal ArticleDOI: 10.1016/J.CHAOS.2020.110057
Abstract: In this paper, we study the effectiveness of the modelling approach on the pandemic due to the spreading of the novel COVID-19 disease and develop a susceptible-infected-removed (SIR) model that provides a theoretical framework to investigate its spread within a community Here, the model is based upon the well-known susceptible-infected-removed (SIR) model with the difference that a total population is not defined or kept constant per se and the number of susceptible individuals does not decline monotonically To the contrary, as we show herein, it can be increased in surge periods! In particular, we investigate the time evolution of different populations and monitor diverse significant parameters for the spread of the disease in various communities, represented by China, South Korea, India, Australia, USA, Italy and the state of Texas in the USA The SIR model can provide us with insights and predictions of the spread of the virus in communities that the recorded data alone cannot Our work shows the importance of modelling the spread of COVID-19 by the SIR model that we propose here, as it can help to assess the impact of the disease by offering valuable predictions Our analysis takes into account data from January to June, 2020, the period that contains the data before and during the implementation of strict and control measures We propose predictions on various parameters related to the spread of COVID-19 and on the number of susceptible, infected and removed populations until September 2020 By comparing the recorded data with the data from our modelling approaches, we deduce that the spread of COVID-19 can be under control in all communities considered, if proper restrictions and strong policies are implemented to control the infection rates early from the spread of the disease

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210 Citations


Open accessJournal ArticleDOI: 10.1016/S1473-3099(20)30227-9
Topics: Outbreak (56%), Betacoronavirus (53%), Viral Epidemiology (50%)

125 Citations


Open accessJournal ArticleDOI: 10.1109/LCSYS.2020.3009912
Francesco Casella1Institutions (1)
01 Jul 2021-
Abstract: This letter studies if and to which extent COVID-19 epidemics can be controlled by authorities taking decisions on public health measures on the basis of daily reports of swab test results, active cases and total cases. A suitably simplified process model is derived to support the controllability analysis, highlighting the presence of very significant time delay; the model is validated with data from several outbreaks. The analysis shows that suppression strategies can be effective if strong enough and enacted early on. It also shows how mitigation strategies can fail because of the combination of delay, unstable dynamics, and uncertainty in the feedback loop; approximate conditions based on the theory of limitation of linear control are given for feedback control to be feasible.

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55 Citations