a0aa9197dffa974e216ec163a308dc46 mathematics_09_00520_v2.pdf 70b7c18c50ed740f2dc02704a1e4c0e8a81c1f9b mathematics_09_00520_v2.pdf 26582dae76ea3ea92cf84a259da2ed8d30083ddbf6f95a148213d389d4973c82 mathematics_09_00520_v2.pdf Title: On a Discrete SEIR Epidemic Model with Exposed Infectivity, Feedback Vaccination and Partial Delayed Re-Susceptibility Subject: 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. Keywords: discrete epidemic model; feedback vaccination control; transmission rate of the exposed; transmission rate of the infectious; delayed re-susceptibility (or immunity loss); COVID-19 pandemic Author: Manuel De la Sen, Santiago Alonso-Quesada and Asier Ibeas Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Mon Mar 8 09:25:35 2021 CET ModDate: Mon Mar 8 09:30:18 2021 CET Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 32 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 5103046 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- KPNHET+VnURWPalladioL Type 1 Custom yes yes no 10 0 GWAMYY+URWPalladioL-Ital Type 1 Custom yes yes no 15 0 DRFISQ+URWPalladioL-Bold Type 1 Custom yes yes no 20 0 JRRQAX+URWPalladioL-Roma Type 1 Custom yes yes no 24 0 DVTHKG+TimesNewRomanPS-BoldItalicMT Type 1C WinAnsi 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TrueType Identity-H yes yes yes 1009 0 Jhove (Rel. 1.22.1, 2019-04-17) Date: 2023-02-14 02:31:49 CET RepresentationInformation: mathematics_09_00520_v2.pdf ReportingModule: PDF-hul, Rel. 1.12.1 (2019-04-17) LastModified: 2023-02-13 01:40:19 CET Size: 5103046 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 1174 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@44c8afef Item: Title: Discrete SEIR Epidemic Model with Vaccination Control and Re-susceptibility Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@7b69c6ba Item: Title: Non-Negativity of the Solution Sequence and Equilibrium Points Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@46daef40 Item: Title: Stability Results Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@12f41634 Children: Item: Title: Stability around the Disease-Free Equilibrium Point Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@13c27452 Item: Title: Stability around the Endemic Equilibrium Point Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@262b2c86 Item: Title: Numerical Examples Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@371a67ec Children: Item: Title: Example 1. Numerical Theoretical Example Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@5ed828d Item: Title: Example 2. Application to the COVID-19 Pandemic Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@50d0686 Item: Title: Conclusions Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@7a3d45bd Item: Title: References Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@1e7c7811 Info: Title: On a Discrete SEIR Epidemic Model with Exposed Infectivity, Feedback Vaccination and Partial Delayed Re-Susceptibility Author: Manuel De la Sen, Santiago Alonso-Quesada and Asier Ibeas Subject: 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. Keywords: discrete epidemic model; feedback vaccination control; transmission rate of the exposed; transmission rate of the infectious; delayed re-susceptibility (or immunity loss); COVID-19 pandemic Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Mon Mar 08 09:25:35 CET 2021 ModDate: Mon Mar 08 09:30:18 CET 2021 ID: 0xbe86b182d9217de39312843671a7faba, 0xbe86b182d9217de39312843671a7faba Filters: FilterPipeline: FlateDecode Fonts: Type1: Font: BaseFont: ROJHWW+CMSY10 FontSubset: true FirstChar: 0 LastChar: 103 FontDescriptor: FontName: ROJHWW+CMSY10 Flags: Symbolic FontBBox: -29, -960, 1116, 775 FontFile: true Font: BaseFont: BSXVLS+URWPalladioL-BoldItal FontSubset: true FirstChar: 78 LastChar: 117 FontDescriptor: FontName: BSXVLS+URWPalladioL-BoldItal Flags: Symbolic FontBBox: -170, -300, 1073, 935 FontFile: true EncodingDictionary: Differences: true Font: BaseFont: LWLIVD+EURM10 FontSubset: true FirstChar: 12 LastChar: 12 FontDescriptor: FontName: LWLIVD+EURM10 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