Mathematical analysis of a symptom-structured epidemic model

• Pesantes Grados, Pedro Isaac ^[1] ; López-Cruz, Roxana
  1. [1] Universidad Nacional Mayor de San Marcos

     Universidad Nacional Mayor de San Marcos

     Perú

     
• Localización: Selecciones Matemáticas, ISSN-e 2411-1783, Vol. 8, Nº. 2, 2021 (Ejemplar dedicado a: August - December), págs. 295-315
• Idioma: inglés
• DOI: 10.17268/sel.mat.2021.02.07
• Títulos paralelos:
  • Análisis matemático de un modelo epidémico estructurado por síntomas
• Enlaces
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• Resumen
  • español

    Se propone una modificación del modelo epidemiológico SLIAR (Susceptible-Latente- Infectado Sintomático-Asintomático-Recuperado) con dinámica vital. Este modelo incluye una estrategia de control por vacunación, y un tratamiento para reducir los síntomas, además la población infectada sintomática se divide en dos estados según su gravedad. El análisis cualitativo muestra la estabilidad local del punto de equilibrio libre de enfermedad y el punto endémico. Las simulaciones y el análisis estadístico de sensibilidad son desarrollados utilizando un conjunto de parámetros para COVID-19, finalmente, encontramos que las tasas de transmisión, reclutamiento y vacunación son objetivos potenciales para controlar un brote epidémico.

  • English

    We propose a modification of the SLIAR (Susceptible- Latent-Symptomatic Infected- Asymptomatic- Recovered) mathematical-epidemiological model with vital dynamics. This model includes a vaccination control strategy, and a treatment to reduce the symptoms, also the symptomatic infected population is divided into two states according to its severity. The qualitative analysis shows the local stability of the disease-free equilibrium point and the endemic point. Simulations and the statistical sensitivity analysis are developed using a set of parameters for COVID-19, and we found that the transmission, recruitment, finally, vaccination rates are potential targets to control an outbreak.

• Referencias bibliográficas
  • Abrams S, Wambua J, Santermans E, Willem L, Kuylen E, Coletti P, et al. Modelling the early phase of the Belgian COVID-19 epidemic using a...
  • Aguilar JB, Faust JS, Westafer LM, Gutierrez JB, Investigating the impact of asymptomatic carriers on COVID-19 transmission, medRxiv (preprint)...
  • Amaya-Muvdi DA, Acercamientos a la epidemología de una enfermedad a través de sistemas compartimentales,B.S. thesis, Bogotá-Universidad de...
  • Arino J, Brauer F, van den Driessche P, Watmough J, Wu J. Simple models for containment of a pandemic. J R Soc Interface. 2006;3(8):453–7.
  • Arino J, Brauer F, van den Driessche P, Watmough J, Wu J. A final size relation for epidemic models. Math Biosci Eng. 2007;4(2):159–75.
  • Arino J, Portet S. A simple model for COVID-19. Infect Dis Model. 2020;5:309–15.
  • Arino J. Mathematical epidemiology in a data-rich world. Infect Dis Model. 2020;5:161–88.
  • Brauer F. Some simple epidemic models. Math Biosci Eng. 2006;3(1):1–15.
  • Castillo-Salgado C, Mujica Ó J, Loyola E, Canela J ,Módulos de principios de epidemiología para el control de enfermedades, segunda edición....
  • Chen J. Pathogenicity and transmissibility of 2019-nCoV-A quick overview and comparison with other emerging viruses. Microbes Infect. 2020;22(2):69–71.
  • Diekmann O, Heesterbeek JAP, Roberts MG. The construction of next-generation matrices for compartmental epidemic models. J R Soc Interface....
  • Kim S, Seo YB, Jung E. Prediction of COVID-19 transmission dynamics using a mathematical model considering behavior changes in Korea. Epidemiol...
  • Kermack WO, McKendrick AG. A contribution to the mathematical theory of epidemics. Proc R Soc Lond A Math Phys Sci. 1927;115(772):700–21.
  • Lai C-C, Shih T-P, Ko W-C, Tang H-J, Hsueh P-R. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and coronavirus disease-2019...
  • Lauer SA, Grantz KH, Bi Q, Jones FK, Zheng Q, Meredith HR, et al. The incubation period of Coronavirus disease 2019 (COVID-19) from publicly...
  • Li R, Pei S, Chen B, Song Y, Zhang T, Yang W, et al. Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus...
  • Liu Y, Gayle AA,Wilder-Smith A, Rockl¨ov J. The reproductive number of COVID-19 is higher compared to SARS coronavirus. J Travel Med. 2020;27(2)....
  • Longini IM Jr, Halloran ME, Nizam A, Yang Y. Containing pandemic influenza with antiviral agents. Am J Epidemiol. 2004;159(7):623–33.
  • Marino S, Hogue IB, Ray CJ, Kirschner DE. A methodology for performing global uncertainty and sensitivity analysis in systems biology. J Theor...
  • MINSA, Resolución Ministerial-139-2020-MINSA: Documento Técnico - Prevención y atención de personas afectadas por COVID-19 en el Perú,(MINSA)...
  • MINSA, Sala situacional COVID-19 Perú, updated to 28/09/2020 [Reviewed 29/09/2020],Ministerio de Salud de la República del Perú (MINSA). Available...
  • Rasmussen AL, Popescu SV. SARS-CoV-2 transmission without symptoms. Science. 2021;371(6535):1206–7.
  • Romero-Brufau S, Chopra A, Ryu AJ, Gel E, Raskar R, Kremers W, et al. Public health impact of delaying second dose of BNT162b2 or mRNA-1273...
  • Tang B, Wang X, Li Q, Bragazzi NL, Tang S, Xiao Y, et al. Estimation of the transmission risk of the 2019-nCoV and its implication for public...
  • van den Driessche P, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission....
  • Wintachai P, Prathom K. Stability analysis of SEIR model related to efficiency of vaccines for COVID-19 situation. Heliyon. 2021;7(4): e06812.
  • Yang CY, Wang J. A mathematical model for the novel coronavirus epidemic in Wuhan, China. Math Biosci Eng. 2020;17(3):2708–24.
  • Yang CY, Wang J. Modeling the transmission of COVID-19 in the US–A case study. Infectious Disease Modelling 2021; 6:195-211.
  • Zhang T, Liu J, Teng Z. Existence of positive periodic solutions of an SEIR model with periodic coefficients. Appl Math (Prague). 2012;57(6):601–16.
  • Zhou F, Yu T, Du R, Fan G, Liu Y, Liu Z, et al. Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan,...