On a model of COVID-19 dynamics

  • Received: 01 June 2020 Revised: 01 September 2020 Published: 19 October 2020
  • Primary:37B25, 92D30;Secondary:92D25

  • A model of COVID-19 in an interconnected network of communities is studied. This model considers the dynamics of susceptible, asymptomatic and symptomatic individuals, deceased but not yet buried people, as well as the dynamics of the virus or pathogen at connected nodes or communities. People can move between communities carrying the virus to any node in the region of $ n $ communities (or patches). This model considers both virus direct (person to person) and indirect (contaminated environment to person) transmissions. Using either matrix and graph-theoretic methods and some combinatorial identities, appropriate Lyapunov functions are constructed to study global stability properties of both the disease-free and the endemic equilibrium of the corresponding system of $ 5n $ differential equations.

    Citation: Jorge Rebaza. On a model of COVID-19 dynamics[J]. Electronic Research Archive, 2021, 29(2): 2129-2140. doi: 10.3934/era.2020108

    Related Papers:

  • A model of COVID-19 in an interconnected network of communities is studied. This model considers the dynamics of susceptible, asymptomatic and symptomatic individuals, deceased but not yet buried people, as well as the dynamics of the virus or pathogen at connected nodes or communities. People can move between communities carrying the virus to any node in the region of $ n $ communities (or patches). This model considers both virus direct (person to person) and indirect (contaminated environment to person) transmissions. Using either matrix and graph-theoretic methods and some combinatorial identities, appropriate Lyapunov functions are constructed to study global stability properties of both the disease-free and the endemic equilibrium of the corresponding system of $ 5n $ differential equations.



    加载中


    [1] A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Classics in Applied Mathematics, 9, SIAM, Philadelphia, PA, 1994. doi: 10.1137/1.9781611971262
    [2] Global stability analysis of a general model of Zika virus. Nonauton. Dyn. Syst. (2019) 6: 18-34.
    [3] M. Calmon, Considerations of coronavirus (COVID-19) impact and the management of the dead in Brazil, Forensic Science Internat: Reports, 2020. In press. doi: 10.1016/j.fsir.2020.100110
    [4] Center for Disease Control and Prevention (CDC), Coronavirus Disease (COVID-19), 2020. Available from: https://www.cdc.gov/coronavirus/2019-ncov/index.html.
    [5] Dynamics of a networked connectivity model of epidemics. Discrete Contin. Dyn. Syst. Ser. B (2016) 21: 3379-3390.
    [6] R. Cui, Asymptotic profiles of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with saturated incidence rate, Discrete Contin. Dyn. Syst. Ser. B, (2020). doi: 10.3934/dcdsb.2020217
    [7] On the definition and the computation of the basic reproduction number ratio $R_0$ in models for infectious diseases in heterogeneous populations. J. Math. Biol. (1990) 28: 365-382.
    [8] Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures. Proceed. Nat. Acad. of Scienc. (2020) 117: 10484-10491.
    [9] Generalized reproduction numbers and the prediction of patterns in waterborne disease. Proceed. Nat. Acad. of Scienc. (2012) 109: 19703-19708.
    [10] Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy. Nature Medicine (2020) 26: 855-860.
    [11] J. K. Hale, Ordinary Differential Equations, Second edition. Robert E. Krieger Publishing Co., Inc., Huntington, N.Y., 1980.
    [12] On the dynamics of a class of multi-group models for vector-borne diseases. J. Math. Anal. Appl. (2016) 441: 723-743.
    [13] B. Ivorra, M. R. Ferrández, M. Vela-Pérez and A. M. Ramos, Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China, Commun. Nonlinear Sci. Numer. Simul., 88 (2020), 105303, 21 pp. doi: 10.1016/j.cnsns.2020.105303
    [14] Global dynamics of a SEIR model with varying total population size. Math. Biosci. (1999) 160: 191-213.
    [15] Global stability of an epidemic model in a patchy environment. Can. Appl. Math. Q. (2009) 17: 175-187.
    [16] Global stability problems for coupled systems of differential equation on networks. J. Differential Equations (2010) 248: 1-20.
    [17] S. Li and S. Guo, Permanence and extinction of a stochastic SIS epidemic model with three independent Brownian motions, Discrete Contin. Dyn. Syst. Ser. B, (2020). doi: 10.3934/dcdsb.2020201
    [18] M. Mandal, S. Jana, S. K. Nandi, A. Khatua, S. Adak and T. K. Kar, A model based study on the dynamics of COVID-19: Prediction and control, Chaos Solitons Fractals, 136 (2020), 109889, 12 pp. doi: 10.1016/j.chaos.2020.109889
    [19] Asymptotic behaviour of the solutions to a virus dynamics model with diffusion. Discrete Contin. Dyn. Syst. Ser. B (2018) 23: 525-541.
    [20] Global stability of infectious disease models using Lyapunov functions. SIAM J. Appl. Math. (2013) 73: 1513-1532.
    [21] Modelling and control of cholera on networks with a common water source. J. Biol. Dyn. (2015) 9: 90-103.
    [22] (1995) The Theory of the Chemostat: Dynamics of Microbial Competition.Cambridge University Press.
    [23] J. P. Tian, S. Liao and J. Wang, Analyzing the infection dynamics and control strategies of cholera, Discrete Contin. Dyn. Syst., (2013), 747–757. doi: 10.3934/proc.2013.2013.747
    [24] Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. (2002) 180: 29-48.
    [25] Further notes on the basic reproduction number. Lecture Notes in Mathematics (2008) 1945: 159-178.
    [26] A mathematical model for the novel coronavirus epidemic in Wuhan, China. Math. Biosci. Eng. (2020) 17: 2708-2724.
    [27] Identifying airborne transmission as the dominant route for the spread of COVID-19. Proc. of National Acad. of Sciences (2020) 117: 14857-14863.
  • Reader Comments
  • © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(1200) PDF downloads(333) Cited by(1)

Article outline

Figures and Tables

Figures(2)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog