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Modified SEIR epidemic model including asymptomatic and hospitalized cases with correct demographic evolution

Author

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  • Castañeda, Antonio Rafael Selva
  • Ramirez-Torres, Erick Eduardo
  • Valdés-García, Luis Eugenio
  • Morandeira-Padrón, Hilda María
  • Yanez, Diana Sedal
  • Montijano, Juan I.
  • Cabrales, Luis Enrique Bergues

Abstract

The aim of this study is to propose a modified Susceptible-Exposed-Infectious-Removed (SEIR) model that describes the time behaviour of symptomatic, asymptomatic and hospitalized patients in an epidemic, taking into account the effect of the demographic evolution. Unlike most of the recent studies where a constant ratio of new individuals is considered, we consider a more correct assumption that the growth ratio is proportional to the total population, following a Logistic law, as is usual in population growth studies for humans and animals. An exhaustive theoretical study is carried out and the basic reproduction number R0 is computed from the model equations. It is proved that if R0<1 then the disease-free manifold is globally asymptotically stable, that is, the epidemics remits. Global and local stability of the equilibrium points is also studied. Numerical simulations are used to show the agreement between numerical results and theoretical properties. The model is fitted to experimental data corresponding to the pandemic evolution of COVID-19 in the Republic of Cuba, showing a proper behaviour of infected cases which let us think that can provide a correct estimation of asymptomatic cases. In conclusion, the model seems to be an adequate tool for the study and control of infectious diseases.

Suggested Citation

  • Castañeda, Antonio Rafael Selva & Ramirez-Torres, Erick Eduardo & Valdés-García, Luis Eugenio & Morandeira-Padrón, Hilda María & Yanez, Diana Sedal & Montijano, Juan I. & Cabrales, Luis Enrique Bergue, 2023. "Modified SEIR epidemic model including asymptomatic and hospitalized cases with correct demographic evolution," Applied Mathematics and Computation, Elsevier, vol. 456(C).
    • Handle: RePEc:eee:apmaco:v:456:y:2023:i:c:s0096300323002916
    DOI: 10.1016/j.amc.2023.128122
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    References listed on IDEAS

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    1. Warwick McKibbin & Roshen Fernando, 2021. "The Global Macroeconomic Impacts of COVID-19: Seven Scenarios," Asian Economic Papers, MIT Press, vol. 20(2), pages 1-30, Summer.
    2. Ndaïrou, Faïçal & Area, Iván & Nieto, Juan J. & Torres, Delfim F.M., 2020. "Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    3. L. Ingber, 1993. "Simulated annealing: Practice versus theory," Lester Ingber Papers 93sa, Lester Ingber.
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