Existencia de soluciones periódicas para modelos epidemiológicos estacionales con cuarentena

  • Carlos Osvaldo Osuna Castro Universidad Michoacana de San Nicolás de Hidalgo
  • Shaday Guerrero Flores
  • Geiser Villavicencio Pulido

Resumen

En este trabajo establecemos la existencia de órbitas periódicas para un modelo epidemiológico estacional con cuarentena y tasa de incidencia saturada. Para realizar lo anterior, usamos un esquema variacional basado en
la teoría de grado de Leray-Schauder. También presentamos algunos ejemplos numéricos para ilustrar nuestros resultados analíticos.

Palabras clave: Grado de Leray-Schauder, modelos SIQS, órbitas periódicas, número reproductivo básico

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Citas

[1] Adnani J., Hattaf K. and Yousfi N., “Stability Analysis of a Stochastic SIR Epidemic Model
with Specific Nonlinear Incidence Rate”, Int. J. Stoch. Anal. (2013), Art. ID 431257, 4 pp.

[2] Capasso V. and Serio G., “A generalisation of the Kermack-McKendrick deterministic epi-
demic model”, Math. Biosci. 42 (1978), 43–61.

[3] Feng Z. and Thieme H. R., “Endemic models with arbitrarily distributed periods of infection
II: Fast disease dynamics and permanent recovery”, SIAM J. Appl. Math 61 (2000), No. 3, 983–1012.

[4] Feng Z. and Thieme H. R., “Recurrent outbreaks of childhood diseases revisited: the impact
of isolation”, Math. Biosci. 128 (1995), 93–130.

[5] Hethcote H., Zhien M. and Shengbing L., “Effects of quarantine in six endemic models for
infectious diseases”, Math. Biosci. 180 (2002), 141–160.

[6] Kar T. and Batabyal A., “Modeling and Analysis of an Epidemic Model with Non-
monotonic Incidence Rate under Treatment”, J. Math. Res. 2 (2010), No. 1, 103–115.

[7] Katriel G., “Existence of periodic solutions for periodically forced SIR model”, J. Math.
Sci. (N.Y.) 201 (2014), No. 3, 335–342.

[8] Liu W., Levin S. and Iwasa Y., “ Influence of nonlinear incidence rates upon the behaviour
of SIRS epidemiological models”, J. Math. Biol. 23 (1986), 187–204.

[9] Liu, W., Hethcote H. and Levin S., “Dynamical behaviour of epidemiological models with
nonlinear incidence rates”, J. Math. Biol. 25 (1987), 359–380.

[10] Shang L., Meng F. and Xinmiao R., “Global threshold dynamics of SIQS epidemic model
in time fluctuating environment”, Int. J. Biomath. 10 (2017), No. 4, 1750060.

[11] Van den Driessche P. andWatmough J., “Reproduction numbers and sub-threshold endemic
equilibria for compartmental models of disease transmission”, Math. Biosci. 180 (2002), 29–48.

[12] Xiao D. and Ruan S., “Global analysis of an epidemic model with non monotone incidence
rate”, Math. Biosci. 208 (2007), 419–429.
Publicado
2018-07-18