Research and Innovation Articles
Published 2018-07-18
Keywords
- Leray-Schauder degree,
- SIQS models,
- periodic orbits,
- reproductive number
How to Cite
Osuna Castro, C. O., Guerrero Flores, S., & Villavicencio Pulido, G. (2018). Existence of periodic solutions for seasonal epidemic models with quarantine. Revista Integración, Temas De matemáticas, 36(1), 37–47. https://doi.org/10.18273/revint.v36n1-2018003
Abstract
In this work, we establish the existence of periodic orbits for a seasonal saturated epidemiological model of a population consisting of susceptible, infectious and quarantined individuals (an SIQS model). To do so,
we use Leray-Schauder degree theory. We also provide numerical examples of these solutions.
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References
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rate”, Math. Biosci. 208 (2007), 419–429.
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.