A non-linear discrete-time dynamical system related to epidemic SISI model

Sobirjon K. Shoyimardonov

Communications in Mathematics (2021)

  • Volume: 29, Issue: 3, page 505-525
  • ISSN: 1804-1388

Abstract

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We consider SISI epidemic model with discrete-time. The crucial point of this model is that an individual can be infected twice. This non-linear evolution operator depends on seven parameters and we assume that the population size under consideration is constant, so death rate is the same with birth rate per unit time. Reducing to quadratic stochastic operator (QSO) we study the dynamical system of the SISI model.

How to cite

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Shoyimardonov, Sobirjon K.. "A non-linear discrete-time dynamical system related to epidemic SISI model." Communications in Mathematics 29.3 (2021): 505-525. <http://eudml.org/doc/298002>.

@article{Shoyimardonov2021,
abstract = {We consider SISI epidemic model with discrete-time. The crucial point of this model is that an individual can be infected twice. This non-linear evolution operator depends on seven parameters and we assume that the population size under consideration is constant, so death rate is the same with birth rate per unit time. Reducing to quadratic stochastic operator (QSO) we study the dynamical system of the SISI model.},
author = {Shoyimardonov, Sobirjon K.},
journal = {Communications in Mathematics},
keywords = {Quadratic stochastic operator; fixed point; discrete-time; SISI model; epidemic},
language = {eng},
number = {3},
pages = {505-525},
publisher = {University of Ostrava},
title = {A non-linear discrete-time dynamical system related to epidemic SISI model},
url = {http://eudml.org/doc/298002},
volume = {29},
year = {2021},
}

TY - JOUR
AU - Shoyimardonov, Sobirjon K.
TI - A non-linear discrete-time dynamical system related to epidemic SISI model
JO - Communications in Mathematics
PY - 2021
PB - University of Ostrava
VL - 29
IS - 3
SP - 505
EP - 525
AB - We consider SISI epidemic model with discrete-time. The crucial point of this model is that an individual can be infected twice. This non-linear evolution operator depends on seven parameters and we assume that the population size under consideration is constant, so death rate is the same with birth rate per unit time. Reducing to quadratic stochastic operator (QSO) we study the dynamical system of the SISI model.
LA - eng
KW - Quadratic stochastic operator; fixed point; discrete-time; SISI model; epidemic
UR - http://eudml.org/doc/298002
ER -

References

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  2. Ganikhodzhaev, R.N., Mukhamedov, F.M., Rozikov, U.A., 10.1142/S0219025711004365, Inf. Dim. Anal. Quant. Prob. Rel. Fields, 14, 2, 2011, 279-335, (2011) MR2813492DOI10.1142/S0219025711004365
  3. Greenhalgh, D., Diekmann, O., Jong, M. de, 10.1016/S0025-5564(00)00012-2, Math.Biosc., 165, 1, 2000, 25 pp, (2000) DOI10.1016/S0025-5564(00)00012-2
  4. Lyubich, Y.I., Mathematical structures in population genetics, 1992, Springer-Verlag, Berlin, (1992) 
  5. Müller, J., Kuttler, Ch., Methods and models in mathematical biology, 2015, Springer, (2015) MR3380784
  6. Rozikov, U.A., Shoyimardonov, S.K., Leslie's prey-predator model in discrete time, Inter. Jour. Biomath, 13, 6, 2020, 2050053, (2020) MR4146966
  7. Rozikov, U.A., Shoyimardonov, S.K., Ocean ecosystem discrete time dynamics generated by l-Volterra operators, Inter. Jour. Biomath., 12, 2, 2019, 24 pp, (2019) MR3923067
  8. Rozikov, U.A., Shoyimardonov, S.K., R.Varro, Planktons discrete-time dynamical systems, Nonlinear Studies, 28, 2, 2021, (2021) MR4318135

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