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Article

Keywords:
Quadratic stochastic operator; fixed point; discrete-time; SISI model; epidemic
Summary:
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.
References:
[1] Devaney, R.L.: An Introduction to Chaotic Dynamical System. 2003, Westview Press, MR 1979140
[2] Ganikhodzhaev, R.N., Mukhamedov, F.M., Rozikov, U.A.: Quadratic stochastic operators and processes: results and open problems. Inf. Dim. Anal. Quant. Prob. Rel. Fields, 14, 2, 2011, 279-335, DOI 10.1142/S0219025711004365 | MR 2813492
[3] Greenhalgh, D., Diekmann, O., Jong, M. de: Subcritical endemic steady states in mathematical models for animal infections with incomplete immunity. Math.Biosc., 165, 1, 2000, 25 pp, DOI 10.1016/S0025-5564(00)00012-2
[4] Lyubich, Y.I.: Mathematical structures in population genetics. 1992, Springer-Verlag, Berlin,
[5] Müller, J., Kuttler, Ch.: Methods and models in mathematical biology. 2015, Springer, MR 3380784
[6] Rozikov, U.A., Shoyimardonov, S.K.: Leslie's prey-predator model in discrete time. Inter. Jour. Biomath, 13, 6, 2020, 2050053, MR 4146966
[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, MR 3923067
[8] Rozikov, U.A., Shoyimardonov, S.K., R.Varro: Planktons discrete-time dynamical systems. Nonlinear Studies, 28, 2, 2021, MR 4318135
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