×
Shoyimardonov, Sobirjon K.

A non-linear discrete-time dynamical system related to epidemic SISI model. (English) Zbl 1492.37089

Commun. Math. 29, No. 3, 505-525 (2021).
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.

MSC:

37N25 Dynamical systems in biology
39A60 Applications of difference equations
92D25 Population dynamics (general)
92D30 Epidemiology

Keywords:

quadratic stochastic operator; fixed point; discrete-time; SISI model; epidemic
PDF BibTeX XML Cite
\textit{S. K. Shoyimardonov}, Commun. Math. 29, No. 3, 505--525 (2021; Zbl 1492.37089)
Full Text: DOI arXiv

References:

[1] R.L. Devaney: An Introduction to Chaotic Dynamical System. Westview Press (2003).
[2] R.N. Ganikhodzhaev, F.M. Mukhamedov, U.A. Rozikov: Quadratic stochastic operators and processes: results and open problems. Inf. Dim. Anal. Quant. Prob. Rel. Fields 14 (2) (2011) 279-335. · Zbl 1242.60067
[3] D. Greenhalgh, O. Diekmann, M. de Jong: Subcritical endemic steady states in mathematical models for animal infections with incomplete immunity. Math.Biosc. 165 (1) (2000) 25 pp. · Zbl 0983.92007
[4] Y.I. Lyubich: Mathematical structures in population genetics. Springer-Verlag, Berlin (1992). · Zbl 0747.92019
[5] J. Müller, Ch. Kuttler: Methods and models in mathematical biology. Springer (2015).
[6] U.A. Rozikov, S.K. Shoyimardonov: Leslie’s prey-predator model in discrete time. Inter. Jour. Biomath 13 (6) (2020) 2050053. · Zbl 1464.92233
[7] U.A. Rozikov, S.K. Shoyimardonov: Ocean ecosystem discrete time dynamics generated by l-Volterra operators. Inter. Jour. Biomath. 12 (2) (2019) 24 pp. · Zbl 1490.92131
[8] U.A. Rozikov, S.K. Shoyimardonov, R.Varro: Planktons discrete-time dynamical systems. Nonlinear Studies 28 (2) (2021).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.