Evolution algebras and dynamical systems of a worm propagation model

ABSTRACT

We consider an evolution algebra identifying the coefficients of SIS–SIR worm propagation models as the structure constants of the algebra. The basic properties of this algebra are studied. We prove that it is a commutative (and hence flexible), not associative and baric algebra. We describe the full set of idempotent elements and the full set of absolute nilpotent elements. We find all the fixed points of the dynamical systems. We also study several properties of the algebra connecting them to dynamical systems.

Keywords:

• Evolution algebra
• evolution operator
• worm propagation

2010 Mathematics Subject Classifications:

• Primary: 37N25
• Secondary: 92D10

Acknowledgements

We thank the referees for the helpful comments and suggestions that contributed to the improvement of this paper. The authors thanks Prof. F. T. Adilova and Prof. U. A. Rozikov for useful discussions. This work was partially supported by a grant from the IMU-CDC. The first author (U.J.) thanks the University of Santiago de Compostela (USC), Spain, for the kind hospitality and for providing all facilities. The authors were partially supported by Agencia Estatal de Investigación (Spain), grant MTM2016-79661-P and by Xunta de Galicia, grant ED431C 2019/10 (European FEDER support included, UE).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by a grant from the International Mathematical Union (IMU)- CDC. The authors were partially supported by Agencia Estatal de Investigación (Spain), grant MTM2016-79661-P and by Xunta de Galicia, grant ED431C 2019/10 (European FEDER support included, UE).