Phase portraits of an SIR epidemic model

Abstract

In this paper, we classify the phase portraits of an SIR epidemic dynamics model. Depending on the values of the parameters, this model can exhibit seven different phase portraits. In particular, from a biological point of view we prove that the unique attractors of this model are one or two equilibrium points depending on the values of the parameters and from the phase portraits follow the basins of attraction of these equilibria.

Keywords:

• Polynomial differential systems
• equilibrium points
• phase portraits
• Hopf bifurcation
• limit cycles
• SIR epidemic dynamics model

2010 MSCs:

• 34C05
• 34A34

Disclosure statement

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

Additional information

Funding

The first author is partially supported by the Ministerio de Ciencia, Innovación y Universidades, Agencia Estatal de Investigación grants PID2019-104658GB-I00 (FEDER), the Agència de Gestió d'Ajuts Universitaris i de Recerca grant 2017SGR1617, and the H2020 European Research Council grant MSCA-RISE-2017-777911. The second author is partially supported by the Algerian Ministry of Higher Education and Scientific Research.