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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. [ABSTRACT FROM AUTHOR]

In this paper we study the existence and non-existence of limit cycles for the class of polynomial differential systems of the form x ̇ = λ x + P n (x , y) , y ̇ = μ y + Q n (x , y) , where P n and Q n are homogeneous polynomials of degree n. [ABSTRACT FROM AUTHOR]