Rich dynamics of an SIR epidemic model. (English) Zbl 1217.93072

Pathak, S.; Maiti, A.; Samanta, G. P.

Nonlinear Anal., Model. Control 15, No. 1, 71-81 (2010).

Summary: This paper aims to study an SIR epidemic model with an asymptotically homogeneous transmission function. The stability of the disease-free and the endemic equilibrium is addressed. Numerical simulations are carried out. Implications of our analytical and numerical findings are discussed critically.

MSC:

93C15	Control/observation systems governed by ordinary differential equations
93A30	Mathematical modelling of systems (MSC2010)
92D30	Epidemiology

Keywords:

SIR model; transmission function; basic reproduction number; disease-free equilibrium; endemic equilibrium; stability