Influences of nonlinear incidence in an eco-epidemiological model of the Salton Sea

Abstract

In this paper we modify an eco-epdemiological model proposed by Chattopadhyay and Bairagi ( Ecological Modelling, 136, pp.103-112, 2001) by taking into account non-linear incidence rate instead of bilinear incidenc rate as considered by Chattopadhyay and Bairagi. We observe that limit cycle oscillations around the positive interior equilibrium may be controlled by suitable choice of non-linear incidence rates. The value for which the disease will be spread and also the system around positive equilibrium enters into Hopf-bifurcation are obtained. It is also observed that the bifurcating branches are super-critical. To subtantiate the analytical finding numerical simulations are also performed for a hypothetical set of parameter values.