Journal of Theoretical and Computational Studies
SIMPLE DYNAMICS IN A VECTOR-BORNE DISEASE MODEL
A. K. Supriatna and E. Soewono
Department of Mathematics, Universitas Padjadjaran, Jl Raya Bandung-Sumedang Km 21
Industrial and Financial Mathematics Group, Institut Teknologi Bandung, Jl Ganesha 10 Bandung, Indonesia 40132
In this paper we review a simple model of an infectious disease transmission. In general the rate of incidences can be model by mass action principle, so that its functional is bilinear. In some circumstances, disease transmission might be more complicated involving different species, for example in the case of the transmission of the disease required a vector (vector-borne disease), such as in malaria and dengue infection cases, the rate of incidences takes a nonlinear functional form. In this paper we show the conditions needed for the endemic equilibrium in the model to exist and to be stable. The analysis reveals that there is a simple transcritical bifurcation in the dynamics of the model, despite the complex interaction of the disease transmission.