SIS criss-cross models of tuberculosis in heterogenous populations

We propose a model of tuberculosis (TB) transmission in a heterogeneous population consisting of two different subpopulations, like homeless and non-homeless people. We use the criss-cross model to describe the illness dynamics. This criss-cross model is based on the simple SIS model with constant inflow into both subpopulations and bilinear transmission function. We find conditions for the existence and stability of stationary states (disease free and endemic) and fit the model to epidemic data from Warmian-Masurian Province of Poland. Basic reproduction number R_0 is considered as a threshold parameter for the general model. Applying local center manifold theory we show that when R_0=1 a supercritical bifurcation occurs, and  with R_0  increasing above this threshold the disease-free stationary state loses stability and locally asymptotically stable endemic stationary state appears. The talk is a summary of our results so far.