Criss-cross modeling of TB

We consider a criss-cross model describing tuberculosis epidemic dynamics. The case in study considers Warmian-Masurian province of Poland and is related to actions of active detecting of tuberculosis in homeless people subpopulation. In the model the population is divided into subpopulations of non-homeless and homeless people. Each of the subpopulation consists of two groups - susceptible and infected people. The analysis of model will be presented. The most important property of the model is related to its Malthusian origin. This means that in general the size of the whole population (meaning homeless and non-homeless together) grows unboundedly or the population goes to extinction. It can also happen that the subpopulation of non-homeless people goes to extinction while the subpopulation of homeless people grows unboundedly, which seems to be absurd. Therefore, we propose a modification of this model.