TNF and melanoma: For initial conditions such that the number of differentiated melanoma cells, , is large, the number of injected T-cells, , is small, and the numbers of dedifferentiated melanoma cells, , and TNF-α molecules, , are small or equal to zero, the deterministic system is attracted to : the T-cell population, , increases in presence of its target x, TNF-α is secreted, and the population of differentiated melanoma cells, , shrinks due to killing and TNF-α induced switching, whereas the population of dedifferentiated melanoma cells, , grows.