The subpopulation of cancer stem cells in itself becomes highly heterogeneous dictating population level dynamics that vary from longterm dormancy to aggressive progression.

Inheritable traits of cells may be genetically or epigeneti-cally altered, and traits that confer increased fitness to the cell Will be selected for on the population level .

Different cell kinetics result in different overall tumor population dynamics ranging from population level dormancy to aggressive growth and invasion [17].

Indeed, the most common phenotypes in the smallest tumor have increased value of proliferation capacity suggesting competition between CSCs and CCs and long population level dormancy periods as previously described [16,30].

However, the majority of existing studies have focussed on emergence at the population level , and not within a host.

Generally, the focus has been on detection of emerging diseases at the population level , in order to track and control their spread [1, 2].

Recently, Hartf1eld and Alizon [21] tackled a related problem, regarding how epidemiological feedbacks affect disease emergence at the host population level .

In order to find an analytical solution for the within-host emergence of a mutated strain, we follow the approach of Hartfield and Alizon [21] , which investigated the appearance of a new infectious pathogen from a preexisting strain at the population level .