Fig. 6

Size of the invasion window for different values of \({R}_{RW}\). Value of \({f}_{R}\) for the lower bound of the invasion window, \({R}_{INV}=1\), as a function of the basic reproduction ratio of the wild-type pathogen in resistant hosts (\({R}_{RW}\)) (panel a), the basic reproduction ratio of the escape mutant in non-resistant hosts (\({R}_{NE}\)) (panel b), and the basic reproduction ratio of the escape mutant in resistant hosts (\({R}_{RE}\)). For levels of cross resistance of 0, 0.5 and 1 (dashed, light green lines). In panel (a), for cross resistance of 0, the line lies on the y-axis. The value of \({f}_{R}\) from which the wild-type pathogen dies out (upper bound of the invasion window) is shown by the solid green line. The invasion window for the different cross-resistance levels is indicated by the arrows. For \({R}_{NW}=1.5\), \({R}_{RW}=0.8\) (panels b and c), \({R}_{NE}=1.1\) (panels a and c), and \({R}_{RE}=1.5\) (panels a and b)