Figure 7

Case with immunity. Threshold condition R _* = 1  as a function of the across-groups mixing ɛ and of the children fraction α for Europe (panel A) and Mexico (panel B): comparison of the no-immunity case with the case of pre-existing immunity and of travel reduction, modeled by setting w ₀ = 0.5, consistently with the empirically observed drop to/from Mexico during the early stage of the 2009 H1N1 pandemic [37]. Here we consider: R ₀ = 1.2 in Europe and R ₀ = 1.4 in Mexico, i.e. the lower bound of the reproductive number estimated for the country from the initial outbreak data [2]. All travelers are adults (r = 0). The three lines, continuous red, dashed red and continuous blue, correspond to pre-existing immunity, no-immunity and travel reduction, respectively. Global epidemic invasion region is above each critical curve. The patterned gray area refers to the region of parameter values that do not satisfy the consistency relation ɛ < min {α, η(1 − α)}.