Fig. 2

Illustrative example of the time evolution of the epidemic spreading process. Evolution of the epidemic in terms of the total infection counts for strain 1 (\(I_1(t)+{\tilde{I}}_1(t)\)) and 2 (\(I_2(t)+{\tilde{I}}_2(t)\)), averaged over 1000 independent Monte Carlo simulations for a different values of \(\lambda _1\) with \(\lambda _2 = 2\lambda _1\) being twice infectious than the first variant. Here \(\lambda _1\) is varied from 0 to 0.2, thus representing cases where both variants are in the non-epidemic regime and transition to an epidemics as \(\lambda _1\) increases. b Re-infection parameter of the second variant \(\rho _{22}\) with \(\rho _{21}=\rho _{22}\) and \(\lambda _1=\lambda _2=0.2\). c \(\lambda _1\) varies between 0 and 0.5, while \(\lambda _2 = 0.5-\lambda _1\). d Number of re-infected individuals varying the cross-strain re-infection probability \(\rho _{12}\) with \(\lambda _1=\lambda _2=0.2\)