. 2021 Jul 14;12:4313. doi: 10.1038/s41467-021-24566-y

Table 1.

Possible infection histories in terms of the lineage of first infection and lineages encountered since.

1st Infection	Lineages encountered later	Symbol	Susceptibility to B/Vic	Susceptibility to B/Yam
None	None	P₀	1	1
V	None	P_V,0	(1 − χ_VV)(1 − R_V)	(1 − χ_YV)
V	Y	P_V,Y	(1 − χ_VV)(1 − R_V)	(1 − χ_YY)
Y	None	P_Y,0	1 − χ_VY	(1 − χ_YY)(1 − R_Y)
Y	V	P_Y,V	1 − χ_VV	(1 − χ_YY)(1 − R_Y)
A	None	P_A,0,0	1 − χ_VA	1 − χ_YA
A	V	P_A,V,0	1 − χ_VV	$1 - \max (χ_{Y A}, χ_{Y V})$
A	Y	P_A,Y,0	$1 - \max (χ_{V A}, χ_{V Y})$	1 − χ_YY
A	V and Y (any order)	P_A,{VY}	1 − χ_VV	1 − χ_YY

Susceptibility to each lineage depends on within-lineage (χ_VV, χ_YY) and cross-lineage (χ_VY, χ_YV, χ_VA, χ_YA) cross-protection from prior infections regardless of their order and on additional protection against the lineage first encountered (R_V and R_Y). Only the strongest cross-lineage protection term is assumed to affect susceptibility. Within-lineage protection is constrained to be stronger than cross-lineage protection against the same lineage.

A, strains circulating before 1988, V B/Victoria, Y B/Yamagata.