Variant emergence continues to pose a threat to public health, despite the widespread use of vaccination. To quantify how vaccine strain compositions shape evolutionary and epidemiological outcomes, we extend a previous genotype-structured transmission model with vaccination and study the impact of different vaccination formulations on variant emergence. It consists of a set of partial differential equations coupled with an integro-differential one. We begin by showing that the model reproduces variant emergence followed by a period of co-circulation in the absence of vaccination. Then, we introduce vaccination and show important trade-offs shaped by the breadth and cross-protection of vaccine-induced immunity. In our simulations, narrow-spectrum vaccines substantially reduce the immediate infection burden but inadvertently promote the emergence of non-targeted variants. After that, we study the effects of more complex shapes such as triangular and M-shaped configurations. We show that M-triangular distributions outperform triangular ones by limiting secondary variant expansion for vaccines with narrow cross-protection. In contrast, triangular compositions are more protective when considering broader cross-protection. We also show that targeting the genetic area between co-circulating variants is more beneficial than focusing on specific variants when using vaccines with a broad cross-protection. Together, these results highlight how vaccine breadth and antigenic targeting influence both epidemic size and the trajectory of variant emergence, offering quantitative guidance for monovalent and multivalent vaccine design.
Bouchnita et al. (2026) studied this question.