A Genotype-Structured PDE Model of Vaccine-Induced Control of Variant Emergence

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.