Pathogen evolution under strategy changes in vaccination campaigns: A game-theoretic framework

In existing models of pathogen evolution under voluntary vaccination, vaccination behaviour is typically assumed to be static, overlooking the conflicts between individual and collective interests. To address this, we develop a multi-scale model within a game-theoretic framework that couples the dynamic processes of disease transmission, vaccination decision-making, and pathogen evolution. By reformulating vaccine uptake as a time-dependent strategic choice and incorporating a heterogeneous update mechanism, we establish the evolutionary model of vaccination strategies. Numerical results show that heterogeneous updating rules will capture autonomous population decision-making. The co-evolutionary dynamics are highly sensitive to the evolutionary adaptation rates and exhibit an asymmetric relationship between population and evolutionary dynamics. At the early stage of a vaccination scenario, we observe that imitation behaviour dominates due to limited information. Enhancing vaccine uptake is effective in limiting the emergence of detrimental variants, and the long-term evolutionary outcome may favour the emergence of specialist variants. This framework provides quantitative methods and key methodological advancements for multi-scale mathematical modelling in the context of pathogen evolution.