“…We also demonstrated the impact of the new strain's introduction on disease dynamics and individual vaccination behavior, as well as the total vaccine coverage considering the time delay. The concept of social efficiency deficit (SED), which is the difference between Nash equilibrium (NE) and the social optimum, is incorporated into our model (SO), to generate a social dilemma, taking into account the vaccine's efficacy and cost ( Ariful Kabir & Tanimoto, 2019 ; Kabir et al., 2021 ; Tori & Tanimoto, 2022 ; Tanimoto, 2019 ; Tanimoto, 2015 ; Tanimoto, 2021 ; Arefin, Kabir, Jusup, Ito, & Tanimoto, 2020 ; Huang, Wang, & Xia, 2020 ; wang & Xia, 2020 ; Khan, Arefin, & Tanimoto, 2022a ; Khan, Arefin, & Tanimoto, 2022b ).…”