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. 2022 Jan 31;6(2):207–216. doi: 10.1038/s41562-022-01289-8

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© The Author(s), under exclusive licence to Springer Nature Limited 2022

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Fig. 1 — a, The multistrain model. A linear strain space and local movement by a one-direction stepwise mutation are considered. M denotes the number of possible strains; μ_m denotes the mutation probability per infection. b, The SVEIRD model. Susceptible individuals (S) become vaccinated (V) at a vaccination rate determined by the global vaccine allocation strategy. Vaccinated individuals become susceptible after losing vaccinal immunity. Exposed individuals ( $E_{m}^{S}$ and $E_{m}^{V}$ ) are those infected by strain m and are divided into two classes, either with or without vaccinal immunity. Exposed individuals first become infectious ( $I_{m}^{S}$ and $I_{m}^{V}$ ) and then transition to either the recovered state (R) or the deceased state (D). For simplicity, we assume that co-infection is not possible and recovered individuals are immune to the disease. c, The SVEIRD-based metapopulation model. Due to travel restrictions, infectious and deceased individuals do not move between countries.