Fig 1.
Final size of an epidemic spreading with basic reproduction number of R0 = 6 after 55% of the population of the USA is vaccinated with no age prioritization. Removed population refers to those recovered or dead. The computation considers a vaccination campaign in which A: Vaccines are allocated to all ages. B: Vaccine allocation is limited to ages 20 and above. C: Vaccine allocation is limited to ages 20 and above, 20% of the population has preexisting immunity recovered from COVID-19, and the prevalence of active cases is 0.5% of the population. The text in all graphs corresponds to the percent of non-vaccinated removed individuals in each age group.
Fig 2.
Vaccination coverage required for herd immunity.
A: Vaccine coverage Vthreshold required to achieve herd immunity threshold as a function of the reproduction number R0 for the USA demography and contact structure where and
correspond to beproduction numbers at which herd immunity cannot be achieved without vaccination of age groups 0 − 19 and 0 − 9, respectively. B: Vaccine allocations at which herd immunity is achieved at minimal vaccine coverage and when all the population is eligible for vaccination. C: Same as B, but when ages ten and older are eligible for vaccination.
Fig 3.
Critical reproduction numbers.
Reproduction numbers and
at which herd immunity cannot be achieved without vaccination of age groups 0 − 19 and 0 − 9, respectively. Computed using A: age-dependent susceptibility profile of SARS-CoV-19: Ages 0–19 are roughly half as susceptible as adults [15]. B: Same susceptibility profile as in A, but with increased susceptibility in the age group 10–19: Ages 10–19 are as susceptible as adults. C: Same susceptibility profile as in A, where ages 10–19 are as susceptible as adults.
Fig 4.
Impact of change in reproduction number.
Overall infections of non-vaccinated individuals (top graphs) and overall mortality (centered graphs) as function of the basic reproduction number R0 after completion of a vaccination campaign for allocations minimizing infections (left panels) and allocations minimizing mortality (right panels). The outcomes are presented for the following cases: All ages are eligible for vaccination (), only ages 10 and older are eligible (
), and only ages 20 and older are eligible (
). Bottom panels present the corresponding allocations.
Fig 5.
R0 = 4. Top graph presented outcomes of random allocations when all ages are eligible for vaccination (square blue markers) and only ages 20 and older are eligible (round yellow markers). Super-imposed are the Pareto fronts in the case ages 20 and older are eligible for vaccination (black solid), ages 10 and older are eligible (yellow dash-dotted) and when all ages are eligible (purple dashed). The latter two curves are indistinguishable. Bottom graphs present vaccine allocation along the Pareto fronts in the case of ages 20 and older are eligible for vaccination, and when all ages or ages 10 and older are eligible for vaccination.
Fig 6.
Same as Fig 5 with R0 = 6.
Fig 7.
Same as Fig 5 with R0 = 8.
Fig 8.
Effect of change in childrens’ susceptibility on vaccination coverage required for herd immunity.
A,C: Vaccine coverage Vthreshold required to achieve herd immunity threshold as a function of the reproduction number R0 for the USA demography and contact structure. The gray curves correspond to the case in which the relative susceptibility of age group 0–19 is half that of adults. B,D: Vaccine allocations at which herd immunity is achieved at minimal vaccine coverage and when there is no age restriction on vaccine allocation.
Fig 9.
Impact of change in reproduction number when adolescents (age group 10–19) are equally susceptible as adults.
Same as Fig 5 except the susceptibility of age group 10–19 is increased by factor of 2 to that of older age groups. Susceptibility of age group 0–9 is not modified.
Fig 10.
Impact of change in reproduction number when children (age group 0–19) are equally susceptible as adults.
Same as Fig 5 except the susceptibility of age group 0–19 is increases by factor of 2 to that of older age groups.
Fig 11.
Pareto front—Vaccination of an additional 0.3 million people in Israel.
Top graph presents outcomes of random allocations when all ages are eligible for vaccination (square blue markers). Black solid curve is the Pareto front when all ages are eligible for vaccination. Bottom Graphs: Vaccine allocations along the Pareto front.