Fig 1.
(A) Schematic of individual immunity progression after infection or vaccination. (B) Model flow diagram, extended from Fig 3A of [6]. Each colour denotes an infection or immunity class. (C) Schematic of the range of population-level outcomes based on severity-blocking immunity.
Fig 2.
Dynamics of different durations of natural and vaccinal severity protection, with variable vaccination rates, for different strengths of immunity.
(A), (B), (C), and (D) have vaccination rates ν = 0.0025 per week, ν = 0.01 per week, ν = 0.02 per week, and ν = 0.04 per week, respectively. In all panels, we assume that years and that
years. For each column, we assume that the duration of severity-blocking immunity imparted from vaccination or infection is the same and is equal to the columnar label ℓc, i.e.
and
. Thus,
years and
years. In each panel, the top, middle, and bottom rows depict the fraction of individuals in Iw, the fraction of infections that are in Iw (i.e.
, where
), and the relative change in
for each ε compared to ε = 1, i.e.
, respectively (for weeks when f1(t) > 0). Other parameters are
week−1 and μ = 0.02 years−1, as in previous work [6, 20–22]. The initial conditions here and throughout are a fraction 10−9 of individuals with primary infection (IP) and the remainder fully susceptible (SP), which is as in previous work with the simpler model [6].
Fig 3.
Impacts of longer transmission-blocking vaccines on severity dynamics.
In (A) and (B), the vaccination rates are 0.01 per week and 0.02 per week, respectively. In both panels, the top row denotes the total fraction Itotal = IP + IS + Iw of individuals that are infected. The second to fourth rows are as in the rows of each panel of Fig 2 (see caption of Fig 2 for definitions). Across both panels, we assume that the duration of vaccinal transmission-blocking immunity is 90% of the duration of severity-blocking immunity (the columnar label), and that transmission-blocking and severity-blocking immunity after infection last 0.25 years and 1.5 years, respectively (i.e. years and
years).
Fig 4.
Synoptic landscapes of severity-blocking immunity.
The top, middle and bottom rows have vaccination rates 0.0025, 0.01, and 0.02 per week, respectively. The leftmost two columns illustrate scenarios with a less durable vaccine, i.e. years, whereas the rightmost two columns represent scenarios with a more durable vaccine, i.e.
years. The first and third columns assume faster waning of severity-blocking immunity, with the first column having
years and the third column having
years (since the vaccine is more durable) and
years. On the other hand, the second and fourth columns assume slower waning of severity-blocking immunity, with the second column having
years and
years, and the fourth column having
years and
years. In each panel, the left and right axes of the top plot are Iw and the fraction
, respectively, and the area plot colours correspond to the compartments in Fig 1B. In all panels, ε = 0.8. All other parameters are as in Figs 2 and 3, and the colours in the area plots are as in Fig 1B.
Fig 5.
Synoptic landscapes with vaccine heterogeneities, caused by either unequal access or hesitancy.
We assume a 2% weekly vaccination rate (c.f.bottom row, Fig 4), and keep the average vaccination rate constant across each row so that the vaccination rate among vaccine-adopters is ν, where νN1 = 0.02 (N1 = 1 − N2 is the fraction of vaccine adopters, and N2 is the fraction of individuals that are vaccine-hesitant). The columnar scenarios are as in those of Fig 4.
Fig 6.
Cumulative infections with waned severity-blocking immunity after the onset of vaccination up to year 5 as a function of the fraction of individuals that are vaccine-hesitant.
The top left, top right, bottom left, and bottom right panel depict the same scenarios as the first, second, third, and fourth columns of Figs 4 and 5, respectively. As in Fig 5, the average vaccination rate is constant. In each panel, the different lines denote different relative transmissibility values for vaccine hesitants.