Impact of waning immunity against SARS-CoV-2 severity exacerbated by vaccine hesitancy

Abstract

The SARS-CoV-2 pandemic has generated a considerable number of infections and associated morbidity and mortality across the world. Recovery from these infections, combined with the onset of large-scale vaccination, have led to rapidly-changing population-level immunological landscapes. In turn, these complexities have highlighted a number of important unknowns related to the breadth and strength of immunity following recovery or vaccination. Using simple mathematical models, we investigate the medium-term impacts of waning immunity against severe disease on immuno-epidemiological dynamics. We find that uncertainties in the duration of severity-blocking immunity (imparted by either infection or vaccination) can lead to a large range of medium-term population-level outcomes (i.e. infection characteristics and immune landscapes). Furthermore, we show that epidemiological dynamics are sensitive to the strength and duration of underlying host immune responses; this implies that determining infection levels from hospitalizations requires accurate estimates of these immune parameters. More durable vaccines both reduce these uncertainties and alleviate the burden of SARS-CoV-2 in pessimistic outcomes. However, heterogeneity in vaccine uptake drastically changes immune landscapes toward larger fractions of individuals with waned severity-blocking immunity. In particular, if hesitancy is substantial, more robust vaccines have almost no effects on population-level immuno-epidemiology, even if vaccination rates are compensatorily high among vaccine-adopters. This pessimistic scenario for vaccination heterogeneity arises because those few individuals that are vaccine-adopters are so readily re-vaccinated that the duration of vaccinal immunity has no appreciable consequences on their immune status. Furthermore, we find that this effect is heightened if vaccine-hesitants have increased transmissibility (e.g. due to riskier behavior). Overall, our results illustrate the necessity to characterize both transmission-blocking and severity-blocking immune time scales. Our findings also underline the importance of developing robust next-generation vaccines with equitable mass vaccine deployment.

Fig 1. Model formulation.

(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 $\frac{1}{\delta }=0.25$ years and that $\frac{1}{{\delta }_V}=0.33$ 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 ℓ_c, i.e. $\frac{1}{\delta }+\frac{1}{{\delta }_{\text{sev}}}={\ell }_c$ and $\frac{1}{{\delta }_V}+\frac{1}{{\delta }_{V,\text{sev}}}={\ell }_c$. Thus, $\frac{1}{{\delta }_{\text{sev}}}=({\ell }_c-0.25)$ years and $\frac{1}{{\delta }_{V,\text{sev}}}=({\ell }_c-0.33)$ years. In each panel, the top, middle, and bottom rows depict the fraction of individuals in I_w, the fraction of infections that are in I_w (i.e. $\frac{I_w}{I_{\text{total}}}$, where $I_{\text{total}}=I_P+I_S+I_w$), and the relative change in $f_{\epsilon }\left(t\right)=\frac{I_w\left(t\right)}{I_{\text{total}}\left(t\right)}$ for each ε compared to ε = 1, i.e. $\frac{f_{\epsilon }\left(t\right)-f_1\left(t\right)}{f_1\left(t\right)}$, respectively (for weeks when f₁(t) > 0). Other parameters are $\gamma =\frac{7}{5}$ week⁻¹ and μ = 0.02 years⁻¹, as in previous work [, –22]. The initial conditions here and throughout are a fraction 10⁻⁹ of individuals with primary infection (I_P) and the remainder fully susceptible (S_P), 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 I_total = I_P + I_S + I_w 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. $\frac{1}{\delta }=0.25$ years and $\frac{1}{\delta }+\frac{1}{{\delta }_{\text{sev}}}=1.5$ 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. $\frac{1}{{\delta }_V}=0.33$ years, whereas the rightmost two columns represent scenarios with a more durable vaccine, i.e. $\frac{1}{{\delta }_V}=1.33$ years. The first and third columns assume faster waning of severity-blocking immunity, with the first column having $\frac{1}{{\delta }_V}+\frac{1}{{\delta }_{V,\text{sev}}}=\frac{1}{\delta }+\frac{1}{{\delta }_{\text{sev}}}=0.5$ years and the third column having $\frac{1}{{\delta }_V}+\frac{1}{{\delta }_{V,\text{sev}}}=1.5$ years (since the vaccine is more durable) and $\frac{1}{\delta }+\frac{1}{{\delta }_{\text{sev}}}=0.5$ years. On the other hand, the second and fourth columns assume slower waning of severity-blocking immunity, with the second column having $\frac{1}{\delta }+\frac{1}{{\delta }_{\text{sev}}}=1.5$ years and $\frac{1}{{\delta }_V}+\frac{1}{{\delta }_{V,\text{sev}}}=2$ years, and the fourth column having $\frac{1}{\delta }+\frac{1}{{\delta }_{\text{sev}}}=1.5$ years and $\frac{1}{{\delta }_V}+\frac{1}{{\delta }_{V,\text{sev}}}=3$ years. In each panel, the left and right axes of the top plot are I_w and the fraction $\frac{I_w}{I_P+I_S+I_w}$, 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.