A prototype vaccination model for endemic Covid-19 under waning immunity and imperfect vaccine take-up
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Abstract
In this paper, for an infectious disease such as Covid-19, we present a SIR model which examines the impact of waning immunity, vaccination rates, vaccine efficacy, and the proportion of the susceptible population who aspire to be vaccinated. Under an assumed constant control reproduction number, we provide simple conditions for the disease to be eliminated, and conversely for it to exhibit the more likely endemic behaviour. With regard to Covid-19, it is shown that if the control reproduction number is set to the basic reproduction number (say 6) of the dominant delta (B1.617.2) variant, vaccination alone, even under the most optimistic of assumptions about vaccine efficacy and high vaccine coverage, is very unlikely to lead to elimination of the disease. The model is not intended to be predictive but more an aid to understanding the relative importance of various biological and control parameters. For example, from a long-term perspective, it may be found that in the UK, through changes in societal behaviour (such as mask use, ventilation, and level of homeworking), without formal government interventions such as on-off lockdowns, the control reproduction number can still be maintained at a level significantly below the basic reproduction number. Even so, our simulations show that endemic behaviour ensues. The model obtains equilibrium values of the state variables such as the infection prevalence and mortality rate under various scenarios.
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SciScore for 10.1101/2021.11.06.21266002: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
No key resources detected.
Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:A limitation of our model is that it is age-homogeneous. For example, we assume that θ, the target vaccination coverage, is the same for all ages, whereas in fact it has been larger for elderly and vulnerable people who have higher infection fatality rates. This would bias death rates to high values. In practice, one might eventually …
SciScore for 10.1101/2021.11.06.21266002: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
No key resources detected.
Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:A limitation of our model is that it is age-homogeneous. For example, we assume that θ, the target vaccination coverage, is the same for all ages, whereas in fact it has been larger for elderly and vulnerable people who have higher infection fatality rates. This would bias death rates to high values. In practice, one might eventually hope for a uniformly high rate of θ throughout the age and vulnerability spectrum. Meanwhile, waning rates (ω) and vaccination rate (γ) in the real world are likely to be age-dependent. Additionally, we have assumed that transmissibility is the same for vaccinated and unvaccinated infectives. To overcome such limitations, one might develop an agent-based simulation model which could also include a more nuanced treatment of continuous waning of immunity, rather than the implicit binary waning of our compartmental model. One might expect such an approach to yield different results to ours in the short-term, but it remains to be seen whether the same is true in estimating equilibrium behaviour.
Results from TrialIdentifier: No clinical trial numbers were referenced.
Results from Barzooka: We did not find any issues relating to the usage of bar graphs.
Results from JetFighter: We did not find any issues relating to colormaps.
Results from rtransparent:- Thank you for including a conflict of interest statement. Authors are encouraged to include this statement when submitting to a journal.
- Thank you for including a funding statement. Authors are encouraged to include this statement when submitting to a journal.
- No protocol registration statement was detected.
Results from scite Reference Check: We found no unreliable references.
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