A prototype vaccination model for endemic Covid-19 under waning immunity and imperfect vaccine take-up

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.

The far-right and anti-vaccine attitudes: lessons from Spain’s mass COVID-19 vaccine roll-out

“…For instance, the second most important country of origin of the immigrant population in Spain is Romania, a country whose main religion is not catholic (Orthodox Christianity) and simultaneously have very low levels of vaccine take-up. 27 However, we cannot further explore this hypothesis in our data since we do not have information on the country of origin nor on the specific religion for the non-catholic respondents.…”

“…Most current Vox voters used to vote for PP. 27 In some ways, Vox can be considered a far-right splinter party from the conservative PP since it was founded by individuals who had previously been PP members. On a scale 1 (left) to 10 (right) 10, 21% VOX voters located themselves at 10, while only 7% of PP voters did so (CIS Barometer December 2020).…”