A COVID-19 vaccination model for Aotearoa New Zealand

Abstract

We develop a mathematical model to estimate the effect of New Zealand's vaccine rollout on the potential spread and health impacts of COVID-19. The main purpose of this study is to provide a basis for policy advice on border restrictions and control measures in response to outbreaks that may occur during the vaccination roll-out. The model can be used to estimate the theoretical population immunity threshold, which represents a point in the vaccine rollout at which border restrictions and other controls could be removed and only small, occasional outbreaks would take place. We find that, with a basic reproduction number of 6, approximately representing the Delta variant of SARS-CoV-2, and under baseline vaccine effectiveness assumptions, reaching the population immunity threshold would require close to 100% of the total population to be vaccinated. Since this coverage is not likely to be achievable in practice, relaxing controls completely would risk serious health impacts. However, the higher vaccine coverage is, the more collective protection the population has against adverse health outcomes from COVID-19, and the easier it will become to control outbreaks. There remains considerable uncertainty in model outputs, in part because of the potential for the evolution of new variants. If new variants arise that are more transmissible or vaccine resistant, an increase in vaccine coverage will be needed to provide the same level of protection.

Figure 1

High vaccine coverage greatly reduces potential morbidity and mortality but, for a highly transmissible variant ($R_0=6$), population immunity is unlikely to be achieved via vaccination alone: (a–c) effective reproduction number $R_v$ after vaccination; (d–f) total infections; (g–i) total hospitalisation; (j–l) total fatalities; (m–o) peak hospital occupancy for an unmitigated epidemic over a two-year period as a function of total vaccine courses administered, assuming there is no further vaccination after the outbreak begins. Results are shown for three values of the basic reproduction number: $R_0=3.0$, $R_0=4.5$, $R_0=6.0$. Along the horizontal axis, the roll-out begins in the 65 + year-old age group; once 90% of the 65 + year old group is vaccinated (left-hand vertical line), vaccination of the 15–64-year-old group begins; once 90% of the 15–64-year-old group is vaccinated (right-hand vertical line), vaccination of the under 15-year-old age group begins. Vaccine effectiveness assumptions as shown in Table 1.

Figure 2

Number of vaccinated individuals required to reach the population immunity threshold (i.e. $R_v=1$) for varying values of $R_0$ under the same age-prioritised roll-out sequence and maximum 90% coverage as in this figure. Points above the thin horizontal line require vaccination of under 15-year-olds. Vertical dotted lines indicate the largest value of $R_0$ for which the population immunity threshold can be reached with 90% coverage of over 15-year-olds. Vertical dashed lines indicate the largest value of $R_0$ for which the population immunity threshold can be reached with 90% coverage of the total population.

Figure 3

Detection and control of small outbreaks as vaccine coverage increases: (a–c) number of infections when a community outbreak is first detected; (d–f) probability an outbreak is eliminated before reaching 1000 cases without population-level interventions; (g–i) time from detection to elimination with population-level interventions; (j–l) total number of hospitalisations before outbreak is eliminated. Results are shown for three values of $R_0$ and three values of the probability of testing for symptomatic individuals in the period before the outbreak is detected: $p_{\mathit{detect}}^{\mathit{pre}}=5\%$ (red), $p_{\mathit{detect}}^{\mathit{pre}}=10\%$ (amber) and $p_{\mathit{detect}}^{\mathit{pre}}=15\%$ (green). In (d–f), case isolation and contact tracing are introduced after outbreak detection giving 43% reduction in $R_{\mathit{eff}}$; in (g–l), population-level restrictions are also introduced after outbreak detection giving a total 81% reduction in $R_{\mathit{eff}};$ note that in (i) and (l) when $R_0=6$, an 81% reduction in $R_{\mathit{eff}}$ is insufficient to achieve elimination when vaccine coverage is less than around 20%. The black vertical line represents the point in the vaccine roll-out at which vaccination of under 15-year-olds begins. Points are the median and error bars represent the interquartile range of 10,000 independently initialised realisations of the stochastic model.