Sensitivity of endemic behaviour of COVID-19 under a multi-dose vaccination regime, to various biological parameters and control variables.

For an infectious disease such as COVID-19, we present a new four-stage vaccination model (unvaccinated, dose 1 + 2, booster, repeated boosters), which examines the impact of vaccination coverage, vaccination rate, generation interval, control reproduction number, vaccine efficacies and rates of waning immunity upon the dynamics of infection. We derive a single equation that allows computation of equilibrium prevalence and incidence of infection, given knowledge about these parameters and variable values. Based upon a 20-compartment model, we develop a numerical simulation of the associated differential equations. The model is not a forecasting or even predictive one, given the uncertainty about several biological parameter values. Rather, it is intended to aid a qualitative understanding of how equilibrium levels of infection may be impacted upon, by the parameters of the system. We examine one-at-a-time sensitivity analysis around a base case scenario. The key finding which should be of interest to policymakers is that while factors such as improved vaccine efficacy, increased vaccination rates, lower waning rates and more stringent non-pharmaceutical interventions might be thought to improve equilibrium levels of infection, this might only be done to good effect if vaccination coverage on a recurrent basis is sufficiently high.

Sensitivity of UK Covid-19 deaths to the timing of suppression measures and their relaxation.

In this paper I examine the sensitivity of total UK Covid-19 deaths and the demand for intensive care and ward beds, to the timing and duration of suppression periods during a 500- day period. This is achieved via a SEIR model. Using an expected latent period of 4.5 days and infectious period of 3.8 days, R 0 was first estimated as 3.18 using observed death rates under unmitigated spread and then under the effects of the total lockdown ( R 0 =0.60) beginning 23 March. The case fatality rate given infection is taken as 1%. Parameter values for mean length of stay and conditional probability of death for ICU and non-ICU hospital admissions are guided by Ferguson et al. (2020). Under unmitigated spread the model predicts around 600,000 deaths in the UK. Starting with one exposed person at time zero and a suppression consistent with an R 0 of 0.60 on day 72, the model predicts around 39,000 deaths for a first wave, but this reduces to around 11,000 if the intervention takes place one week earlier. If the initial suppression were in place until day 200 and then relaxed to an R 0 of 1.5 between days 200 and 300, to be followed by a return to an R 0 of 0.60, the model predicts around 43,000 deaths. This would increase to around 64,000 if the release from the first suppression takes place 20 days earlier. The results indicate the extreme sensitivity to timing and the consequences of even small delays to suppression and premature relaxation of such measures.

The scale and dynamics of COVID-19 epidemics across Europe.

The number of COVID-19 deaths reported from European countries has varied more than 100-fold. In terms of coronavirus transmission, the relatively low death rates in some countries could be due to low intrinsic (e.g. low population density) or imposed contact rates (e.g. non-pharmaceutical interventions) among individuals, or because fewer people were exposed or susceptible to infection (e.g. smaller populations). Here, we develop a flexible empirical model (skew-logistic) to distinguish among these possibilities. We find that countries reporting fewer deaths did not generally have intrinsically lower rates of transmission and epidemic growth, and flatter epidemic curves. Rather, countries with fewer deaths locked down earlier, had shorter epidemics that peaked sooner and smaller populations. Consequently, as lockdowns were eased, we expected, and duly observed, a resurgence of COVID-19 across Europe.