Individual costs and societal benefits of interventions during the COVID-19 pandemic (preprint)

Individual and societal reactions to an ongoing pandemic can lead to social dilemmas: In some cases, each individual is tempted to not follow an intervention, but for the whole society it would be best if they did. Now that in most countries the extent of regulations to reduce SARS-CoV-2 transmission is very small, interventions are driven by individual decision-making. Assuming that individuals act in their best own interest, we propose a framework in which this situation can be quantified, depending on the protection the intervention provides to a user and to others, the risk of getting infected, and the costs of the intervention. We discuss when a tension between individual and societal benefits arises and which parameter comparisons are important to distinguish between different regimes of intervention use.

Evolution of resistance to COVID-19 vaccination with dynamic lockdown (preprint)

The COVID-19 pandemic has led to an unprecedented global response in terms of social lockdown in order to slow the spread of the virus 1,2. Currently the greatest hope is based on world-wide vaccination3,4. The expectation is that social and economic activities can gradually resume as more and more people become vaccinated. Yet, a relaxation of social distancing that allows increased transmissibility, coupled with selection pressure due to vaccination, will likely lead to the emergence of vaccine resistance 5. Here we analyze the evolutionary dynamics of COVID-19 in the presence of dynamic lockdown and in response to vaccination. We use infection and vaccination data of 6 different countries (Israel, US, UK, Brazil, France and Germany) to assess the probability and timing for the wave of vaccine resistant mutant2. For slow vaccination rates, resistant mutants will appear inevitably even if strict lockdown is maintained. For fast vaccination rates (such as those used in Israel) the emergence of the mutant can be prevented if strict lockdown is maintained during vaccination. Our mathematical results provide quantitative guidelines for a combined vaccination and lockdown policy that minimizes the probability of emergence of vaccine resistance variants for current and future vaccination programs.

Vaccination strategies when vaccines are scarce: On conflicts between reducing the burden and avoiding the evolution of escape mutants (preprint)

When vaccine supply is limited but population immunisation urgent, the allocation of the available doses needs to be carefully considered. One aspect of dose allocation is the time interval between the primer and the booster injections in two-dose vaccines. By stretching this interval, more individuals can be vaccinated with the first dose more quickly. Even if the level of immunity of these half-vaccinated individuals is lower than that of those who have received both shots, delaying the second injection can be beneficial in reducing case numbers, provided a single dose is sufficiently effective. On the other hand, there has been concern that intermediate levels of immunity in partially vaccinated individuals may favour the evolution of vaccine escape mutants. In that case, a large fraction of half-vaccinated individuals would pose a risk - but only if they encounter the virus. This raises the question whether there is a conflict between reducing the burden and the risk of vaccine escape evolution or not. We develop a minimal model to assess the population-level effects of the timing of the booster dose. We set up an SIR-type model, in which more and more individuals become vaccinated with a two-dose vaccine over the course of a pandemic. As expected, there is no trade-off when vaccine escape evolves at equal probabilities in unvaccinated and half-vaccinated patients. If vaccine escape evolves more easily in half-vaccinated patients, the presence or absence of a trade-off depends on the reductions in susceptibility and transmissibility elicited by the primer dose.