Researchers in the EF Program have worked on several projects and published multiple papers on different aspects of the management of the spread of an infectious disease.

Optimal lockdown duration and intensity

In multiple papers with colleagues from the TU Wien, University of Vienna and Carnegie Mellon University Wrzaczek analysed the optimal lockdown duration and intensity in dependence of several different parameters and in multiple scenarios.

Development in the Triple Skiba Point © Dieter Grass

One of the principal ways nations are responding to the COVID-19 pandemic is by locking down portions of their economies to reduce infectious spread. This is expensive in terms of lost jobs, lost economic productivity, and lost freedoms. So it is of interest to ask: What is the optimal intensity with which to lockdown, and how should that intensity vary dynamically  over the course of an epidemic? This paper explores such questions with an optimal control model that recognizes the particular risks when infection rates surge beyond the healthcare system’s capacity to deliver appropriate care. The analysis shows that four broad strategies emerge, ranging from brief lockdowns that only ‘‘smooth the curve’’ to sustained lockdowns that prevent infections from spiking beyond the healthcare system’s capacity. Within this model, it can be optimal to have two separate periods of locking down, so returning to a lockdown after initial restrictions have been lifted is not necessarily a sign of failure. Relatively small changes in judgments about how to balance health and economic harms can alter dramatically which strategy prevails. Indeed, there are constellations of parameters for which two or even three of these distinct strategies can all perform equally well for the same set of initial conditions; these correspond to so-called triple Skiba points. The performance of trajectories can be highly nonlinear in the state variables, such that for various times t, the optimal unemployment rate could be low, medium, or high, but not anywhere in between. These complex dynamics emerge naturally from modeling the COVID-19 epidemic and suggest a degree of humility in policy debates. Even people who share a common understanding of the problem’s economics and epidemiology can prefer dramatically different  policies. Conversely, favoring very different policies is not evident that there are fundamental disagreements.


Caulkins, J.P., Grass, D., Feichtinger, G., Hartl, R.F., Kort, P.M., Fürnkranz-Prskawetz, A., Seidl, A., & Wrzaczek, S. (2022). COVID-19 and Optimal Lockdown Strategies: The Effect of New and More Virulent Strains. In: Pandemics: Insurance and Social Protection. Eds. Boado-Penas, M.C., Eisenberg, J., & Şahin‬‬‬, Ş., pp. 163-190 Springer, Cham. ISBN 978-3-030-78334-1 10.1007/978-3-030-78334-1_9.

Caulkins, J.P., Grass, D., Feichtinger, G., Hartl, R.F., Kort, P.M., Prskawetz, A., Seidl, A., & Wrzaczek, S. (2021). The optimal lockdown intensity for COVID-19. Journal of Mathematical Economics 93 e102489. 10.1016/j.jmateco.2021.102489.

Caulkins, J., Grass, D., Feichtinger, G., Hartl, R., Kort, P.M., Prskawetz, A., Seidl, A., & Wrzaczek, S. (2020). How long should the COVID-19 lockdown continue? PLoS ONE 15 (12) e0243413. 10.1371/journal.pone.0243413.

Caulkins, J.P., Grass, D., Feichtinger, G., Hartl, R.F., Kort, P.M., Prskawetz, A., Seidl, A., & Wrzaczek, S. (2020). The optimal lockdown intensity for COVID-19. IIASA Working Paper. Laxenburg, Austria: WP-20-015

Regional application of lockdown & testing

In a paper published in the Journal of Public Economic Theory Freiberger, Wrzaczek and Kuhn investigated the the optimal heterogeneous transmission reduction efforts and testing strategies during a pandemic together with colleagues from the ASA Program and the University of Vienna.

SIR state transitions © Michael Freiberger

During the COVID-19 pandemic countries invested significant amounts of resources into its containment. In early stages of the pandemic most of the (nonpharmaceutical) interventions can be classified into two groups: (i) testing and identification of infected individuals, (ii) social distancing measures to reduce the transmission probabilities. Furthermore, both groups of measures may, in principle, be targeted at certain subgroups of a networked population. To study such a problem, we propose an extension of the SIR model with additional compartments for quarantine and different courses of the disease across several network nodes. We develop the structure of the optimal allocation and study a numerical example of three symmetric regions that are subject to an asymmetric progression of the disease (starting from an initial hotspot). Key findings include that (i) for our calibrations policies are chosen in a “flattening-the-curve,” avoiding hospital congestion; (ii) policies shift from containing spillovers from the hotspot initially to establishing a symmetric pattern of the disease; and (iii) testing that can be effectively targeted allows to reduce substantially the duration of the disease, hospital congestion and the total cost, both in terms of lives lost and economic costs.


Lockdown and vaccination strategy

How does the uncertain time of admission of a vaccine impact the optimal lockdown strategy of policy makers and how does the strategy change after the vaccine has been approved. These two questions were examined by Wrzaczek and Freiberger in cooperation with colleagues from the University of Padua in a paper published in PLOSOne. For the solution of the model the authors used the 2SOCS model.

Optimal Lockdown Strategy © Muttoni

Optimal Lockdown Strategy depending on the time of vaccine approval.


Immediately after the start of the COVID-19 pandemic in Early 2020, most affected countries reacted with strict lockdown to limit the spread of the virus. Since that time, the measures were adapted on a short time basis according to certain measures (i.e. number of infected, utilization of intensive care units). Implementing a long-term optimal strategy was not possible since a forecast when R&D will succeed in developing an effective vaccination was not available. This paper closes this gap by assuming a stochastic arrival rate of the COVID-19 vaccine with the corresponding change in the optimal policy regarding the accompanying optimal lockdown measures. The first main finding is that the lockdown should be intensified after the vaccine approval if the pace of the vaccination campaign is rather slow. Secondly, anticipation of the vaccination arrival also leads to a stricter lockdown in the period without vaccination. For both findings an intuitive explanation is offered.


Lockdowns and vaccines: a balancing act

A new study investigates whether COVID-19 lockdowns and vaccines complement or substitute each other, offering insights to policymakers about optimizing public health and economic outcomes (see press release).

Conceptual image of COVID-19 vaccine and COVID infection on a world map © Kts |

The COVID-19 pandemic has devastated lives and economies around the world. Initially a primary response was locking down parts of the economy to reduce social interactions and, hence, the virus spread. After vaccines have been  developed and produced in sufficient quantity, they can largely replace broad lock downs. This paper explores how lockdown policies should be varied during the year or so gap between when a vaccine is approved and when all who wish have  been vaccinated. Are vaccines and lockdowns substitutes during that crucial time, in the sense that lockdowns should be reduced as vaccination rates rise? Or might they be complementary with the prospect of imminent vaccination  increasing the value of stricter lockdowns, since hospitalization and death averted then may be permanently prevented, not just delayed? We investigate this question with a simple dynamic optimization model that captures both epidemiological and economic considerations. In this model, increasing the rate of vaccine deployment may increase or reduce the optimal total lockdown intensity and duration, depending on the values of other model parameters. That vaccines and  lockdowns can act as either substitutes or complements even in a relatively simple model casts doubt on whether in more complicated models or the real world one should expect them to always be just one or the other. Within our model, for  parameter values reflecting conditions in developed countries, the typical finding is to ease lockdown intensity gradually after substantial shares of the population have been vaccinated, but other strategies can be optimal for other parameter  values. Reserving vaccines for those who have not yet been infected barely outperforms simpler strategies that ignore prior infection status. For certain parameter combinations, there are instances in which two quite different policies can  perform equally well, and sometimes very small increases in vaccine capacity can tip the optimal solution to one that involves much longer and more intense lockdowns.