What to do if COVID-19 is here to stay
It is now almost four months since COVID-19 was declared a global pandemic. As the epidemic was unfolding in February 2020, with little information about the new coronavirus SARS-CoV-2, scientists from across disciplines offered projections of the epidemic and proposed optimal policy measures that had one target in common: getting through the worst phase of the epidemic and flattening the curve.
Early contributions attempted to quantify and simulate optimal policy measures, and broadly proposed a two to three-month strict lockdown to be imposed some weeks into the epidemic. Some analyses recommended a severe 60% lockdown starting at two weeks after the outbreak and lasting for three months (Alvarez et al. 2020). Others recommended an even stricter lockdown of 67% for a bit less than two months (Gonzalez-Eiras and Niepelt 2020). More recently, Gollier (2020) shows that uncertainty about the basic reproduction rate means the optimal containment policy is less severe than a setting in which the reproduction number is known.
Four months on, uncertainty around COVID-19 persists. Global daily confirmed cases are steadily increasing and global daily deaths have plateaued at about 4,500-5,000 per day for most of June and early July 2020. While strict lockdown measures are being lifted in many countries, new infection spikes have appeared in others, as the world wakes up to the fact that this coronavirus is likely to stay for a long time.
One great unknown about COVID-19 is whether individuals who recover from it can be reinfected. At the emergence of any new virus, it is impossible to know whether immunity is permanent or wanes, until enough time has passed for longitudinal studies to take place. At the moment, and with limited available data, medical scientists and epidemiologists are instead comparing SARS-CoV-2 to related coronaviruses, such as HCoV-HKU1 and HCoV-OC43, which are known to exhibit waning immunity. An early contribution by Kissler et al. (2020) assumed that immunity to SARS-CoV-2 wanes in approximately 45 weeks. A recent medical study (Long et al. 2020) found a significant drop in specific antibody levels after three months. Nevertheless, the duration of immunity in general is still far from understood.
Optimal containment policy with waning immunity
In Giannitsarou et al. (2020), we explicitly consider a setting in which immunity is temporary. We derive a stylised optimal containment policy and contrast it to policies assuming that once recovered, individuals are forever immune.
We work with a flexible epidemic model known as SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible). The model allows for natural births and deaths, disease induced deaths, a pre-symptomatic state in which individuals are exposed to the virus and can be infectious without exhibiting symptoms, and importantly, waning immunity. In such a framework, because immunity may slowly disappear from recovered people, there is the potential for a second (and even third) wave of infection.
An important feature of this epidemiological model is that with waning immunity (the SEIRS model) the disease becomes endemic. This means that if left uncontrolled, it will never be eradicated, in sharp contrast to a model in which recovery confers permanent immunity (the SEIR model). In the SEIR model, the disease will be always eradicated in the long run once herd immunity is achieved, even when left uncontrolled. This observation has important implications for the design of optimal policy while we wait for a vaccine or other pharmaceutical interventions to become available.
Our policy analysis assumes that a vaccine or medical treatment is not currently available, but will become available in six years from the onset of the epidemic.1 The only instrument available to the policymaker is a broadly defined measure of social distancing which, within the context of the model, simply reduces the contact rate between susceptible and infectious individuals.
We calibrate the epidemic model and optimal policy problem to the most up-to-date estimated population and epidemic parameters from the US, and then perform comparative analysis with different assumptions about the waning period.
Figure 1 shows the number of infected individuals over time when the disease is left uncontrolled (top panel); when the disease is optimally controlled using social distancing measures (middle panel); and the path of optimal social distancing (bottom panel). In each, the light blue line shows the model with permanent immunity (SEIR) and the red line corresponds to the model with immunity waning in one year.
Figure 1 Infections and optimal social distancing with and without waning immunity
When immunity is permanent, the path of optimal social distancing is straightforward and looks a lot like policies that have been used so far across the world to control the evolution of COVID-19: in the beginning of the epidemic there is little social distancing; it sharply increases as the peak of the epidemic approaches; then sharply decreases as infected individuals recover, gain immunity, and remain healthy thereafter. We note that at around the peak of the epidemic, optimal social distancing in the SEIR framework reaches its maximum level of about 25.5%, however this lasts for a short period and is completely phased out by week 40.2 The effects of the social distancing policy are, as expected, a flattening of the curve and a slightly lengthier epidemic. Under the optimal social distancing policy, about 20% fewer individuals are infected than for the uncontrolled model.
If immunity wanes, the optimal social distancing policy is quite different. While restrictions start out at a higher level than in the SEIR model, the level never reaches more than 16.5%. These measures are sustained at a relatively stable level for about six months from the start of the epidemic, and then dropped temporarily, only to be increased again intermittently when the second and following smaller waves arise. To make sense of this different policy design, we note that when immunity wanes, all those infected in the initial wave of the epidemic go through the phases of the disease only to become susceptible to infection again. In this sense, policy efforts to severely supress the first wave of the epidemic are ineffective: the optimal policy now primarily aims at delaying as much as possible the different phases of the epidemic, while also dampening the disease incidence. Overall, the optimal social distancing has two main phases: an initial phase with suppression that is not as aggressive as in the SEIR setting, and a second phase characterised by a varying low-level management of subsequent infection waves. Here, the number of infected individuals under the optimal social distancing policy at the first peak of the epidemic is about 8.5% smaller than in the uncontrolled model. But the optimal policy now also flattens future waves of the epidemic and ensures that the long run endemic level of infected individuals is lower than in the uncontrolled model.
Some closing thoughts
In summary, we find that if immunity to SARS-CoV-2 is temporary, the disease will become endemic. The optimal policy will make an initial effort to reduce the first great infection wave and then engage in a permanent low level management of the persistent infection in the population in order to keep it under control. In practice, this means that partial lockdown or social distancing measures may become the norm for some years to come.
Our analysis assumed that, currently, the only policies at our disposal are broad-based non-medical interventions such as social distancing and lockdown measures. At the initial stages of the COVID-19 pandemic, such policies proved to be extremely costly from social, economic, and health care perspectives. But going forward, we expect that individuals, businesses, and governments are likely to adapt how they do things and operate to mitigate the costs of this initial dramatic shock. People may become more cautious in everyday dealings, businesses may come to depend less on third parties or off-shoring, while other organisations such as schools, transport, intermediate goods producers, and local governments may find innovative ways to become more flexible and resilient in the ways they deliver services and products. We hope that with creativity and resourcefulness, humanity will learn to navigate and live with the disease, should it turn out to be here for the long term.
Alvarez, F, D Argente and F Lippi (2020), “A Simple Planning Problem for COVID-19 Lockdown”, CEPR Discussion Paper 14658.
Giannitsarou, C, S Kissler and F Toxvaerd (2020), “Waning Immunity and the Second Wave: Some Projections for SARS-CoV-2”, CEPR Discussion Paper 14852.
Gollier, C (2020), “Pandemic economics: Optimal Dynamic Confinement under Uncertainty and Learning”, Covid Economics 34.
Gonzalez-Eiras, M and D Niepelt (2020), “On the Optimal ‘Lockdown’ During an Epidemic”, Covid Economics 7.
Kissler, S M, C Tedijanto, E Goldstein, Y H Grad and M Lipsitch (2020), “Projecting the Transmission Dynamics of SARS-CoV-2 through the Postpandemic Period”, Science 368(6493), 860-686.
Long, Q, X Tang, Q Shi et al. (2020), “Clinical and Immunological Assessment of Asymptomatic SARS-CoV-2 Infections”, Nature Medicine, 18 June.
1 The estimated horizon for a vaccine to be available for commercial use is, in the most optimistic cases, at least 1.5 years from around the start of the epidemic. Most sources and studies suggest that at least five years are needed, while there is a good chance that it will take more than a decade for a vaccine to become available.
2 The severity of lockdown measures depends not only on the epidemic parameters but also on assumptions about the welfare losses of infected individuals, as well as the economic costs of social distancing. We assumed that on average social distancing measures account for 10-25% income loss per individual.