Models for the COVID-19 Second Wave

Europe, the Middle East, Oceania, part of South Asia and the U.S. progressively exit the COVID-19 lockdowns and relax the most severe social distancing measures.

In the meantime, China, Singapore and South Korea, the countries that were hit first and succeeded in controlling the first wave, appear to face different dynamics after easing of anti-COVID-19 measures.

South Korea appeared to have fully controlled local contagion, until 10 May (Hyonhee Shin, Josh Smith, “South Korea scrambles to contain nightclub coronavirus outbreak“, Reuters, 11 May 2020). In two days South Korea reported 69 new cases linked to nightclubs and bars in Seoul and races to test contact cases, still needing to trace more than 3000 people. Its borders are closed and entry is submitted to strict quarantines.

China seemed to fare quite well, despite struggling with clusters and imported cases notably in Heilongjiang (William Yang, “China tries to contain new coronavirus outbreak“, DW, 29 April 2020). Then, on 11 May, just above a months after the end of the lockdown, a new cluster arose in Wuhan, the original center of the epidemic, linked to asymptomatic cases (“China’s Wuhan reports first coronavirus cluster since lifting of lockdown“, Reuters, 11 May 2020). On 9 May, it was Northeastern Jilin province that reported a new small cluster, which triggered a lockdown for the city of Shulan (Ibid.).

Singapore knows what can be seen as a second wave, focused on migrant workers, with cases rising exponentially starting early April 2020 (James Crabtree, “How Singapore’s second wave is exposing economic inequalities“, New Statesman, 6 May 2020).

Meanwhile, history shows that for the 1918-1919 so-called “Spanish” Influenza pandemic, the second and third waves were more lethal than the first spring wave (Jeffery K. Taubenberger and David M Morens, “1918 Influenza: the mother of all pandemics,” Emerging infectious diseases vol. 12,1, 2006).

Thus, what are we to expect in the near future regarding this COVID-19 second wave?

Epidemiologists have modelled various types of scenarios to help policy-makers handle the pandemic and create responses that will mitigate, as much as possible, fatalities. This article looks at four such models and scenarios and highlight what they tell us about future waves of COVID-19. Comparing briefly the scenarios with the reality of the situation in China, Singapore and South Korea, we highlight the scenarios that look more likely and underline the need for further research focused on other factors.

The waves as a result of our interactions with the COVID-19

It is now generally accepted that we shall have to live with the COVID-19. The pandemic, whatever the shape of the outbreaks, is expected to persist until immunisation is reached, assuming this is possible. Immunisation will result either from vaccination or from natural immunity. At best, according to our estimates, and considering the need to manufacture billions of doses immunisation will not happen before winter 2022 (see Helene Lavoix, The COVID-19 Pandemic, Surviving and Reconstructing, The Red Team Analysis Society, 24 March 2020). This timeframe does not take into account the time necessary for an immense mass vaccination campaign.

Actors handled the first outbreak of the COVID-19 or first wave as they could, considering that all countries were caught unprepared, with possibly the exception of South Korea. A range of measures were created and applied, including a stringent lockdown across the world, that allowed to handle the surprise and mitigate fatalities. The main objective of these measures was to stop the contagion while not seeing health systems break down. What we successfully did was not to end the epidemic but to change its course. We avoided an immediate possible worst case scenario (Helene Lavoix, Worst Case Baseline Scenarios for the COVID-19 Pandemic, The Red Team Analysis Society, 24 March 2020).

However, the price to pay was that activity stopped, with an immense cost to ways of life, including the economy.

Now, we are entering a new phase, where we shall start learning to live with the COVID-19. The fear is that once activity restarts, then the epidemic will spread and develop again, bringing about a second wave, with its corollary of death, sufferings and danger to see health systems break down. Political authorities are thus rushing to design sets of measures and policies that should allow us living with the COVID-19, instead of being frozen by the danger, until another kind of death takes us all.

The possibility of a second wave, and of next waves in general depend upon the interactions between the virus, and notably the epidemiology of the SARS-CoV-2,, and the responses and actions the various actors will design and implement.

We are thus both dependent for our activity upon the waves of COVID-19 while, in the same time, also contributing to create and shape them.

Second and recurring waves

The Imperial College COVID-19 Response Team March study

First and foremost, we have the influential study of the Imperial College COVID-19 Response Team, Impact of non-pharmaceutical interventions (NPIs) to reduce COVID19 mortality and healthcare demand (16 March 2020). Many governments used this report to build their first wave’s lockdown policies.

(A partir de ce point, traduction française automatique par intelligence artificielle.)

In this study, the objective is to minimise fatalities, which demands not overwhelming hospitals and notably the number of intensive care units bed requirements (ICU). The policy measures taken into account are as follows:

• Case isolation in the home (CI),
• Voluntary home quarantine (for 14 days – HQ),
• Social distancing of those over 70 years of age (SDO),
• Social distancing of entire population (similar to lockdown – SD),
• Closure of schools and universities (PC).

The study, among other critical factors, considers the R₀ (R-nought) or basic reproduction number of an infectious disease. This is a measure that represents “the expected number of secondary cases produced by a typical infected individual early in an epidemic” (O Diekmann; J.A.P. Heesterbeek and J.A.J. Metz (1990). “On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations”, Journal of Mathematical Biology 28: 356–382). They “examine values between 2.0 and 2.6”, which is in the range of most estimates. They also take into account the acquired immunity against the SARS-CoV-2 and consider it to be similar to what is obtained against the seasonal influenza, i.e. re-infection cannot reoccur the next season.

With this model, the Imperial College COVID-19 Response Team finds that, for a R₀=2.2, after the end of the first wave and once the social distancing of entire population measures are relaxed and school and universities re-open, assuming all other measures stay in place, a new wave starts. It triggers the need to start a new period of social distancing of entire population and school and university closure one month after the beginning of the relaxation.

As a whole, over two years, the full range of measures “is in force approximately 2/3 of the time” (p.12). In two years, we thus have, excluding the first wave, eleven waves of two months each, however the apex of each wave is lower. The second wave thus starts immediately once the lockdown stops, but starts being experienced as such one month after the exit strategy, when the need for SD is triggered.

Although further monitoring will be needed, this seems to correspond approximately to the new clusters emerging in China and South Korea. Yet, we are still far in these two countries from the Imperial College estimated needs in ICU one month after exit from lockdown, as shown in the diagram above for example.

The Harvard T.H. Chan School of Public Health’s model

Scientists of the Harvard T.H. Chan School of Public Health created a model allowing notably for different sensitivity of the virus to seasonality (Stephen M. Kissler, et al. “Projecting the transmission dynamics of SARS-CoV-2 through the postpandemic period“, Science, 14 April 2020).

It obtained scenarios similar to those of the Imperial College, with recurring waves into 2022 “requiring social distancing measures to be in place between 25% (for wintertime R₀ = 2 and seasonality…) and 75% (for wintertime R₀ = 2.6 and no seasonality …) of that time”.

Obviously, the lower the R₀ considered and the more important the seasonality factor, the shorter the social distancing period.

Here, as for the Imperial College’s model, the second wave would start immediately as social distancing measures are relaxed. In the Harvard model, in the U.S. case, new social distancing measures would be needed one month after the end of SD if the virus is not seasonal. If the virus is seasonal and if the first wave took place in Spring, as is more or less the case in the U.S., new social distancing measures would be needed 2,5 months after the end of SD.

The emergence of new clusters in South Korea and China in May would tend to indicate that the virus is not or not strongly seasonal. The Singapore case and the April wave anyway showed that heat and humidity do not appear to deter the virus and the disease.

Three possible scenarios for the CIDRAP

On 30 April 2020, the Centre for Infectious Disease Research and Policy (CIDRAP) of the University of Minnesota published “The future of the COVID-19 pandemic: lessons learned from pandemic influenza,” (Kristine Moore, MD, MPH, Marc Lipsitch, DPhil, John Barry, MA, and Michael Osterholm, PhD, MPH).

Pointing out useful similarities but also differences between influenza and the SARS-CoV-2, notably a higher viral transmissibility for the latter, the CIDRAP outlines three possible scenarios. These scenarios give the outlook of the future wave but are not precise enough to allow estimating when the second wave will start.

The first scenario of the CIDRAP is very similar to the scenario of the Imperial College and of Harvard T.H. Chan School of Public Health. According to this first scenario, “the first wave of COVID-19 in spring 2020 is followed by a series of repetitive smaller waves that occur through the summer and then consistently over a 1- to 2-year period, gradually diminishing sometime in 2021.” The strength and timing of waves may vary with the efficiency of the controlling measures taken as well as according to other demographic and geographic factors. This first scenario also expects that full SD measures may have to be implemented regularly.

CIDRAP’s second scenario is inspired by the pattern of the 1918-1919 Spanish Flu pandemic. “The first wave of COVID-19 in spring 2020 is followed by a larger wave in the fall or winter of 2020 and one or more smaller subsequent waves in 2021.” Thus, the main difference with the Imperial College and Harvard scenarios is first about intensity. The second wave is the most lethal. Second, it is about timing. The second wave would take place in the next fall or winter. Finally it is about the number of subsequent waves following the second one, creating two sub-scenarios: only one further wave or subsequent smaller waves.

Considering what is happening in China, Singapore and South Korea, the timing does not seem to correspond. The difference probably comes from the measures implemented for the COVID-19, which are likely to have “artificially” stopped the first wave, compared with the 1918 Influenza pandemic. However, the possibility of a more lethal second wave is serious enough to keep this scenario and further detail comparatively the 1918 pandemic and the COVID-19.

The third CIDRAP scenario is different from the previous models. It envisions that “the first wave of COVID-19 in spring 2020 is followed by a “slow burn” of ongoing transmission and case occurrence, but without a clear wave pattern.” In that case the most severe social distancing measures will not have to be reimplemented but “cases and deaths will continue to occur”.

This scenario does not fit what took place in Singapore. It may be, however, too early to discard it. It may also not be universal. In some countries, excess death and sufferings are not acceptable, while there is always the risk that contagion spreads again exponentially. Thus, even a few cases would trigger SD measures, as possibly in New Zealand, or in Shulan in China (e.g. Amy Gunia, “Why New Zealand’s Coronavirus Elimination Strategy Is Unlikely to Work in Most Other Places“, Time, 28 April 2020; Ibid.).

Mobility and Second wave

The most recent study, again by the Imperial College COVID-19 Response Team, focuses on Italy (Report 20: Using mobility to estimate the transmission intensity of COVID-19 in Italy: A subnational analysis with future scenarios, 4 May 2020).

It models scenarios for a relaxation of isolation measures on 4 May 2020, using increase in mobility as a proxy. A second wave is quasi in-built in their model as mobility is the parameter used to make “the time related reproduction number or effective reproduction number (Rt)” change. Thus, what the model tells us is the extent of infection and death in excess, i.e. the size of the wave.

In the first scenario modelled, mobility increases by 20% above pre-lockdown levels, and in the second, it increases by 40%. However, these scenarios do not account for other anti-COVID-19 measures such as school closures, hygiene, face masks, or testing and contact tracing. It only focuses on the mobility factor.

The first finding, unsurprisingly, is that the situation varies according to region. This could indicate that the way China or Germany, for example, handle the COVID-19 could be the way forward, at least as far as the mobility factor is concerned.

In scenario 1 (20% mobility) the number of excess death rises above 100 on approximately 8 June 2020 in Piedmont, 20 June in Veneto and 13 July in Tuscany, before to rise exponentially.

In scenario 2 (40% mobility) the number of excess death rises above 100 on approximately 28 May in Piedmont, 4 June in Veneto, 10 June in Tuscany, 22 June in Lombardy and 4 July in Emilia Romagna and Liguria, before to rise exponentially.

As the authors highlight, these scenarios must be seen as worst case scenarios, knowing that other measures will be implemented.

Thus, except in the third scenario of the CIDRAP, all epidemiological models suggest that we shall face a second wave. Most models consider also following recurring waves.

Now, a brief comparison with the dynamics of the epidemic in China, South Korea and Singapore tend to indicate that the models and scenarios anticipating recurring waves are the most likely. It could also indicate that models are pessimistic in terms of the timing of the second wave, except in the case of Singapore. Yet, in Singapore, other factors not included in the epidemiological models are also at work. Meanwhile, the size thus lethality of the second wave remains a high impact uncertainty that must be considered carefully.

Can we thus find other factors that could help improving assessments of the coming waves? These factors would make foresight even more actionable. They would thus contribute to the design of efficient policies. This is what we shall see with the next article.

Further Bibliographical references

Taubenberger, Jeffery K, and David M Morens. “1918 Influenza: the mother of all pandemics.” Emerging infectious diseases vol. 12,1 (2006): 15-22. doi:10.3201/eid1201.050979

Featured image: Image par Elias Sch. de Pixabay [Public Domain]