New research shows that the COVID-19 pandemic could decrease during the summer months but return in the fall with a strong recovery next winter


Researchers at Karolinska Institutet in Sweden and the University of Basel in Switzerland have produced a mathematical model that shows that the spread of the new coronavirus can decline in the summer and then return in the autumn and winter.

The analysis has been published in the scientific journal Swiss Medical Weekly.

“Even if the spread should decrease in the summer, we cannot conclude that the pandemic is contained because such a decline can be temporary and due to a combination of infection control efforts and seasonal variation in how the virus spreads,” says Jan Albert, professor of infectious disease control at the Department of Microbiology, Tumor and Cell Biology, Karolinska Institutet.

“Instead, it can be seen as an opportunity to prepare the healthcare systems and invest in the development of vaccines and antiviral drugs.”

Jan Albert and his colleagues at the University of Basel have tried to predict the effect of seasonal variations in the transmission efficiency of the new coronavirus (SARS-CoV-2) on the northern hemisphere.

In their mathematical model, they take into account the likelihood that the spread of the virus will exhibit the same seasonal variation as common and closely related respiratory coronaviruses, namely that it spreads best in the winter.

Could be a new peak in winter 2020/2021

“A possible scenario is that there is a peak in spring 2020 in temperate regions of the Northern Hemisphere, a decline in the summer and a new peak in winter 2020/2021,” says Jan Albert.

The researchers have used the available figures and data on SARS-CoV-2 and four related “common” coronaviruses called HKU1, NL63, OC43 and 229E.

Since these related coronaviruses are common cold viruses, there’s a great deal of data on their seasonal variations.

The researchers emphasise that there’s a lot of uncertainty in the various parameters that they base their analysis on and that it must be remembered that it’s only a model that attempts to examine conceivable scenarios.

The analysis of the results of more than 52,000 patient samples from Karolinska University Hospital shows that infection with any of the four “common” coronaviruses, HKU1, NL63, OC43 or 229E, was ten times more common in the December to April period than it was in July through September.

The researchers have then taken all the available data and used a so-called SIR model, which is often used in mathematical modelling of infectious diseases.

Many things that come into play

The researchers emphasise that there’s a lot of uncertainty in the various parameters that they base their analysis on and that it must be remembered that it’s only a model that attempts to examine conceivable scenarios.

“There are many things that come into play in the spread of a virus and that we haven’t been able to factor in, such as what public measures are taken and how successful isolation/quarantine is,” says Jan Albert.

“With our analysis, we want to point out that it is important to remember the possibility of seasonality when data on the spread of the pandemic are evaluated.”


Micaela Martinez of Columbia University to investigate a phenomenon recognized 2500 years ago by Hippocrates and Thucydides: Many infectious diseases are more common during specific seasons. “It’s a very old question, but it’s not very well studied,” Martinez says.

It’s also a question that has suddenly become more pressing because of the emergence of coronavirus disease 2019 (COVID-19).

Different diseases have different patterns. Some peak in early or late winter, others in spring, summer, or fall. Some diseases have different seasonal peaks depending on latitude. And many have no seasonal cycle at all. So no one knows whether SARS-CoV-2, the virus that causes COVID-19, will change its behavior come spring.

“I would caution overinterpreting that hypothesis,” Nancy Messonnier, the point person for COVID-19 at the U.S. Centers for Disease Control and Prevention, said at a press conference on 12 February.

If the seasons do affect SARS-CoV-2, it could nevertheless defy that pattern in this first year and keep spreading, because humanity has not had a chance to build immunity to it.

Even for well-known seasonal diseases, it’s not clear why they wax and wane during the calendar year.

“It’s an absolute swine of a field,” says Andrew Loudon, a chronobiologist at the University of Manchester. Investigating a hypothesis over several seasons can take 2 or 3 years. “Postdocs can only get one experiment done and it can be a career killer,” Loudon says. The field is also plagued by confounding variables.

“All kinds of things are seasonal, like Christmas shopping,” says epidemiologist Scott Dowell, who heads vaccine development and surveillance at the Bill & Melinda Gates Foundation and in 2001 wrote a widely cited perspective that inspired Martinez’s current study. And it’s easy to be misled by spurious correlations, Dowell says.

Despite the obstacles, researchers are testing a multitude of theories. Many focus on the relationships between the pathogen, the environment, and human behavior. Influenza, for example, might do better in winter because of factors such as humidity, temperature, people being closer together, or changes in diets and vitamin D levels. Martinez is studying another theory, which Dowell’s paper posited but didn’t test: The human immune system may change with the seasons, becoming more resistant or more susceptible to different infections based on how much light our bodies experience.

Beyond the urgent question of what to expect with COVID-19, knowing what limits or promotes infectious diseases during particular times of year could inform disease surveillance, predictions, and the timing of vaccination campaigns.

It might even point to new ways to prevent or treat them. “If we knew what suppressed influenza to summertime levels, that would be a lot more effective than any of the flu vaccines we have,” Dowell says.

MARTINEZ BECAME interested in seasonality when, as an undergraduate at the University of Alaska Southeast, she had a job tagging Arctic ringed seals, doing skin biopsies, and tracking their daily and seasonal movements. While working on her Ph.D., her focus on seasonality shifted to polio, a much-feared summer disease before the advent of vaccines.

(Outbreaks often led to the closing of swimming pools, which had virtually nothing to do with viral spread.) Polio seasonality in turn made her curious about other diseases.

In 2018, she published “The calendar of epidemics” in PLOS Pathogens, which included a catalog of 68 diseases and their peculiar cycles.

Except in the equatorial regions, respiratory syncytial virus (RSV) is a winter disease, Martinez wrote, but chickenpox favors the spring. Rotavirus peaks in December or January in the U.S. Southwest, but in April and May in the Northeast.

Genital herpes surges all over the country in the spring and summer, whereas tetanus favors midsummer; gonorrhea takes off in the summer and fall, and pertussis has a higher incidence from June through October. Syphilis does well in winter in China, but typhoid fever spikes there in July. Hepatitis C peaks in winter in India but in spring or summer in Egypt, China, and Mexico. Dry seasons are linked to Guinea worm disease and Lassa fever in Nigeria and hepatitis A in Brazil.

Seasonality is easiest to understand for diseases spread by insects that thrive during rainy seasons, such as African sleeping sickness, chikungunya, dengue, and river blindness. For most other infections, there’s little rhyme or reason to the timing.

“What’s really amazing to me is that you can find a virus that peaks in almost every month of the year in the same environment in the same location,” says Neal Nathanson, an emeritus virologist at the University of Pennsylvania Perelman School of Medicine.

“That’s really crazy if you think about it.” To Nathanson, this variation suggests human activity—such as children returning to school or people huddling indoors in cold weather—doesn’t drive seasonality. “Most viruses get transmitted between kids, and under those circumstances, you’d expect most of the viruses to be in sync,” he says.

Nathanson suspects that, at least for viruses, their viability outside the human body is more important. The genetic material of some viruses is packaged not only in a capsid protein, but also in a membrane called an envelope, which is typically made of lipids.

It interacts with host cells during the infection process and helps dodge immune attacks. Viruses with envelopes are more fragile and vulnerable to adverse conditions, Nathanson says, including, for example, summertime heat and dryness.

A 2018 study in Scientific Reports supports the idea. Virologist Sandeep Ramalingam at the University of Edinburgh and his colleagues analyzed the presence and seasonality of nine viruses—some enveloped, some not—in more than 36,000 respiratory samples taken over 6.5 years from people who sought medical care in their region. “Enveloped viruses have a very, very definite seasonality,” Ramalingam says.

RSV and human metapneumovirus both have an envelope, like the flu, and peak during the winter months. None of the three is present for more than one-third of the year. Rhinoviruses, the best-known cause of the common cold, lack an envelope and—ironically—have no particular affinity for cold weather: The study found them in respiratory samples on 84.7% of the days of the year and showed that they peak when children return to school from summer and spring holidays. Adenoviruses, another set of cold viruses, also lack an envelope and had a similar, nonseasonal pattern, circulating over half the year.

Ramalingam’s team also studied the relationship between viral abundance and daily weather changes. Influenza and RSV both did best when the change in relative humidity over a 24-hour period was lower than the average (a 25% difference).

“There’s something about the lipid envelope that’s more fragile” when the humidity changes sharply, Ramalingam concludes.

Jeffrey Shaman, a climate geophysicist at Columbia, contends that what matters most for the influenza virus is absolute humidity—the total amount of water vapor in a given volume of air—and not relative humidity, which measures how close the air is to saturation.

In a 2010 paper in PLOS Biology, Shaman and epidemiologist Marc Lipsitch of the Harvard T.H. Chan School of Public Health reported that drops in absolute humidity better explained the onset of influenza epidemics in the continental United States than relative humidity or temperature. And absolute humidity drops sharply in winter, because cold air holds less water vapor.

Why lower absolute humidity might favor some viruses remains unclear, however. Variables that could affect the viability of the viral membrane could include changes in osmotic pressure, evaporation rates, and pH, Shaman says. “Once you get down to the brass tacks of it, we don’t have an answer.”

Will SARS-CoV-2, which has an envelope, prove fragile in spring and summer, when absolute and relative humidity climb? The most notorious of the other coronavirus diseases, severe acute respiratory syndrome (SARS) and Middle East respiratory syndrome (MERS), offer no clues.

SARS emerged in late 2002 and was driven out of the human population in the summer of 2003 through intensive containment efforts. MERS sporadically jumps from camels to humans and has caused outbreaks in hospitals, but has never shown widespread human-to-human transmission. Neither virus circulated for long enough, on a wide enough scale, for any seasonal cycle to emerge.

Four human coronaviruses that cause colds and other respiratory diseases are more revealing. Three have “marked winter seasonality,” with few or no detections in the summer, molecular biologist Kate Templeton, also at the University of Edinburgh, concluded in a 2010 analysis of 11,661 respiratory samples collected between 2006 and 2009. These three viruses essentially behave like the flu.

That does not mean COVID-19 will as well. The virus can clearly transmit in warm, humid climates: Singapore already has more than 240 cases.

Two new papers published on preprint servers last week come to opposite conclusions. One, co-authored by Lipsitch, looked at COVID-19 spread in 19 provinces across China, which ranged from cold and dry to tropical, and found sustained transmission everywhere.

The second study concludes that transmission appears to occur only in specific bands of the globe that have average temperatures between 5°C and 11°C and 47% to 70% relative humidity.

The other coronaviruses may be more susceptible to seasonal changes in the environment simply because they’ve been infecting people for much longer. Once a high percentage of the population develops immunity, an unfavorable environment can provide the extra push needed to temporarily exile those viruses.

But that’s not the situation with COVID-19. “Even though there might be a big seasonal decline, if enough susceptible people are around, it can counter that and continue for a long time,” Martinez says. Lipsitch doesn’t think the virus will go poof in April either. Any slowdown “is expected to be modest, and not enough to stop transmission on its own,” he wrote in a recent blog post.

IN SURREY, MARTINEZ is investigating a different factor that might eventually affect COVID-19 incidence. Her subjects have returned to the clinic repeatedly—at the winter and summer solstices and again at the spring and fall equinoxes—so the researchers can evaluate how their immune system and other physiology change over the course of the day and from season to season.

She doesn’t expect to show that our immunity is, say, weaker in the winter and stronger in the summer. But by counting different immune system cells, assessing metabolites and cytokines in the blood, deciphering the fecal microbiome, and measuring hormones, Martinez’s team hopes to learn whether the seasons “restructure” the immune system, making some types of cells more abundant in certain parts of the body, and others less, in ways that influence our susceptibility to pathogens.

Animal studies support the idea that immunity changes with the seasons. Ornithologist Barbara Helm from the University of Groningen and her colleagues, for example, studied European stonechats, small songbirds that they caught and then bred in captivity.

By taking multiple blood samples over the course of 1 year, they found that the birds ramp up their immune systems in the summer, but then tamp them down in the fall, the time they migrate, presumably because migration is a big drain on their energy.

Melatonin, a hormone primarily secreted at night by the pineal gland, is a major driver of such changes. The hormone keeps track of the time of day but is also a “biological calendar” for the seasons, says Randy Nelson, an endocrinologist at West Virginia University who specializes in circadian rhythms.

When nights are long, more melatonin is released.

“The cells say, ‘Oh, I’m seeing quite a bit of melatonin, I know, it’s a winter night.’” In studies of Siberian hamsters—which, like humans, are diurnal—Nelson and his coworkers have shown that administering melatonin or altering light patterns can change immune responses by up to 40%.

The human immune system, too, seems to have an innate circadian rhythm. For instance, a vaccine trial in 276 adults by researchers at the University of Birmingham randomly assigned half to receive an influenza vaccine in the morning and the other half in the afternoon. Participants in the morning group had significantly higher antibody responses to two of the three flu strains in the vaccine, the researchers reported in 2016.

There’s evidence of seasonal variation in the actions of human immune genes as well. In a massive analysis of blood and tissue samples from more than 10,000 people in Europe, the United States, Gambia, and Australia, researchers at the University of Cambridge found some 4000 genes related to immune function that had “seasonal expression profiles.”

In one German cohort, expression in white blood cells of nearly one in four genes in the entire genome differed by the seasons. Genes in the Northern Hemisphere tended to switch on when they were switched off south of the equator, and vice versa.

Just how these massive changes might affect the body’s ability to fight pathogens is unclear, however, as immunologist Xaquin Castro Dopico and colleagues explain in a 2015 paper describing the findings. And some changes could be the result of an infection, instead of the cause.

The team tried to eliminate people who had acute infections, but “of course a seasonal infectious burden likely plays a part,” says Dopico, who is now at the Karolinska Institute. And seasonal immunity changes could not explain all the complex variation in seasonality that diseases show.

“They’re all out of sync with each other,” Nathanson points out. He’s also skeptical that a seasonal immune system change could be large enough to make a difference. “It would have to be pretty markedly different.”

Martinez, however, says she has found intriguing hints. Early analyses from her Surrey study, which collected its final data in December 2019, don’t reveal anything about seasonality yet, but they do show that specific subsets of white blood cells that play central roles in immune system memory and response are elevated at certain times of day. She hopes to firm up the finding by launching a similar but larger study next year.

Martinez cautions that artificial light may play havoc with natural circadian rhythms, with unpredictable effects on disease susceptibility.

To explore possible impacts, she has a separate study underway, with Helm, in both urban and rural parts of New York and New Jersey. They have installed light sensors on trees and poles and outfitted participants with devices that monitor light exposure and body temperature. “The fact that people really are just kind of washing out the rhythms in light exposure can be problematic,” she says.

Seasonal coronavirus prevalence

Data on seasonal variation of HKU1, NL63, OC43 and 229E diagnoses in respiratory samples was obtained from the routine molecular diagnostics at the Karolinska University Hospital, Stockholm, Sweden.

The laboratory provides diagnostic services to six of seven major hospitals and approximately half of outpatient care in the Stockholm county (2.2 million inhabitants). We extracted pseudonymised data on all analyses for the four viruses between 1 January 2010 and 31 December 2019.

The dataset included a total of 52,158 patient samples with 190,257 diagnostic tests, of which 2084 were positive for any of the coronaviruses (229E = 319; NL63 = 499; OC43 = 604; HKU1 = 355; OC43/HKU1 = 307).

Metadata included information about date of sampling and age of patient. In the period of 1 January 2010 to 5 November 2017, the coronavirus diagnostic was done using in-house assays [25].

From 6 November 2017 to 31 December 2019, samples were analysed using the commercial kit Allplex Respiratory Panels (Seegene Inc., Seoul (South Korea)). This commercial kit does not distinguish between HKU1 and OC43, and for this reason positive tests for these two viruses were combined for the entire study period.

The fraction of tests that were positive for the four seasonal CoVs showed a strong and consistent seasonal variation, see figure 1. From December to April approximately 2% of tests were positive, while less than 0.2% of tests were positive between July to September, i.e., a 10-fold difference (fig. 1, right).

While the fraction of positive tests is not a direct measure of prevalence, it is a reasonable proxy that we expect to be well correlated with prevalence. The strength of variation of the transmission rate through the year could be of high relevance to the spread of SARS-CoV-2 in 2020 and following years.

Figure 1
Seasonal variation in the fraction of positive CoV tests in Stockholm, Sweden. Panel A shows test results between 2010 and 2019. Panel B shows aggregated data for all years. All CoVs show a marked decline in summer and autumn, with HKU1/OC43 peaking January–December, and NL63 and 229E peaking in February–March.

Basic model

We consider simple SIR models [26] with an additional category E of exposed individuals of the form (equation 1)

(d/dt)S = b(1 ‒ S) ‒ β(t)SI

(d/dt)E = β(t)SI ‒ (µ + b)E

(d/dt)I = µE ‒ (ν + b)I

R = 1 ‒ S ‒ I ‒ E

where β(t) is the rate at which an infected individual infects a susceptible one, µ is the inverse latency time, ν is the recovery rate and b is the population turn-over rate. Depending on the analysis below, we implement several such populations that exchange individuals through migration, for details see Supplementary Methods. Stochasticity is implemented through Poisson resampling of the population once every serial interval µ−1 + (ν + b)−1.

The population turnover b rate is immaterial for a pandemic scenario, but important for our analysis of seasonal CoVs, and should be interpreted as the sum of the birth rate and the rate at which previously immune individuals become susceptible due to immune waning and escape. We review general properties of such model in the supplementary materials. Following previous work, we parameterise transmissibility as (equation 2)

β(t) = β0 (1 + ε cos(2π(t − θ)))

where β0 is the average annual infection rate, ε is the amplitude of seasonal forcing which modulates transmissibility through the year, and θ is the time of peak transmissibility [2728]. For simulations of the pandemic, we will add an additional term to β(t) that accounts for infection control measures in heavily affected areas, see supplementary materials.

Model parametrisation using seasonal CoV observations

Seasonal CoVs are endemic throughout the world and we therefore expect that viruses are imported throughout the year.

We model this import through migration of susceptible individuals with rate m that return exposed with probability x. Humans develop immune responses to CoVs rapidly and subsequent challenge studies show reduced susceptibility and less severe disease for a year [29].

Antibodies against SARS-CoV1 persist for several years [30].This is consistent with the observation that about 50% of all positive samples in our data come from patients older than 10 years with a flat distribution across age groups.

In analogy to the attack rate of seasonal influenza, we assume humans suffer from a seasonal CoV infection on average every 10 years (b = 0.1/y). Furthermore, we use (R0) = 2.3, a recovery rate of 0.2 days−1, and an incubation period of 5 days.

With these assumptions, we can solve the model and compare the resulting trajectories to the seasonal variation in prevalence of seasonal CoVs, see figure 2.

In Stockholm, seasonal variation of CoVs (especially HKU1/OC43) is very consistent across years (see supplementary figure S3 in appendix 1). We therefore fit the SIER model to the average seasonal variation across years by calculating the squared deviation of observed and predicted prevalence relative to their respective mean values.

Simulations of the model are compatible with observations in two separate regions of parameter space: If Northern Europe was very isolated with less than 1 in 1,000 susceptible individuals returning with a seasonal CoV infection from abroad each year, weak seasonality of around ε = 0.15 would be sufficient to generate strong variation through the year compatible with observations (fig. 2, bottom-left ridge).

In this regime, prevalence is oscillating intrinsically with a period that is commensurate with annual seasonal oscillations giving rise to a resonance phenomenon with annual or biennial patterns even for weak seasonal forcing [2728].

Figure 2
Compatibility of SEIR model trajectories with observations. The heatmap shows the inverse mean squared deviation between the model trajectories and the observed seasonal forcing in seasonal CoV prevalence. Model and observations are compatible (yellow shading) in a region of parameter values corresponding to low migration/weak seasonality and second region at high migration/strong seasonality. Migration refers to the rate per year of a susceptible to return from a abroad with a CoV infection.

If the rate of import of seasonal CoV infections is higher, imports dampen the resonance and much stronger seasonality, with values between ε = 0.3 and 0.7, is required to fit the observations (fig. 2, top-right-and-centre ridge). In this regime, seasonal variation in transmissibility modulates the size of micro-outbreaks triggered by imported cases in a mostly immune population.

These two scenarios differ slightly in the time of year at which peak transmissibility θ occurs: When transmission is mostly local and seasonality is amplified by resonance, θ needs to be around October–November to fit the data with most cases in December–January.

In the second scenario with high connectivity, θ needs to be in December–January coinciding with the peak in prevalence. Given that most countries are highly connected, we focus here on exploring the high-import and strong seasonal forcing scenario.

This scenario, with maximal β in mid-winter, is also more compatible with climate variation around the year. The qualitative behaviour of the fit is robust to uncertainty in R0 and the frequency of reinfection b.

Scenarios for SARS-CoV-2 pandemics in 2020 and 2021

The analysis of seasonal CoV prevalence patterns allowed us to constrain parameter ranges and explore different scenarios of SARS-CoV-2 spread around the globe, in particular in temperate climates like Northern Europe.

Here we explore scenarios where temperate regions have a seasonal forcing of between ε = 0.3 and 0.7 and migration rates of 0.01/year. Early estimates suggest an incubation time of about 5 days and an average serial interval of 7–8 days [11]. Our model uses an average latency time of 5 days [31] and an infectious period of 5 days.

To match the R0 estimates for the early outbreak with our parameterisation of transmissibility in equation 2 we need to account for the fact that December/January are winter months in Hubei and peak transmissibility in Hubei likely corresponds to θ ≈ 0 (0 being the beginning of the year, so a θ in December/January).

An R0 ≈ 3 in winter in Hubei and a seasonal forcing of ε = 0.4 implies an annual average ‹R0› = β0/ν = 2.2. This reasoning leads to our parameter choice of β0 = 158/year, ν = 72/year, θ = 0. We assume the outbreak started at t = 2019.8 in Hubei with one infected individual and use N = 6 × 107 as population size.

To incorporate infection control measures, transmissibility is reduced by 50% once prevalence reached 3% (third order Hill-function, see appendix 1). Introductions to a location like Northern Europe with ε = 0.5 (i.e., slightly stronger seasonal forcing then Hubei) are assumed to happen at a rate of 0.01 per year for each infected individual elsewhere.

The simulation of the SIER model in different regions is deterministic, but migration is implemented stochastically by Poisson resampling of the average number of migrating individuals. Figure 3 shows simulated trajectories of SARS-CoV-2 prevalence in the temperate Northern Hemisphere assuming the outbreak started in Hubei early December 2019.

Depending whether the peak transmissibility of SARS-CoV-2 in the northern temperate zone is in November, January or March, the simulation predicts a main peak in the first half of 2020, a main peak in winter 2020/2021, or two similarly sized peaks.

Figure 3
Model predictions for SARS-CoV-2 case numbers in temperate zones for a pandemic scenario. Panel A shows example trajectories assuming SARS-CoV-2 transmissibility peaks in November, January, or March. These outbreaks in Northern Europe (‘NE’) are assumed to be seeded by the outbreak in Hubei (model trajectory shown as a dashed line). Within the model, these cases are exported at rate of 0.01/year to temperate Northern Europe with an average ‹R0› = 2.2 and seasonal forcing of ε = 0.5. Corresponding graphs for different values of (R0) and the migration rate are shown in supplementary figure S4. Panel B shows the ratio of the first and second peak for a range of different combinations of R0 and θ. The yellow area corresponds to parameter combinations with essentially only an early peak similar to the yellow line on the left. The blue/purple area shows parameter combinations for which a peak in late 2020 dominates, as with the purple line on the left, while the central pink/orange band shows the combinations giving rise to two comparable peaks. These simulations are for ε = 0.5. Similar re

To explore possible scenarios more systematically, we ran such simulations for a range of values for R0 and peak transmissibility θ and recorded whether we observe and early peak, a late peak, or two peaks.

The right panel of figure 3 shows the ratio of the height of these peaks for different values. Rapid growth (high R0) and late transmission peaks result in a large peak in the first half 2020, while lower R0 and transmission peaks in early winter favour a large secondary peak.

These two scenarios are separated by a band of parameter values that give rise to two pandemic waves in the winters of 2020 and 2021 in the Northern Hemisphere. Individual trajectories for a variety of parameter combinations are given in figure S4.

The qualitative behaviour is robust to model perturbations and parameter variation as long as seasonal forcing is strong. With weak forcing (ε = 0.15), the model predicts a single peak for most combinations of (R0) and migration rates (see figure S5 in appendix 1).

The uncertainty in parameter values and the potential impact of infection control measures imply that all scenarios are plausible and should be considered when developing pandemic prevention and containment strategies.

Global projections

In absence of control measures, outbreaks initially grow exponentially within well-mixed communities, and at a certain rate the virus will be carried to other regions and potentially seed new outbreaks.

Such export to new locations is initially unlikely, but becomes next to certain once the outbreak size exceeds the inverse probability that a given individual migrates while infected. We have witnessed such rapid dispersal to SARS-CoV-2 to many countries across the globe during January and February 2020.

Every location has a different socio-economic profile such that the growth rate of the epidemic (and hence R0) might differ. The superposition of many such subpopulations with a range of ‹R0› values and seasonal variation in transmission will result in dynamics that are qualitatively different from a single population SIR model.

In particular, such variation result in a pandemic spread out over 2 years before the virus possibly becomes endemic.

Figure 4 shows the result of such a simulation of 1000 populations. Populations were divided between northern temperate (50%), southern temperate (10%), and tropical (40%) and assigned parameters as follows:

  • ‹R0› was drawn from a normal distribution with mean 2.2 (see figure S7 in appendix 1 for ‹R0› = 1.5 and 3.0) and standard deviation 0.5.
  • Seasonal forcing ε was drawn from a uniform distribution between 0.25 and 0.75 for temperate regions, between 0 and 0.2 for tropical regions.
  • Peak transmissibility θ of temperate regions was drawn from normal distributions with standard deviation 0.1 and peak at 0 for northern regions and 0.5 for southern regions; θ for tropical regions was chosen uniformly from between 0 and 1.
  • Population sizes were drawn from a log-normal distribution with σ = 1 and a mean such that all populations sum to 7.6 billion.
  • Migration rates were sampled from a log-normal distribution with σ = 1 and a mean of 0.01.
Figure 4
Extended circulation through overlapping epidemics in variable subpopulations. These simulations of a pandemic scenario assume 1,000 sub-populations with an average ‹R0› of 2.2 and standard deviation 0.5, 40% of which have weak seasonal forcing ε ∈ [0, 0.2] (tropical) and the remainder have strong variation with ε ∈ [0.25, 0.75]. The super-position of many variable epidemics can result in a global prevalence that decays only slowly through 2020 and 2021. Lighter lines have lower R0, darker lines have higher R0. The actual observed case counts reported for Hubei are added (brown line) and multiplied by three to account for possible under-reporting of mild cases. A subset of 30 randomly chosen simulations are plotted for each region. Analogous figures for different R0 parameter values are shown in figure S7 (appendix 1).

For Hubei, we use the same parameters as described in the previous section “Scenarios for SARS-CoV-2 pandemics in 2020 and 2021”.

The variation in R0 and migration rate result in a super-position of fast and slow epidemics seeded at different times. The initial phase is dominated by fast epidemics driving rapid dispersal, in particular in the tropics, while slow epidemics dominate later in 2020 and 2021.

With the parameter setting used in figure 4, the Northern temperate regions see most circulation in winter 2020/2021. In accordance with figure 3, this peak shifts more towards early 2020 for higher R0, see figure S7 (appendix 1).

After several years, SARS-CoV-2 could become a seasonal CoV with characteristic winter outbreaks as shown in figure 1. Such a scenario is demonstrated in figure 5 where a simulation similar to the one shown in figure 4 is run for 12 years, with the added assumption that after infection an individual become susceptible to SARS-CoV-2 again at a rate of 0.1 per year as we assumed for seasonal CoV above. After a pronounced low in 2020–2024, prevalence recovers and settles into a seasonal pattern, similar to that of the four existing seasonal CoVs.

Figure 5
Transition to an endemic seasonal virus. If previously infected individuals can be reinfected after some time, as for example by seasonal influenza virus, SARS-CoV-2 could develop into a seasonal CoV that returns every winter. This would typically happen at much lower prevalence than peak pandemic levels. These simulations assume reinfection on average every 10 years.

Code and data availability

All relevant data and script that generate the graphs are available in a dedicated github repository at

Karolinska Institute


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Appendix 1

Impact of seasonal forcing on a potential SARS-CoV-2 pandemic

The appendix is available as a separate file for downloading at:


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