Ecology

Affiliations

Ecosystem Dynamics and Forest Management Group, Technical University of Munich, Freising, Germany
Cornelius Senf & Rupert Seidl

Institute for Silviculture, University of Natural Resources and Life Sciences (BOKU), Vienna, Austria
Cornelius Senf & Rupert Seidl

Berchtesgaden National Park, Berchtesgaden, Germany
Rupert Seidl

Authors
Cornelius Senf

Rupert Seidl

Corresponding author
Correspondence to Cornelius Senf. More

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Characteristics of the NMs
Commercially available spherical (10, 60, and 100 nm) and rod-shaped (10 × 45 nm and 50 × 100 nm) citrate-coated Au-NMs from Nanopartz (USA) were characterized in Milli-Q (MQ) water in terms of particle size and morphology using transmission electron microscopy (TEM) (Supplementary Fig. 1). The physicochemical properties of the Au-NMs in MQ water are summarized in Supplementary Table 1. A negative zeta potential (a measure of colloidal dispersion electrostatic stability) was observed for all Au-NMs and ranged from −21 to −25 mV in MQ water and from −17 to −19 mV in the algal exposure medium (without algae). The stability of the particles against dissolution and agglomeration in the algal exposure medium without algae was monitored throughout the exposure duration (72 h). The dissolved fraction of the Au-NMs was More

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Wintertime outbreaks in the northern hemisphere
In Fig. 1a we use case data (see “Methods”) to estimate the effective reproductive number of infection for New York City from the start of 2020 to the present (July 2020)14. Estimated values of Reffective peak early in the outbreak and then settle close to 1 in the summer months as NPIs act to lower transmission. We assume the Reffective values approximate R0 and compare them to the predicted seasonal R0, derived from our climate-driven SIRS model. The model assumes the climate sensitivity of betacoronavirus HKU1 and that seasonal variations in transmission are driven by specific humidity. Current rates (average over second and third weeks of July) of Reffective in New York city are found to be approximately 35% below the R0 levels predicted by our climate-driven model. We assume this 35% decline is due to the efficacy of NPIs. To project future scenarios we assume that R0 remains at either the current levels (constant) or a relative 35% decrease in our climate-driven R0, which means R0 oscillates with specific humidity (Fig. 1a, top plot).
Fig. 1: Wintertime outbreaks in New York City.

Estimated and projected R0 values (top plot) assuming a 35% and b 15% reduction in R0 due to NPIs. Corresponding time series show the simulated outbreaks in the climate (blue) or constant (black/dashed) scenarios, with middle row plots assuming a 10% reporting rate and bottom row plots assuming a 3% reporting rate. Corresponding susceptible time series are shown in orange (susceptibles = S/population = N). Case data from New York City are shown in gray. Surface plots (top) show the peak wintertime proportion infected (infected = I/population = N) in the scenarios with c the constant R0 and d the climate-driven R0. e shows the difference between the climate and constant R0 scenario. The timing of peak incidence in years from July is shown for the f constant and g climate scenarios. The difference between climate and constant scenario is shown in h. Points in c–h show the scenarios is a, b. Dashed line shows estimated susceptibility in New York based on ref. 24.

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In Fig. 1a (lower plots) we show the proportion infected over time using the climate-driven and constant R0 values. We also vary the reporting rate of observed cases relative to modeled cases; while this accounts for under-reporting it also allows us to vary the proportion susceptible over a feasible range (see “Methods”). In the middle figure, the reporting rate is 10% (estimates for US reporting rates are  1 for both the climate and constant scenario and case numbers begin to grow exponentially. With a 10% reporting rate a large secondary outbreak is observed in both the constant and climate scenarios (Fig. 1b, middle plot). With a 3% reporting rate, meaning a larger depletion of susceptibles, the secondary outbreak appears much larger in the climate scenario: this supports the hypothesis that the disease will become more sensitive to climate as the susceptible proportion declines, much like the seasonal endemic diseases.
In Fig. 1c–h we simulate model outcomes across a broad range of parameter space varying the proportion susceptible (in July) and the reduction in R0 due to NPIs. The proportion susceptible is varied by initializing the epidemic with different sizes of the infected population (initializing with a large number results in a relatively larger outbreak and initializing with a small number results in a smaller outbreak). We vary this starting number over a feasible range given the case data, i.e., such that observed cases never exceed modeled cases or that the reporting rate never drops below 1%. Over this range, the model plausibly tracks the observed case data.
Figure 1e shows the change in winter peak size (max proportion infected between September–March) due to climate. Peak size results for the constant and climate scenarios are shown in Fig. 1c and d, respectively. When the susceptible proportion is high and the effect of NPIs are minimal (relative R0 given NPI = 1), large outbreaks are possible in both the climate and constant R0 scenarios meaning the relative effect of climate on peak size and timing is close to 0 (top right Fig. 1e). As the proportion susceptible declines (moving left along the x-axis of Fig. 1e), case trajectories become more sensitive to the wintertime weather resulting in larger peaks in the climate scenario. However, sufficiently strong NPIs, in combination with low susceptibility, reduce incidence to zero in both the climate and control scenarios (bottom left Fig. 1e). NPIs are not as effective at reducing cases when susceptibility is higher (bottom right Fig. 1e).
We also consider the effect of climate on secondary peak timing. Figure 1f, g shows the peak timing in years (relative to July 2020) in the constant and climate scenarios, respectively. In the climate scenario, peak timing for New York is clustered in the winter months (Fig. 1a, b). In the constant R0 scenario, secondary peaks can occur at a wide range of times over the next 1.5 years. As in the peak size results, high susceptibility and limited NPIs reduce the effect of climate and peak timing is matched for both the climate and control scenarios (top right Fig. 1h). Gray areas represent regions where there is no secondary peak in either the climate or control scenario.
Climate effects on global risk
We next consider the relative effect of climate on peak size for nine global locations (Fig. 2b). In this case, as opposed to using estimated Reffective values (given case data are not available for several of the global cities), we simulate the epidemic from July 2020 using a fixed number of infecteds and vary the starting proportion of susceptibles (example results from select global locations, using estimated Reffective, are shown in Supplementary Figs. 1–3). Results from the New York surface in Fig. 2b qualitatively match our tailored simulation in Fig. 1. Locations in the southern hemisphere are expected to be close to their maximum wintertime R0 values in mid-2020 (Fig. 2a), meaning that secondary peaks in the climate scenario are lower than the constant R0 scenario for these locations (Fig. 2b). Tropical locations experience minimal difference in the climate versus constant R0 scenario given the relatively mild seasonal variations in specific humidity in the tropics. Broadly, the results across hemisphere track the earlier results from New York: high susceptibility and a lack of NPIs lead to a limited role of climate, but an increase in NPI efficacy or a reduction in susceptibility may increase climate effects. This result is more striking in regions with a large seasonality in specific humidity (e.g. New York, Delhi and Johannesburg).
Fig. 2: Climate sensitivity of outbreaks across global locations.

a The climate effect on R0 assuming a 35% reduction due to NPIs shown for August and December. b The effect of climate, changing susceptibility, and NPIs on peak proportion infected (infected = I/population = N), post July 2020, for nine global locations.

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Drivers of variability in secondary outbreak size
Our results suggest that climate may play an increasing role in determining the future course of the SARS-CoV-2 pandemic, depending on levels of susceptibility and NPIs. We next evaluate the extent to which interannual variability in specific humidity could influence peak size. We simulate separate New York pandemic trajectories using 11 years (2008–2018) of specific humidity data. Figure 3a shows the variability in R0 and secondary peak size based on these runs (with 35% reduction in R0 due to NPIs and 10% reporting rate—the same as Fig. 1a). While a relatively large peak occurs in all years, the largest peak (0.038 proportion infected) is almost double the smallest peak year (0.020 proportion infected). In Fig. 3b we calculate the coefficient of variation of the peak size for different susceptible proportions and NPI intensities. These results qualitatively track Fig. 1e. Sensitivity to interannual variation appears most important when the susceptible population has been reduced by at least 20% and minimal controls are in place.
Fig. 3: Climate variability and wintertime cases in New York.

a Climate-driven R0 and corresponding infected time series (infected = I/population = N) based on the last 10 years of specific humidity data for New York, assuming a 35% reduction due to NPIs. b The effect of changing susceptibility and NPIs on the coefficient of variation of peak incidence for simulations using specific humidity data from 2008 to 2018. Dashed line shows estimated susceptibility in New York based on ref. 24.

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Many factors, including weather variability, determine the size of a possible secondary outbreak. Another factor that may play an important role is the length of immunity to the disease. While the length of immunity may not affect the dynamics in the early stage of the pandemic, it could have complex and uncertain outcomes for future trajectories16. In our main results, we assume a length of immunity equal to betacoronvirus HKU1, based on prior estimates1. We also assume a climate sensitivity based on estimates for HKU1. However parameters for SARS-CoV-2, such as immunity length and climate sensitivity, are still fundamentally uncertain.
We consider the possible contribution of uncertainty in parameters to the variance in the wintertime peak size following the method developed by Yip et al.17 (see “Methods”). We run our simulation for New York while varying parameter values for the efficacy of NPIs, the length of immunity to the disease, the reporting rate of prior cases (which defines susceptibility in July), the climate sensitivity of the pathogen (in terms of the strength of the relationship with specific humidity), and the weather variability (interannual variability determined by historic weather observations from a particular year, 2009–2018). We then perform an analysis of variance (ANOVA) on the determinants of wintertime peak size.
Figure 4 shows contribution to variance in wintertime peak size of these five parameters: NPIs efficacy, immunity length, reporting rate, climate sensitivity of the virus, and interannual weather variability. We find that climate sensitivity is an important factor but secondary to the efficacy of NPIs and immunity length in determining peak transmission. Uncertainty in immunity length and reporting together influence susceptibility and collectively account for the second largest portion of total uncertainty. Uncertainty in interannual variability, i.e. weather, has a smaller impact on peak size. NPIs contribute the largest proportion to total variance in peak size. It is important to note that while other parameters are external features of either the virus, climate, or disease trajectories to date, the efficacy of NPIs is determined directly by policy interventions and therefore the size of future outbreaks is largely under human control.
Fig. 4: Contribution to uncertainty in New York wintertime 20/21 peak size.

The relative importance of NPI efficacy [0–35%], immunity length (10–60 weeks), reporting (1–100%), climate sensitivity of the virus [−32.5 to −227.5], and interannual weather variability [10 years] in determining wintertime peak size. Immunity length and reporting rate collectively determine susceptibility, S.

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