**Background**: As the SARS-Cov-2/Covid-19 pandemic continues to ravage the world, it is important to understanding the characteristics of its spread and possible correlates for control to develop strategies of response.

**Methods: **Here we show how a simple Susceptible-Infective-Recovered (SIR) model applied to data for eight European countries and the United Kingdom (UK) can be used to forecast the descending limb (post-peak) of confirmed cases and deaths as a function of time, and predict the duration of the pandemic once it has peaked, by estimating and fixing parameters using only characteristics of the ascending limb and the magnitude of the first peak.

**Results: **The predicted and actual case fatality ratio, or number of deaths per million population from the start of the pandemic to when daily deaths number less than five for the first time, was lowest in Norway (predicted: 44 5 deaths/million; actual: 36 deaths/million) and highest for the United Kingdom (predicted: 578 +/- 65 deaths/million; actual 621 deaths/million). The inferred pandemic characteristics separated into two distinct groups: those that are largely invariant across countries, and those that are highly variable. Among the former is the infective period, TL = 16.3 2.7 days, the average time between contacts, TR = 3.8+/- 0.5 days and the average number of contacts while infective R = 4.4 +/- 0.5. In contrast, there is a highly variable time lag TD between the peak in the daily number of confirmed cases and the peak in the daily number of deaths, ranging from lows of TD = 2,4 days for Denmark and Italy respectively, to highs of TD = 12, 15 for Germany and Norway respectively. The mortality fraction, or ratio of deaths to confirmed cases, was also highly variable, ranging from low values 3%, 5% and 5% for Norway, Denmark and Germany respectively, to high values of 18%, 20% and 21% for Sweden, France, and the UK respectively. The probability of mortality rather than recovery was a significant correlate of the duration of the pandemic, defined as the time from 12/31/2019 to when the number of daily deaths fell below 5. Finally, we observed a small but detectable effect of average temperature on the probability of infection per contact, with higher temperatures associated with lower infectivity.

**Conclusions:** Our simple model captures the dynamics of the initial stages of the pandemic, from its exponential beginning to the first peak and beyond, with remarkable precision. As with all epidemiological analyses, unanticipated behavioral changes will result in deviations between projection and observation. This is abundantly clear for the current pandemic. Nonetheless, accurate short-term projections are possible, and the methodology we present is a useful addition to the epidemiologist's armamentarium. Our predictions assume that control measures such as lockdown, social distancing, use of masks etc. remain the same post-peak as before peak. Consequently, deviations from our predictions are a measure of the extent to which loosening of control measures have impacted case-loads and deaths since the first peak and initial decline in daily cases and deaths. Our findings suggest that the two key parameters to control and reduce the impact of a developing pandemic are the infective period and the mortality fraction, which are achievable by early case identification, contact tracing and quarantine (which would reduce the former) and improving quality of care for identified cases (which would reduce the latter).

Figure 1

Figure 2

Figure 3

Figure 4

This preprint is available for download as a PDF.

This is a list of supplementary files associated with this preprint. Click to download.

- FigS1.JPG
Figure S1: Parameter fits for the number of daily cases plotted on a linear scale: These plots are the same as those in Figure 2 except that the y axis is shown in a linear scale, rather than a log scale. This is to show the accuracy of the fits which are shown as solid lines. Blue circles are observed data for X_2 (t), the number of cases per day. Solid lines are fits obtained by solving (8) and (9) using the ODE solver ode45 in Matlab. The values of the parameters are shown in the insets and represent the fit shown as the solid red line. The method used for the fits was to find γ(R-1) from the exponential rise in X_2 at early times (Appendix A), estimate the peak value P of X_2 (which gives the value of N using (15)) and find an R value that best fits the data (red solid line). The black lines represent solver results for R varying by 0.5 from the best fit value.

- AppendixA.pdf
- Table1.pdf
Table showing a summary of all results for all 9 countries.

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Posted 29 Oct, 2020

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Posted 29 Oct, 2020

###### No community comments so far

**Background**: As the SARS-Cov-2/Covid-19 pandemic continues to ravage the world, it is important to understanding the characteristics of its spread and possible correlates for control to develop strategies of response.

**Methods: **Here we show how a simple Susceptible-Infective-Recovered (SIR) model applied to data for eight European countries and the United Kingdom (UK) can be used to forecast the descending limb (post-peak) of confirmed cases and deaths as a function of time, and predict the duration of the pandemic once it has peaked, by estimating and fixing parameters using only characteristics of the ascending limb and the magnitude of the first peak.

**Results: **The predicted and actual case fatality ratio, or number of deaths per million population from the start of the pandemic to when daily deaths number less than five for the first time, was lowest in Norway (predicted: 44 5 deaths/million; actual: 36 deaths/million) and highest for the United Kingdom (predicted: 578 +/- 65 deaths/million; actual 621 deaths/million). The inferred pandemic characteristics separated into two distinct groups: those that are largely invariant across countries, and those that are highly variable. Among the former is the infective period, TL = 16.3 2.7 days, the average time between contacts, TR = 3.8+/- 0.5 days and the average number of contacts while infective R = 4.4 +/- 0.5. In contrast, there is a highly variable time lag TD between the peak in the daily number of confirmed cases and the peak in the daily number of deaths, ranging from lows of TD = 2,4 days for Denmark and Italy respectively, to highs of TD = 12, 15 for Germany and Norway respectively. The mortality fraction, or ratio of deaths to confirmed cases, was also highly variable, ranging from low values 3%, 5% and 5% for Norway, Denmark and Germany respectively, to high values of 18%, 20% and 21% for Sweden, France, and the UK respectively. The probability of mortality rather than recovery was a significant correlate of the duration of the pandemic, defined as the time from 12/31/2019 to when the number of daily deaths fell below 5. Finally, we observed a small but detectable effect of average temperature on the probability of infection per contact, with higher temperatures associated with lower infectivity.

**Conclusions:** Our simple model captures the dynamics of the initial stages of the pandemic, from its exponential beginning to the first peak and beyond, with remarkable precision. As with all epidemiological analyses, unanticipated behavioral changes will result in deviations between projection and observation. This is abundantly clear for the current pandemic. Nonetheless, accurate short-term projections are possible, and the methodology we present is a useful addition to the epidemiologist's armamentarium. Our predictions assume that control measures such as lockdown, social distancing, use of masks etc. remain the same post-peak as before peak. Consequently, deviations from our predictions are a measure of the extent to which loosening of control measures have impacted case-loads and deaths since the first peak and initial decline in daily cases and deaths. Our findings suggest that the two key parameters to control and reduce the impact of a developing pandemic are the infective period and the mortality fraction, which are achievable by early case identification, contact tracing and quarantine (which would reduce the former) and improving quality of care for identified cases (which would reduce the latter).

Figure 1

Figure 2

Figure 3

Figure 4

This preprint is available for download as a PDF.

This is a list of supplementary files associated with this preprint. Click to download.

- FigS1.JPG
Figure S1: Parameter fits for the number of daily cases plotted on a linear scale: These plots are the same as those in Figure 2 except that the y axis is shown in a linear scale, rather than a log scale. This is to show the accuracy of the fits which are shown as solid lines. Blue circles are observed data for X_2 (t), the number of cases per day. Solid lines are fits obtained by solving (8) and (9) using the ODE solver ode45 in Matlab. The values of the parameters are shown in the insets and represent the fit shown as the solid red line. The method used for the fits was to find γ(R-1) from the exponential rise in X_2 at early times (Appendix A), estimate the peak value P of X_2 (which gives the value of N using (15)) and find an R value that best fits the data (red solid line). The black lines represent solver results for R varying by 0.5 from the best fit value.

- AppendixA.pdf
- Table1.pdf
Table showing a summary of all results for all 9 countries.

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