Intensity and frequency of extreme novel epidemics

Abstract

Observational knowledge of the epidemic intensity, defined as the number of deaths divided by global population and epidemic duration, and of the rate of emergence of infectious disease outbreaks is necessary to test theory and models and to inform public health risk assessment by quantifying the probability of extreme pandemics such as COVID-19. Despite its significance, assembling and analyzing a comprehensive global historical record spanning a variety of diseases remains an unexplored task. A global dataset of historical epidemics from 1600 to present is here compiled and examined using novel statistical methods to estimate the yearly probability of occurrence of extreme epidemics. Historical observations covering four orders of magnitude of epidemic intensity follow a common probability distribution with a slowly decaying power-law tail (generalized Pareto distribution, asymptotic exponent = -0.71). The yearly number of epidemics varies ninefold and shows systematic trends. Yearly occurrence probabilities of extreme epidemics, P_y, vary widely: P_y of an event with the intensity of the "Spanish influenza" (1918 to 1920) varies between 0.27 and 1.9% from 1600 to present, while its mean recurrence time today is 400 y (95% CI: 332 to 489 y). The slow decay of probability with epidemic intensity implies that extreme epidemics are relatively likely, a property previously undetected due to short observational records and stationary analysis methods. Using recent estimates of the rate of increase in disease emergence from zoonotic reservoirs associated with environmental change, we estimate that the yearly probability of occurrence of extreme epidemics can increase up to threefold in the coming decades.

Keywords: epidemics; extremes; infectious diseases.

Fig. 1.

Empirical exceedance frequency of epidemic intensity i (open circles). Black solid lines show the 95% CI around these empirical frequencies (29). The red line is the GPD distribution obtained from maximum likelihood fitting for i ≥ μ = 1.000 × 10⁻³ ‰/year (μ being the position parameter, scale parameter σ = 0.0113 ‰/year, and shape parameter ξ = 1.40). The value P(i ≤ μ) = 0.62 is determined from the number of observed intensities below μ (244 out of 395, including epidemics—105—for which the number of deaths is not available, but historical information suggests i ≤ μ). The GPD, for large values of its argument, becomes a power law with exponent α = −1/ξ ≅ −0.71. The value $\left|\alpha \right|<1$ denotes a fat-tail behavior in which the probability of intense events decreases slowly with event intensity. The gray area results from the overlap of the 10,000 GPD distributions fitted to sample realizations obtained by applying to each observed intensity a random perturbation uniformly distributed in [−50%, +50%] to account for uncertainties in historical records.

Fig. 2.

(A) Yearly probability of exceedance, H₁(i = 5.7 ‰/year), of an epidemic with the same intensity as the Spanish influenza or greater at different times in history (red). The gray area represents the 95% CI computed from 10,000 realizations obtained by randomly perturbing each historical observation with a perturbation in the range [−50%, +50%] (gray area in Fig. 1). Note that fitting a standard, stationary GEV distribution yields a constant and misleadingly low probability of occurrence. (B) Probability of exceedance of maximum yearly epidemic intensity computed on the basis of the number of epidemic occurrences in the most recent 2000 to 2019 period. Gray area represents the 95% CI as in A.