Intensity and frequency of extreme novel epidemics.

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, Py, vary widely: Py 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.

A kernel-modulated SIR model for Covid-19 contagious spread from county to continent.

The tempo-spatial patterns of Covid-19 infections are a result of nested personal, societal, and political decisions that involve complicated epidemiological dynamics across overlapping spatial scales. High infection "hotspots" interspersed within regions where infections remained sporadic were ubiquitous early in the outbreak, but the spatial signature of the infection evolved to affect most regions equally, albeit with distinct temporal patterns. The sparseness of Covid-19 infections in the United States was analyzed at scales spanning from 10 to 2,600 km (county to continental scale). Spatial evolution of Covid-19 cases in the United States followed multifractal scaling. A rapid increase in the spatial correlation was identified early in the outbreak (March to April). Then, the increase continued at a slower rate and approached the spatial correlation of human population. Instead of adopting agent-based models that require tracking of individuals, a kernel-modulated approach is developed to characterize the dynamic spreading of disease in a multifractal distributed susceptible population. Multiphase Covid-19 epidemics were reasonably reproduced by the proposed kernel-modulated susceptible-infectious-recovered (SIR) model. The work explained the fact that while the reproduction number was reduced due to nonpharmaceutical interventions (e.g., masks, social distancing, etc.), subsequent multiple epidemic waves still occurred; this was due to an increase in susceptible population flow following a relaxation of travel restrictions and corollary stay-at-home orders. This study provides an original interpretation of Covid-19 spread together with a pragmatic approach that can be imminently used to capture the spatial intermittency at all epidemiologically relevant scales while preserving the "disordered" spatial pattern of infectious cases.

Population agglomeration is a harbinger of the spatial complexity of COVID-19.

The spatial template over which COVID-19 infections operate is a result of nested societal decisions involving complex political and epidemiological processes at a broad range of spatial scales. It is characterized by 'hotspots' of high infections interspersed within regions where infections are sporadic to absent. In this work, the sparseness of COVID-19 infections and their time variations were analyzed across the US at scales ranging from 10 km (county scale) to 2600 km (continental scale). It was found that COVID-19 cases are multi-scaling with a multifractality kernel that monotonically approached that of the underlying population. The spatial correlation of infections between counties increased rapidly in March 2020; that rise continued but at a slower pace subsequently, trending towards the spatial correlation of the population agglomeration. This shows that the disease had already spread across the USA in early March such that travel restriction thereafter (starting on March 15th 2020) had minor impact on the subsequent spatial propagation of COVID-19. The ramifications of targeted interventions on spatial patterns of new infections were explored using the epidemiological susceptible-infectious-recovered (SIR) model mapped onto the population agglomeration template. These revealed that re-opening rural areas would have a smaller impact on the spread and evolution of the disease than re-opening urban (dense) centers which would disturb the system for months. This study provided a novel way for interpreting the spatial spread of COVID-19, along with a practical approach (multifractals/SIR/spectral slope) that could be employed to capture the variability and intermittency at all scales while maintaining the spatial structure.

Global convergence of COVID-19 basic reproduction number and estimation from early-time SIR dynamics.

The SIR ('susceptible-infectious-recovered') formulation is used to uncover the generic spread mechanisms observed by COVID-19 dynamics globally, especially in the early phases of infectious spread. During this early period, potential controls were not effectively put in place or enforced in many countries. Hence, the early phases of COVID-19 spread in countries where controls were weak offer a unique perspective on the ensemble-behavior of COVID-19 basic reproduction number Ro inferred from SIR formulation. The work here shows that there is global convergence (i.e., across many nations) to an uncontrolled Ro = 4.5 that describes the early time spread of COVID-19. This value is in agreement with independent estimates from other sources reviewed here and adds to the growing consensus that the early estimate of Ro = 2.2 adopted by the World Health Organization is low. A reconciliation between power-law and exponential growth predictions is also featured within the confines of the SIR formulation. The effects of testing ramp-up and the role of 'super-spreaders' on the inference of Ro are analyzed using idealized scenarios. Implications for evaluating potential control strategies from this uncontrolled Ro are briefly discussed in the context of the maximum possible infected fraction of the population (needed to assess health care capacity) and mortality (especially in the USA given diverging projections). Model results indicate that if intervention measures still result in Ro > 2.7 within 44 days after first infection, intervention is unlikely to be effective in general for COVID-19.