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Register a new userGlobal disease spread: statistics and estimation of arrival times
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Authors
Aurelien Gautreau
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We study metapopulation models for the spread of epidemics in which different subpopulations (cities) are connected by fluxes of individuals (travelers). This framework allows to describe the spread of a disease on a large scale and we focus here on the computation of the arrival time of a disease as a function of the properties of the seed of the epidemics and of the characteristics of the network connecting the various subpopulations. Using analytical and numerical arguments, we introduce an easily computable quantity which approximates this average arrival time. We show on the example of a disease spread on the world-wide airport network that this quantity predicts with a good accuracy the order of arrival of the disease in the various subpopulations in each realization of epidemic scenario, and not only for an average over realizations. Finally, this quantity might be useful in the identification of the dominant paths of the disease spread.
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Metapopulation models describing cities with different populations coupled by the travel of individuals are of great importance in the understanding of disease spread on a large scale. An important example is the Rvachev-Longini model [{it Math. Biosci.} {bf 75}, 3-22 (1985)] which is widely used in computational epidemiology. Few analytical results are however available and in particular little is known about paths followed by epidemics and disease arrival times. We study the arrival time of a disease in a city as a function of the starting seed of the epidemics. We propose an analytical Ansatz, test it in the case of a spreading on the world wide air transportation network, and show that it predicts accurately the arrival order of a disease in world-wide cities.
Major advances in public health have resulted from disease prevention. However, prevention of a new infectious disease by vaccination or pharmaceuticals is made difficult by the slow process of vaccine and drug development. We propose an additional intervention that allows rapid control of emerging infectious diseases, and can also be used to eradicate diseases that rely almost exclusively on human-to-human transmission. The intervention is based on (1) testing every individual for the disease, (2) repeatedly, and (3) isolation of infected individuals. We show here that at a sufficient rate of testing, the reproduction number is reduced below 1.0 and the epidemic will rapidly collapse. The approach does not rely on strong or unrealistic assumptions about test accuracy, isolation compliance, population structure or epidemiological parameters, and its success can be monitored in real time by following the test positivity rate. In addition to the compliance rate and false negatives, the required rate of testing depends on the design of the testing regime, with concurrent testing outperforming random sampling. Provided that results are obtained rapidly, the test frequency required to suppress an epidemic is monotonic and near-linear with respect to R0, the infectious period, and the fraction of susceptible individuals. The testing regime is effective against both early phase and established epidemics, and additive to other interventions (e.g. contact tracing and social distancing). It is also robust to failure: any rate of testing reduces the number of infections, improving both public health and economic conditions. These conclusions are based on rigorous analysis and simulations of appropriate epidemiological models. A mass-produced, disposable test that could be used at home would be ideal, due to the optimal performance of concurrent tests that return immediate results.
Selection, the tendency of some traits to become more frequent than others in a population under the influence of some (natural or artificial) agency, is a key component of Darwinian evolution and countless other natural and social phenomena. Yet a general theory of selection, analogous to the Fisher-Tippett-Gnedenko theory of extreme events, is lacking. Here we introduce a probabilistic definition of selection and show that selected values are attracted to a universal family of limiting distributions. The universality classes and scaling exponents are determined by the tail thickness of the random variable under selection. Our results are supported by data from molecular biology, agriculture and sport.
We consider extinction times for a class of birth-death processes commonly found in applications, where there is a control parameter which determines whether the population quickly becomes extinct, or rather persists for a long time. We give an exact expression for the discrete case and its asymptotic expansion for large values of the population. We have results below the threshold, at the threshold, and above the threshold (where there is a quasi-stationary state and the extinction time is very long.) We show that the Fokker-Planck approximation is valid only quite near the threshold. We compare our analytical results to numerical simulations for the SIS epidemic model, which is in the class that we treat. This is an interesting example of the delicate relationship between discrete and continuum treatments of the same problem.
The COVID-19 has caused more than three million infections and over two hundred thousand deaths by April 20201. Limiting socioeconomic activities (SA) is among the most adopted governmental mitigating efforts to combat the transmission of the virus, though the degree varies dramatically among different regimes2. This study aims to quantify the contribution from the SA and weather conditions to the transmission of COVID-19 at global scale. Ruling out the unobservable factors including medical facilities and other control policies (MOC) through region-by-time fixed effects3,4, we show that the limiting SA has a leading contribution to lower the reproductive number by 18.3%, while weather conditions, including ultraviolet, relative humidity, and wind explain a smaller amount of variation. Temperature might have a non-monotonic impact on the transmission. We further show that in developed countries5 and China, the SA effect is more pronounced whereas the weather effect is significantly downplayed possibly because people tend to stay indoors most of the time with a controlled climate. We finally estimate the reduced reproductive number and the population spared from infections due to restricting SA at 40,964, 180,336, 174,494, in China, United States, and Europe respectively. From late January to mid-April, all regions, except for China, Australia, and south Korea show a steep upward trend of spared infections due to restricting SA. US and Europe, in particular, show far steeper upward trends of spared infections in the analyzed timeframe, signaling a greater risk of reopening the economy too soon.
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