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Register a new userBeyond $R_0$: Heterogeneity in secondary infections and probabilistic epidemic forecasting
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The basic reproductive number -- $R_0$ -- is one of the most common and most commonly misapplied numbers in public health. Although often used to compare outbreaks and forecast pandemic risk, this single number belies the complexity that two different pathogens can exhibit, even when they have the same $R_0$. Here, we show how to predict outbreak size using estimates of the distribution of secondary infections, leveraging both its average $R_0$ and the underlying heterogeneity. To do so, we reformulate and extend a classic result from random network theory that relies on contact tracing data to simultaneously determine the first moment ($R_0$) and the higher moments (representing the heterogeneity) in the distribution of secondary infections. Further, we show the different ways in which this framework can be implemented in the data-scarce reality of emerging pathogens. Lastly, we demonstrate that without data on the heterogeneity in secondary infections for emerging infectious diseases like COVID-19, the uncertainty in outbreak size ranges dramatically. Taken together, our work highlights the critical need for contact tracing during emerging infectious disease outbreaks and the need to look beyond $R_0$ when predicting epidemic size.
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Epidemics generally spread through a succession of waves that reflect factors on multiple timescales. On short timescales, super-spreading events lead to burstiness and overdispersion, while long-term persistent heterogeneity in susceptibility is expected to lead to a reduction in the infection peak and the herd immunity threshold (HIT). Here, we develop a general approach to encompass both timescales, including time variations in individual social activity, and demonstrate how to incorporate them phenomenologically into a wide class of epidemiological models through parameterization. We derive a non-linear dependence of the effective reproduction number Re on the susceptible population fraction S. We show that a state of transient collective immunity (TCI) emerges well below the HIT during early, high-paced stages of the epidemic. However, this is a fragile state that wanes over time due to changing levels of social activity, and so the infection peak is not an indication of herd immunity: subsequent waves can and will emerge due to behavioral changes in the population, driven (e.g.) by seasonal factors. Transient and long-term levels of heterogeneity are estimated by using empirical data from the COVID-19 epidemic as well as from real-life face-to-face contact networks. These results suggest that the hardest-hit areas, such as NYC, have achieved TCI following the first wave of the epidemic, but likely remain below the long-term HIT. Thus, in contrast to some previous claims, these regions can still experience subsequent waves.
We model and calculate the fraction of infected population necessary to reach herd immunity, taking into account the heterogeneity in infectiousness and susceptibility, as well as the correlation between those two parameters. We show that these cause the effective reproduction number to decrease more rapidly, and consequently have a drastic effect on the estimate of the necessary percentage of the population that has to contract the disease for herd immunity to be reached. We quantify the difference between the size of the infected population when the effective reproduction number decreases below 1 vs. the ultimate fraction of population that had contracted the disease. This sheds light on an important distinction between herd immunity and the end of the disease and highlights the importance of limiting the spread of the disease even if we plan to naturally reach herd immunity. We analyze the effect of various lock-down scenarios on the resulting final fraction of infected population. We discuss implications to COVID-19 and other pandemics and compare our theoretical results to population-based simulations. We consider the dependence of the disease spread on the architecture of the infectiousness graph and analyze different graph architectures and the limitations of the graph models.
In this paper, it is shown that the Moyal distribution is an excelent tool to study the SARS-Cov-II (Covid-19) epidemiological associated curves and its propagation. The Moyal parameters give all the information to describe the form and the impact of the illness outbreak in the different affected countries and its global impact. We checked that the Moyal distribution can accurately fit the daily report of {it{new confirmed cases of infected people}} (NCC) per country, in that places where the contagion is reaching their final phase, describing the beginning, the most intense phase and the descend of the contagion, simultaneously . In order to achieve the purpose of this work, it is important to work with a complete and well compilated set of the data to be used to fit the curves. Data from European countries like France, Spain, Italy Belgium, Sweden, United Kingdom, Denmark and others like USA and China, have been used. Also, the correlation between the parameters of the Moyal distribution fitting and the general public health measures imposed in each country, have been discussed. A relation between those policies and the features of the Moyal distribution, in terms of their parameters and critical points, is shown; from that, it can be seen that the knowledge of the time evolution of the epidemiological curve, their critical points, superposition properties and rates of the rising and the ending, could help to find a way to estimate the efficiency of social distancing measures, imposed in each country, and anticipate the different phases of the pandemic.
The nation-wide lockdown starting 25 March 2020, aimed at suppressing the spread of the COVID-19 disease, was extended until 31 May 2020 in three subsequent orders by the Government of India. The extended lockdown has had significant social and economic consequences and `lockdown fatigue has likely set in. Phased reopening began from 01 June 2020 onwards. Mumbai, one of the most crowded cities in the world, has witnessed both the largest number of cases and deaths among all the cities in India (41986 positive cases and 1368 deaths as of 02 June 2020). Many tough decisions are going to be made on re-opening in the next few days. In an earlier IISc-TIFR Report, we presented an agent-based city-scale simulator(ABCS) to model the progression and spread of the infection in large metropolises like Mumbai and Bengaluru. As discussed in IISc-TIFR Report 1, ABCS is a useful tool to model interactions of city residents at an individual level and to capture the impact of non-pharmaceutical interventions on the infection spread. In this report we focus on Mumbai. Using our simulator, we consider some plausible scenarios for phased emergence of Mumbai from the lockdown, 01 June 2020 onwards. These include phased and gradual opening of the industry, partial opening of public transportation (modelling of infection spread in suburban trains), impact of containment zones on controlling infections, and the role of compliance with respect to various intervention measures including use of masks, case isolation, home quarantine, etc. The main takeaway of our simulation results is that a phased opening of workplaces, say at a conservative attendance level of 20 to 33%, is a good way to restart economic activity while ensuring that the citys medical care capacity remains adequate to handle the possible rise in the number of COVID-19 patients in June and July.
Discovering and isolating infected individuals is a cornerstone of epidemic control. Because many infectious diseases spread through close contacts, contact tracing is a key tool for case discovery and control. However, although contact tracing has been performed widely, the mathematical understanding of contact tracing has not been fully established and it has not been clearly understood what determines the efficacy of contact tracing. Here, we reveal that, compared with forward tracing---tracing to whom disease spreads, backward tracing---tracing from whom disease spreads---is profoundly more effective. The effectiveness of backward tracing is due to simple but overlooked biases arising from the heterogeneity in contacts. Using simulations on both synthetic and high-resolution empirical contact datasets, we show that even at a small probability of detecting infected individuals, strategically executed contact tracing can prevent a significant fraction of further transmissions. We also show that---in terms of the number of prevented transmissions per isolation---case isolation combined with a small amount of contact tracing is more efficient than case isolation alone. By demonstrating that backward contact tracing is highly effective at discovering super-spreading events, we argue that the potential effectiveness of contact tracing has been underestimated. Therefore, there is a critical need for revisiting current contact tracing strategies so that they leverage all forms of biases. Our results also have important consequences for digital contact tracing because it will be crucial to incorporate the capability for backward and deep tracing while adhering to the privacy-preserving requirements of these new platforms.
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