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Register a new userModeling COVID-19 uncertainties evolving over time and density-dependent social reinforcement and asymptomatic infections
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The novel coronavirus disease 2019 (COVID-19) presents unique and unknown problem complexities and modeling challenges, where an imperative task is to model both its process and data uncertainties, represented in implicit and high-proportional undocumented infections, asymptomatic contagion, social reinforcement of infections, and various quality issues in the reported data. These uncertainties become even more phenomenal in the overwhelming mutation-dominated resurgences with vaccinated but still susceptible populations. Here we introduce a novel hybrid approach to (1) characterizing and distinguishing Undocumented (U) and Documented (D) infections commonly seen during COVID-19 incubation periods and asymptomatic infections by expanding the foundational compartmental epidemic Susceptible-Infected-Recovered (SIR) model with two compartments, resulting in a new Susceptible-Undocumented infected-Documented infected-Recovered (SUDR) model; (2) characterizing the probabilistic density of infections by empowering SUDR to capture exogenous processes like clustering contagion interactions, superspreading and social reinforcement; and (3) approximating the density likelihood of COVID-19 prevalence over time by incorporating Bayesian inference into SUDR. Different from existing COVID-19 models, SUDR characterizes the undocumented infections during unknown transmission processes. To capture the uncertainties of temporal transmission and social reinforcement during the COVID-19 contagion, the transmission rate is modeled by a time-varying density function of undocumented infectious cases. We solve the modeling by sampling from the mean-field posterior distribution with reasonable priors, making SUDR suitable to handle the randomness, noise and sparsity of COVID-19 observations widely seen in the public COVID-19 case data.
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Coronavirus outbreak is one of the most challenging pandemics for the entire human population of the planet Earth. Techniques such as the isolation of infected persons and maintaining social distancing are the only preventive measures against the epidemic COVID-19. The actual estimation of the number of infected persons with limited data is an indeterminate problem faced by data scientists. There are a large number of techniques in the existing literature, including reproduction number, the case fatality rate, etc., for predicting the duration of an epidemic and infectious population. This paper presents a case study of different techniques for analysing, modeling, and representation of data associated with an epidemic such as COVID-19. We further propose an algorithm for estimating infection transmission states in a particular area. This work also presents an algorithm for estimating end-time of an epidemic from Susceptible Infectious and Recovered model. Finally, this paper presents empirical and data analysis to study the impact of transmission probability, rate of contact, infectious, and susceptible on the epidemic spread.
Macroscopic growth laws, solutions of mean field equations, describe in an effective way an underlying complex dynamics. They are applied to study the spreading of infections, as in the case of CoviD-19, where the counting of the cumulated number $N(t)$ of detected infected individuals is a generally accepted, coarse-grain, variable to understand the epidemic phase. However $N(t)$ does not take into account the unknown number of asymptomatic, not detected, cases $A(t)$. Therefore, the question arises if the observed time series of data of $N(t)$ is a reliable tool for monitoring the evolution of the infectious disease. We study a system of coupled differential equations which includes the dynamics of the spreading among symptomatic and asymptomatic individuals and the strong containment effects due to the social isolation. The solution is therefore compared with a macroscopic law for the population $N(t)$ coming from a single, non-linear, differential equation with no explicit reference to $A(t)$, showing the equivalence of the two methods. Indeed, $N(t)$ takes into account a more complex and detailed population dynamics which permits the evaluation of the number of asymptomatic individuals also. The model is then applied to Covid-19 spreading in Italy where a transition from an exponential behavior to a Gompertz growth for $N(t)$ has been observed in more recent data. Then the information contained in the data analysis of $N(t)$ is reliable to understand the epidemic phase, although it does not describe the total infected population. The asymptomatic population is larger than the symptomatic one in the fast growth phase of the spreading.
We analyze risk factors correlated with the initial transmission growth rate of the recent COVID-19 pandemic in different countries. The number of cases follows in its early stages an almost exponential expansion; we chose as a starting point in each country the first day $d_i$ with 30 cases and we fitted for 12 days, capturing thus the early exponential growth. We looked then for linear correlations of the exponents $alpha$ with other variables, for a sample of 126 countries. We find a positive correlation, {it i.e. faster spread of COVID-19}, with high confidence level with the following variables, with respective $p$-value: low Temperature ($4cdot10^{-7}$), high ratio of old vs.~working-age people ($3cdot10^{-6}$), life expectancy ($8cdot10^{-6}$), number of international tourists ($1cdot10^{-5}$), earlier epidemic starting date $d_i$ ($2cdot10^{-5}$), high level of physical contact in greeting habits ($6 cdot 10^{-5}$), lung cancer prevalence ($6 cdot 10^{-5}$), obesity in males ($1 cdot 10^{-4}$), share of population in urban areas ($2cdot10^{-4}$), cancer prevalence ($3 cdot 10^{-4}$), alcohol consumption ($0.0019$), daily smoking prevalence ($0.0036$), UV index ($0.004$, 73 countries). We also find a correlation with low Vitamin D levels ($0.002-0.006$, smaller sample, $sim 50$ countries, to be confirmed on a larger sample). There is highly significant correlation also with blood types: positive correlation with types RH- ($3cdot10^{-5}$) and A+ ($3cdot10^{-3}$), negative correlation with B+ ($2cdot10^{-4}$). Several of the above variables are intercorrelated and likely to have common interpretations. We performed a Principal Component Analysis, in order to find their significant independent linear combinations. We also analyzed a possible bias: countries with low GDP-per capita might have less testing and we discuss correlation with the above variables.
We develop a minimalist compartmental model to study the impact of mobility restrictions in Italy during the Covid-19 outbreak. We show that an early lockdown shifts the epidemic in time, while that beyond a critical value of the lockdown strength, the epidemic tend to restart after lifting the restrictions. As a consequence, specific mitigation strategies must be introduced. We characterize the relative importance of different broad strategies by accounting for two fundamental sources of heterogeneity, i.e. geography and demography. First, we consider Italian regions as separate administrative entities, in which social interactions between age classs occur. Due to the sparsity of the inter-regional mobility matrix, once started the epidemics tend to develop independently across areas, justifying the adoption of solutions specific to individual regions or to clusters of regions. Second, we show that social contacts between age classes play a fundamental role and that measures which take into account the age structure of the population can provide a significant contribution to mitigate the rebound effects. Our model is general, and while it does not analyze specific mitigation strategies, it highlights the relevance of some key parameters on non-pharmaceutical mitigation mechanisms for the epidemics.
A generalisation of the Susceptible-Infectious model is made to include a time-dependent transmission rate, which leads to a close analytical expression in terms of a logistic function. The solution can be applied to any continuous function chosen to describe the evolution of the transmission rate with time. Taking inspiration from real data of the Covid-19, for the case of cumulative confirmed positives and deaths, we propose an exponentially decaying transmission rate with two free parameters, one for its initial amplitude and another one for its decaying rate. The resultant time-dependent SI model, which under extra conditions recovers the standard Gompertz functional form, is then compared with data from selected countries and its parameters fit using Bayesian inference. We make predictions about the asymptotic number of confirmed positives and deaths, and discuss the possible evolution of the disease in each country in terms of our parametrisation of the transmission rate.
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