Understanding how widely COVID-19 has spread is critical for examining the pandemic's progression. Despite efforts to carefully monitor the pandemic, the number of confirmed cases may underestimate the total number of infections. We introduce a demographic scaling model to estimate COVID-19 infections using an broadly applicable approach that is based on minimal data requirements: COVID-19 related deaths, infection fatality rates (IFRs), and life tables. As many countries lack reliable estimates of age-specific IFRs, we scale IFRs between countries using remaining life expectancy as a marker to account for differences in age structures, health conditions, and medical services. Across 10 countries with most COVID-19 deaths as of May 13, 2020, the number of infections is estimated to be four [95% prediction interval: 2-11] times higher than the number of confirmed cases. Cross-country variation is high. The estimated number of infections is 1.4 million (six times the number of confirmed cases) for Italy; 3.1 million (2.2 times the number of confirmed cases) for the U.S.; and 1.8 times the number of confirmed cases for Germany, where testing has been comparatively extensive. Our prevalence estimates, however, are markedly lower than most others based on local seroprevalence studies. We introduce formulas for quantifying the bias that is required in our data on deaths in order to reproduce estimates published elsewhere. This bias analysis shows that either COVID-19 deaths are severely underestimated, by a factor of two or more; or alternatively, the seroprevalence based results are overestimates and not representative for the total population.
We propose a new mathematical model to study the coinfection dynamics of COVID-19 and bacterial pneumonia. Our model includes two infection ways for pneumonia, corresponding to community-acquired and hospital-acquired infections. We show that the existence and local stability of equilibria depend on three different parameters, which are interpreted as the basic reproduction numbers of COVID-19, bacterial pneumonia, and bacterial population. Numerical simulations are performed to complement our theoretical analysis, and we show that both diseases can persist if the basic reproduction number of …
One clear aspect of behaviour in the COVID-19 pandemic has been people's focus on, and response to, reported or observed infection numbers in their community. We describe a simple model of infectious disease spread in a pandemic situation where people's behaviour is influenced by the current risk of infection and where this behavioural response acts homeostatically to return infection risk to a certain preferred level. This model predicts that the reproduction rate $R$ will be centered around a median value of 1, and that a related measure of relative change in the number of new infections wil…
Relevance: Laboratory diagnosis of the novel coronavirus (SARS-CoV-2) infection combined with quarantine for contacts of infected individuals affects the spread of SARS-CoV-2 infection and levels of related mortality. Practices for testing for SARS-CoV-2 infection vary geographically in Russia. For example, in the city of St. Petersburg, where mortality rate for COVID-19 is the highest in the Russian Federation on Oct. 25, 2020, every death for COVID-19 corresponds to 15.7 detected cases of COVID-19 in the population, while the corresponding number for the whole of Russia is 58.1, suggesting l…
This article reports a first update on the assesment of the model previously presented in arXiv:2003.13890v1. New available data have been used to feed the model and the comparison with real data still shows good agreement. The main novelty of the model is that it keeps track of the date of infection of a single individual and uses stochastic distributions to aggregate individuals who share the same date of infection. In addition, it uses two types of infections, mild and serious, with a different recovery time. These features are implemented in a set of differential equations which determine …
In this paper we study the spatial spread of the COVID-19 infection in Lebanon. We inspect the spreading of the daily new infections across the 26 administrative districts of the country, and implement Moran's $I$ statistics in order to analyze the tempo-spatial clustering of the infection in relation to various variables parameterized by adjacency, proximity, population, population density, poverty rate and poverty density, and we find out that except for the poverty rate, the spread of the infection is clustered and associated to those parameters with varying magnitude for the time span betw…
The coronavirus disease 2019 (COVID-19) pandemic radically impacts our lives, while the transmission/infection and recovery dynamics of COVID-19 remain obscure. A time-dependent Susceptible, Exposed, Infectious, and Recovered (SEIR) model was proposed and applied to fit and then predict the time series of COVID-19 evolution observed in the last three months (till 3/22/2020) in various provinces and metropolises in China. The model results revealed the space dependent transmission/infection rate and the significant spatiotemporal variation in the recovery rate, likely due to the continuous impr…
This document aims to estimate and describe the effects of the social distancing measures implemented in several countries with the expectancy of controlling the spread of COVID-19. The procedure relies on the classic Susceptible-Infected-Removed (SIR) model, which is modified to incorporate a permissiveness index, representing the isolation achieved by the social distancing and the future development of vaccination campaigns and allowing the math model to reproduce more than one infection wave. The adjusted SIR models are used to study the compromise between the economy's reactivation and the…
We comparatively analyzed the spatiotemporal fluctuations of the 2019-novel coronavirus (COVID-19) and SARS outbreaks to understand their epidemiological characteristics. Methodologically, we introduced TPL (Taylor power law) to characterize their spatiotemporal heterogeneity/stability and Hubbell (2001) unified neutral theory of biodiversity (UNTB) [specifically Harris et al. (2015) HDP-MSN model (hierarchical Dirichlet process multi-site neutral model)] to approximate the metapopulation of coronavirus infections. First, TPL analysis suggested that the coronaviruses appear to have a specific …
Aim of this manuscript is to show a simple method to infer the time-course of new COVID-19 infections (the most important information in order to establish the effect of containment strategies) from available aggregated data, such as number of deaths and hospitalizations. The method, that was used for HIV-AIDS and was named `back-calculation', relies on good estimates of the distribution of the delays between infection and the observed events; assuming that the epidemic follows a simple SIR model with a known generation interval, we can then estimate the parameters that define the time-varying…
There are many hard-to-reconcile numbers circulating concerning Covid-19. Using reports from random testing, the fatality ratio per infection is evaluated and used to extract further information on the actual fraction of infections and the success of their identification for different countries.
In India the COVID-19 infected population has not yet been accurately established. As always in the early stages of any epidemic, the need to test serious cases first has meant that the population with asymptomatic or mild sub-clinical symptoms has not yet been analyzed. Using counts of fatalities, and previously estimated parameters for the progress of the disease, we give statistical estimates of the infected population. The doubling time is a crucial unknown input parameter which affects these estimates, and may differ strongly from one geographical location to another. We suggest a method …
We propose to use the mean time between infections (MTBI) metric as obtained from a recently introduced non-homogeneous Markov stochastic model. Different types of parameter calibration are performed. We estimate the MTBI using data from different time windows and from the whole stage history and compare the results. In order to detect waves and stages in the input data, a preprocessing filtering technique is applied. The results of applying this indicator to the COVID-19 reported data of infections from Argentina, Germany and the United States are shown. We find that the MTBI behaves similarl…
Phenomenological and deterministic models are often used for the estimation of transmission parameters in an epidemic and for the prediction of its growth trajectory. Such analyses are usually based on single peak outbreak dynamics. In light of the present COVID-19 pandemic, there is a pressing need to better understand observed epidemic growth with multiple peak structures, preferably using first-principles methods. Along the lines of our previous work [Physica A 574, 126014 (2021)], here we apply 2D random-walk Monte Carlo calculations to better understand COVID-19 spread through contact int…
Epidemiological models with constant parameters may not capture satisfactory infection patterns in the presence of pharmaceutical and non-pharmaceutical mitigation measures during a pandemic, since infectiousness is a function of time. In this paper, an Epidemiology-Informed Neural Network algorithm is introduced to learn the time-varying transmission rate for the COVID-19 pandemic in the presence of various mitigation scenarios. There are asymptomatic infectives, mostly unreported, and the proposed algorithm learns the proportion of the total infective individuals that are asymptomatic infect…
We investigate the distribution of numbers of secondary cases in households in the Office for National Statistics COVID-19 Infection Survey (ONS CIS), stratified by timing of vaccination and infection in the households. This shows a total effect of a statistically significant approximate halving of the secondary attack rate in households following vaccination.
Exploiting the SIQR model for COVID-19, I show that the wavy infection curve in Japan is the result of fluctuation of policy on isolation measure imposed by the government and obeyed by citizens. Assuming the infection coefficient be a two-valued function of the number of daily confirmed new cases, I show that when the removal rate of infected individuals is between these two values, the wavy infection curve is self-organized. On the basis of the infection curve, I classify the outbreak of COVID-19 into five types and show that these differences can be related to the relative magnitude of the …
A model of reactive social distancing in epidemics is proposed, in which the infection rate changes with the number infected. The final-size equation for the total number that the epidemic will infect can be derived analytically, as can the peak infection proportion. This model could assist planners during for example the COVID-19 pandemic.
In this short note we model the region-wise trends of the evolution to COVID-19 infections using a stochastic SIR model. The SIR dynamics are expressed using \textit{Itô-stochastic differential equations}. We first derive the parameters of the model from the available daily data from European regions based on a 24-day history of infections, recoveries and deaths. The derived parameters have been aggregated to project future trends for the Indian subcontinent, which is currently at an early stage in the infection cycle. The projections are meant to serve as a guideline for strategizing the soci…
The relation between the number of passengers in the main stations and the infection rate of COVID19 in Tokyo is empirically studied. Our analysis based on conventional compartment model suggests: 1) Average time from the true day of infection to the day the infections are reported is about $15$ days. 2) The scaling relation between the density of active population and the infection rate suggests that the increase of infection rate is linear to the active population rather than quadratic, as that is assumed in the conventional SIR model. 3) Notable deviations from the overall scaling relation …
Even though laboratory and epidemiological studies have demonstrated the effects of ambient temperature on the transmission and survival of coronaviruses, not much has been done on the effects of weather on the spread of COVID-19. This study investigates the effects of temperature, humidity, precipitation, wind speed and the specific government policy intervention of partial lockdown on the new cases of COVID-19 infection in Ghana. Daily data on confirmed cases of COVID-19 from March 13, 2020 to April 21, 2020 were obtained from the official website of Our World in Data (OWID) dedicated to COV…
We analyse the temporal and regional structure in mortality rates related to COVID-19 infections. We relate the fatality date of each deceased patient to the corresponding day of registration of the infection, leading to a nowcasting model which allows us to estimate the number of present-day infections that will, at a later date, prove to be fatal. The numbers are broken down to the district level in Germany. Given that death counts generally provide more reliable information on the spread of the disease compared to infection counts, which inevitably depend on testing strategy and capacity, t…
An urgent problem in controlling COVID-19 spreading is to understand the role of undocumented infection. We develop a five-state model for COVID-19, taking into account the unique features of the novel coronavirus, with key parameters determined by the government reports and mathematical optimization. Tests using data from China, South Korea, Italy, and Iran indicate that the model is capable of generating accurate prediction of the daily accumulated number of confirmed cases and is entirely suitable for real-time prediction. The drastically disparate testing and diagnostic standards/policies …
Reproduction Numbers R_0, R_t for COVID-19 Infections with Gaussian Distribution of Generation Times, and of Serial Intervals including Presymptomatic Transmission
Some ideas are presented about the physical motivation of the apparent capacity of generalized logistic equations to describe the outbreak of the COVID-19 infection, and in general of quite many other epidemics. The main focuses here are: the complex, possibly fractal, structure of the locus describing the "contagion event set"; what can be learnt from the models of trophic webs with "herd behaviour".
The COVID-19 pandemic has posed significant challenges in modeling its complex epidemic transmissions, infection and contagion, which are very different from known epidemics. The challenges in quantifying COVID-19 complexities include effectively modeling its process and data uncertainties. The uncertainties are embedded 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 apparent in the first two months of the COVID-19 pandemic, when the rele…
Widespread growth signatures in COVID-19 confirmed case counts are reported, with sharp transitions between three distinct dynamical regimes (exponential, superlinear and sublinear). Through analytical and numerical analysis, a novel framework is developed that exploits information in these signatures. An approach well known to physics is applied, where one looks for common dynamical features, independently from differences in other factors. These features and associated scaling laws are used as a powerful tool to pinpoint regions where analytical derivations are effective, get an insight into…
We present a robust data-driven machine learning analysis of the COVID-19 pandemic from its early infection dynamics, specifically infection counts over time. The goal is to extract actionable public health insights. These insights include the infectious force, the rate of a mild infection becoming serious, estimates for asymtomatic infections and predictions of new infections over time. We focus on USA data starting from the first confirmed infection on January 20 2020. Our methods reveal significant asymptomatic (hidden) infection, a lag of about 10 days, and we quantitatively confirm that t…
Last time, an attempt was made to analyze the first wave of COVID-19 in Japan from February to May 2020 by the Avrami equation. This time, all infection waves that occurred repeatedly from February 2020 to September 2021 were simulated by developing the last work. The entire waveform was basically simulated by the superposition of five major waves, and the least-squares method was applied to each wave to determine the parameters of the equation. Despite the simulation using the single equation assuming that the parameters were constants, the accuracy of the simulated cumulative infection D was…
A new epidemic model for Covid-19 has been constructed and simulated for eight US states. The coefficients for this model, based on seven coupled differential equations, are carefully evaluated against recorded data on cases and deaths. These projections reveal that Covid-19 will become endemic, spreading for more than two years. If stay-at-home orders are relaxed, most states may experience a secondary peak in 2021. The number of Covid-19 deaths could have been significantly lower in most states that opened up, if lockdowns had been maintained. Additionally, our model predicts that decreasing…
The first cases of COVID-19 in France were detected on January 24, 2020. The number of screening tests carried out and the methodology used to target the patients tested do not allow for a direct computation of the real number of cases and the mortality rate.In this report, we develop a 'mechanistic-statistical' approach coupling a SIR ODE model describing the unobserved epidemiological dynamics, a probabilistic model describing the data acquisition process and a statistical inference method. The objective of this model is not to make forecasts but to estimate the real number of people infecte…
We present a simple technique to compare the development of the Covid-19 epidemic in different regions, based only on the time series of confirmed cases. Weekly new infections, taken for every day, are interpreted as infection potential of Covid-19. We derive a robust time-varying reproduction rate for the infection potential, including asymptomatic cases, which does not depend on death rate or testing intensity. It requires few assumptions and shows a more plausible time course than official reproduction rates in several countries.
The infections and fatalities due to SARS-CoV-2 virus for cases specific to India have been studied using a deterministic susceptible-exposed-infected-recovered-dead (SEIRD) compartmental model. One of the most significant epidemiological parameter, namely the effective reproduction number of the infection is extracted from the daily growth rate data of reported infections and it is included in the model with a time variation. We evaluate the effect of control interventions implemented till now and estimate the case numbers for infections and deaths averted by these restrictive measures. We fu…
The number of new infections per day is a key quantity for effective epidemic management. It can be estimated relatively directly by testing of random population samples. Without such direct epidemiological measurement, other approaches are required to infer whether the number of new cases is likely to be increasing or decreasing: for example, estimating the pathogen effective reproduction number, R, using data gathered from the clinical response to the disease. For Covid-19 (SARS-CoV-2) such R estimation is heavily dependent on modelling assumptions, because the available clinical case data a…
COVID-19 has forced quarantine measures in several countries across the world. These measures have proven to be effective in significantly reducing the prevalence of the virus. To date, no effective treatment or vaccine is available. In the effort of preserving both public health as well as the economical and social textures, France and Italy governments have partially released lockdown measures. Here we extrapolate the long-term behavior of the epidemics in both countries using a Susceptible-Exposed-Infected-Recovered (SEIR) model where parameters are stochastically perturbed to handle the un…
We adapt the hybrid mechanistic-statistical approach of Ref. [1] to estimate the total number of undocumented Covid-19 infections in Cuba. This scheme is based on the maximum likelihood estimation of a SIR-like model parameters for the infected population, assuming that the detection process matches a Bernoulli trial. Our estimations show that (a) 60% of the infections were undocumented, (b) the real epidemics behind the data peaked ten days before the reports suggested, and (c) the reproduction number swiftly vanishes after 80 epidemic days.
In this paper, we introduce a novel modeling framework for incorporating fear of infection and frustration with social distancing into disease dynamics. We show that the resulting SEIR behavior-perception model has three principal modes of qualitative behavior---no outbreak, controlled outbreak, and uncontrolled outbreak. We also demonstrate that the model can produce transient and sustained waves of infection consistent with secondary outbreaks. We fit the model to cumulative COVID-19 case and mortality data from several regions. Our analysis suggests that regions which experience a significa…
We introduce an epidemic spreading model on a network using concepts from percolation theory. The model is motivated by discussing the standard SIR model, with extensions to describe effects of lockdowns within a population. The underlying ideas and behavior of the lattice model, implemented using the same lockdown scheme as for the SIR scheme, are discussed in detail and illustrated with extensive simulations. A comparison between both models is presented for the case of COVID-19 data from the USA. Both fits to the empirical data are very good, but some differences emerge between the two appr…
Among the many aspects that characterize the COVID-19 pandemic, two seem particularly challenging to understand: (i) the great geographical differences in the degree of virus contagiousness and lethality which were found in the different phases of the epidemic progression, and (ii) the potential role of the infected people's blood type in both the virus infectivity and the progression of the disease. A recent hypothesis could shed some light on both aspects. Specifically, it has been proposed that in the subject-to-subject transfer SARS-CoV-2 conserves on its capsid the erythrocytes' antigens …
After more than 6 million deaths worldwide, the ongoing vaccination to conquer the COVID-19 disease is now competing with the emergence of increasingly contagious mutations, repeatedly supplanting earlier strains. Following the near-absence of historical examples of the long-time evolution of infectious diseases under similar circumstances, models are crucial to exemplify possible scenarios. Accordingly, in the present work we systematically generalize the popular susceptible-infected-recovered model to account for mutations leading to repeatedly occurring new strains, which we coarse grain ba…
The COVID-19 pandemic has posed a policy making crisis where efforts to slow down or end the pandemic conflict with economic priorities. This paper provides mathematical analysis of optimal disease control policies with idealized compartmental models for disease propagation and simplistic models of social and economic costs. Two locally optimal control strategies are found and categorized as `suppression' and `mitigation' strategies. We analyze how these strategies change when we incorporate vaccination into the model and find a new optimal `delay-mitigation' strategy.
Epidemiological models are the mathematical models that capture the dynamics of epidemics. The spread of the virus has two routes - exogenous and endogenous. The exogenous spread is from outside the population under study, and endogenous spread is within the population under study. Although some of the models consider the exogenous source of infection, they have not studied the interplay between exogenous and endogenous spreads. In this paper, we introduce a novel model - the Exo-SIR model that captures both the exogenous and endogenous spread of the virus. We analyze to find out the relations…
After the detection of coronavirus disease 2019 (Covid-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in Wuhan, Hubei Province, China in late December, the cases of Covid-19 have spiralled out around the globe. Due to the clinical similarity of Covid-19 with other flulike syndromes, patients are assayed for other pathogens of influenza like illness. There have been reported cases of co-infection amongst patients with Covid-19. Bacteria for example Streptococcus pneumoniae, Staphylococcus aureus, Klebsiella pneumoniae, Mycoplasma pneumoniae, Chlamydia pneumonia,…
The spread of the coronavirus (COVID-19), starting in late 2019, has determined in Italy several interventions aimed to prevent saturation of the health system. We have examined the effects of such measures by proposing a mean-field model describing the spread of the infection based on a simple diffusion process where all the observable variables (number of people still positive to the infection, hospitalized and fatalities cases, healed people, and total number of people that has contracted the infection) depend on average parameters, namely diffusion coefficient, infection cross-section, and…
The COVID-19 pandemic has affected all countries of the world producing a substantial number of fatalities accompanied by a major disruption in their social, financial, and educational organization. The strict disciplinary measures implemented by China were very effective and thus were subsequently adopted by most world countries to various degrees. The infection duration and number of infected persons are of critical importance for the battle against the pandemic. We use the quantitative landscape of the disease spreading in China as a benchmark and utilize infection data from eight countries…
The sudden spread of Covid-19 outside China has pushed on March 11 the World Health Organization to acknowledge the ongoing outbreak as a pandemic. It is crucial in this phase to understand what should countries which presently lag behind in the spread of the infection learn from countries where the infection spread earlier. The choice of this work is to prefer timeliness to comprehensiveness. By adopting a purely empirical approach, we will limit ourselves to identifying different phases in the plots of different countries, based on their different functional behaviour, and to make a comparat…
Considering the propagation characteristics of COVID-19 in different regions, the dynamics analysis and numerical demonstration of long-term and short-term models of COVID-19 are carried out, respectively. The long-term model is devoted to investigate the global stability of COVID-19 model with asymptomatic infections and quarantine measures. By using the limit system of the model and Lyapunov function method, it is shown that the COVID-19-free equilibrium $V^0$ is globally asymptotically stable if the control reproduction number $\mathcal{R}_{c}<1$ and globally attractive if $\mathcal{R}_{c}=…
The infection fatality rate (IFR) of the Coronavirus Disease 2019 (COVID-19) is one of the most discussed figures in the context of this pandemic. Using German COVID-19 surveillance data and age-group specific IFR estimates from multiple international studies, this work investigates time-dependent variations in effective IFR over the course of the pandemic. Three different methods for estimating (effective) IFRs are presented: (a) population-averaged IFRs based on the assumption that the infection risk is independent of age and time, (b) effective IFRs based on the assumption that the age dist…
The COVID-19 epidemic has been spreading around the world for nearly three years, and asymptomatic infections have exacerbated the spread of the epidemic. To evaluate the role of asymptomatic infections in the spread of the epidemic, we develop mathematical models to assess the proportion of asymptomatic infections caused by different strains of the main covid-19 variants. The analysis shows that when the control reproduction number is less than 1, the disease-free equilibrium point of the model is globally asymptotically stable; and when the control reproduction number is greater than 1, the …
The number of corona virus (COVID-19) infections grows worldwide. In order to create short term predictions to prepare for the extent of the global pandemic we analyze infection data from the top 25 affected countries. It is shown that all country-specific infection rates follow a power law growth behavior and the scaling exponents per country are calculated. We find two different growth patterns: either steady power law growth from the very beginning with moderate scaling exponents of 3-5 or explosive power law growth with dramatic scaling exponents of 8-11. In the case of the USA we even fin…
Redlining is the discriminatory practice whereby institutions avoided investment in certain neighborhoods due to their demographics. Here we explore the lasting impacts of redlining on the spread of COVID-19 in New York City (NYC). Using data available through the Home Mortgage Disclosure Act, we construct a redlining index for each NYC census tract via a multi-level logistical model. We compare this redlining index with the COVID-19 statistics for each NYC Zip Code Tabulation Area. Accurate mappings of the pandemic would aid the identification of the most vulnerable areas and permit the most …
Coronavirus disease 2019 (COVID-19) is a continuously devastating public health and the world economy. One of the major challenges in controlling the COVID-19 outbreak is its asymptomatic infection and transmission, which are elusive and defenseless in most situations. The pathogenicity and virulence of asymptomatic COVID-19 remain mysterious. Based on the genotyping of 20656 Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) genome isolates, we reveal that asymptomatic infection is linked to SARS-CoV-2 11083G>T mutation, i.e., leucine (L) to phenylalanine (F) substitution at the res…
Within-host models of COVID-19 infection dynamics enable the merits of different forms of antiviral therapy to be assessed in individual patients. A stochastic agent-based model of COVID-19 intracellular dynamics is introduced here, that incorporates essential steps of the viral life cycle targeted by treatment options. Integration of model predictions with an intercellular ODE model of within-host infection dynamics, fitted to patient data, generates a generic profile of disease progression in patients that have recovered in the absence of treatment. This is contrasted with the profiles obtai…
Despite commercial airlines mandating masks, there have been multiple documented events of COVID-19 superspreading on flights. We used available data from three flights, including cabin layout and seat locations of infected and uninfected passengers, to suggest interventions to mitigate COVID-19 superspreading events during air travel. Specifically, we studied: 1) London to Hanoi with 201 passengers, including 13 secondary infections among passengers; 2) Singapore to Hangzhou with 321 passengers, including 12 to 14 secondary infections; 3) a non-superspreading event on a private jet in Japan w…
