Attempts to curb the spread of coronavirus by introducing strict quarantine measures apparently have different effect in different countries: while the number of new cases has reportedly decreased in China and South Korea, it still exhibit significant growth in Italy and other countries across Europe. In this brief note, we endeavour to assess the efficiency of quarantine measures by means of mathematical modelling. Instead of the classical SIR model, we introduce a new model of infection progression under the assumption that all infected individual are isolated after the incubation period in such a way that they cannot infect other people. Disease progression in this model is determined by the basic reproduction number $\mathcal{R}_0$ (the number of newly infected individuals during the incubation period), which is different compared to that for the standard SIR model. If $\mathcal{R}_0 >1$, then the number of latently infected individuals exponentially grows. However, if $\mathcal{R}_0 <1$ (e.g.~due to quarantine measures and contact restrictions imposed by public authorities), then the number of infected decays exponentially. We then consider the available data on the disease development in different countries to show that there are three possible patterns: growth dynamics, growth-decays dynamics, and patchy dynamics (growth-decay-growth). Analysis of the data in China and Korea shows that the peak of infection (maximum of daily cases) is reached about 10 days after the restricting measures are introduced. During this period of time, the growth rate of the total number of infected was gradually decreasing. However, the growth rate remains exponential in Italy. Arguably, it suggests that the introduced quarantine is not sufficient and stricter measures are needed.
In this paper, we propose a new model for the dynamics of COVID-19 infections. Our approach consists of seven phenotypes: the susceptible humans, exposed humans, infectious humans, the recovered humans, the quarantine population, the recovered-exposed and deceased population. We proved first through mathematical approach the positivity, boundness and existence of a solution to considered model. We also studied the existence of the disease free equilibrium and corresp onding stability. Hence, the actual reproduction number was calculated . We analyzed the dependence of basic reproductions R_0 o…
Coronavirus disease 2019 (CoViD-19) is an infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Among many symptoms, cough, fever and tiredness are the most common. People over 60 years old and with associated comorbidities are most likely to develop a worsening health condition. This paper proposes a non-integer order model to describe the dynamics of CoViD-19 in a standard population. The model incorporates the reinfection rate in the individuals recovered from the disease. Numerical simulations are performed for different values of the order of the fract…
The goal of this work is to analyse the effects of control policies for the coronavirus (COVID-19) epidemic in Brazil. This is done by considering an age-structured SEIR model with a quarantine class and two types of controls. The first one studies the sensitivity with regard to the parameters of the basic reproductive number R0 which is calculated by the next generation method. The second one evaluates different quarantine strategies by comparing their relative total number of deaths.
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}=…
A coronavirus disease 2019 (COVID-19) model with quarantine and standard incidence rate is first developed, then a novel analysis approach for finding the ultimate lower bound of COVID-19 infectious individuals is proposed, which means that the COVID-19 pandemic is uniformly persistent if the control reproduction number $\mathcal{R}_{c}>1$. This approach can be applied to other related biomathematical models, and some existing works can be improved by using it. In addition, the COVID-19-free equilibrium $V^0$ is locally asymptotically stable (LAS) if $\mathcal{R}_{c}<1$ and linearly stable if …
A simple Monte-Carlo method will be put forward herein, to enable the extraction of an estimate for the quarantine duration, applicable to visitors to high-risk regions. Results will be obtained on the basis of an analysis of the upper tail of the cumulative distribution function of the time span between the departure of the travellers from the place where the infection occurs and the time instant when COVID-19 infections may currently be detected. As expected, the quarantine duration is a decreasing function of the fraction of the infected travellers, which one is prepared to identify as `acc…
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…
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 …
During pandemic events, strategies such as social distancing can be fundamental to curb viral spreading. Such actions can reduce the number of simultaneous infections and mitigate the disease spreading, which is relevant to the risk of a healthcare system collapse. Although these strategies can be suggested, their actual implementation may depend on the population perception of the disease risk. The current COVID-19 crisis, for instance, is showing that some individuals are much more prone than others to remain isolated, avoiding unnecessary contacts. With this motivation, we propose an epidem…
The COVID-19 pandemic led several countries to resort to social distancing, the only known way to slow down the spread of the virus and keep the health system under control. Here we use an individual based model (IBM) to study how the duration, start date and intensity of quarantine affect the height and position of the peak of the infection curve. We show that stochastic effects, inherent to the model dynamics, lead to variable outcomes for the same set of parameters, making it crucial to compute the probability of each result. To simplify the analysis we divide the outcomes in only two categ…
Since the first recording of what we now call Covid-19 infection in Wuhan, Hubei province, China on Dec 31, 2019, the disease has spread worldwide and met with a wide variety of social distancing and quarantine policies. The effectiveness of these responses is notoriously difficult to quantify as individuals travel, violate policies deliberately or inadvertently, and infect others without themselves being detected. In this paper, we attempt to interpret and extrapolate from publicly available data using a mixed first-principles epidemiological equations and data-driven neural network model. Le…
Corona Virus Disease 2019 (COVID-19), due to its extremely high infectivity, has been spreading rapidly around the world and bringing huge influence to socioeconomic development as well as people's daily life. Taking for example the virus transmission that may occur after college students return to school, we analyze the quantitative influence of the key factors on the virus spread, including crowd density and self-protection. One Campus Virus Infection and Control Simulation model (CVICS) of the novel coronavirus is proposed in this paper, fully considering the characteristics of repeated con…
In a move described as unprecedented in public health history, starting 24 January 2020, China imposed quarantine and isolation restrictions in Wuhan, a city of more than 10 million people. This raised the question: is mass quarantine and isolation effective as a social tool in addition to its scientific use as a medical tool? In an effort to address this question, using a epidemiological model driven approach augmented by machine learning, we show that the quarantine and isolation measures implemented in Wuhan brought down the effective reproduction number R(t) of the CoVID-19 spread from R(t…
We consider the pandemic spreading of COVID-19 for some selected countries after the outbreak of the coronavirus in Wuhan City, China. We estimated the infection rate and the initial infected individuals of COVID-19 by using the officially reported data at the early stage of the epidemic for the susceptible (S), infectable (I), quarantined (Q), and the cofirmed recovered (Rk) population model, so called SIQRk model. In the reported data we know the quarantined cases and the recovered cases. We can not know the recovered cases from the asymptomatic cases. In the SIQRk model we can estimated the…
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 …
By the end of July 2020, the COVID-19 pandemic had infected more than seventeen million people and had spread to almost all countries worldwide. In response, many countries all over the world have used different methods to reduce the infection rate, such as including case isolation, the closure of schools and universities, banning public events, and mostly forcing social distancing, including local and national lockdowns. We use a Monte-Carlo (MC) based algorithm to predict the virus infection rate for different population densities using the most recent epidemic data in our work. We test the …
In mid of March 2020, Coronaviruses such as COVID-19 is declared as an international epidemic. More than 125000 confirmed cases and 4,607 death cases have been recorded around more than 118 countries. Unfortunately, a coronavirus vaccine is expected to take at least 18 months if it works at all. Moreover, COVID -19 epidemics can mutate into a more aggressive form. Day level information about the COVID -19 spread is crucial to measure the behavior of this new virus globally. Therefore, this study presents a comparison of day level forecasting models on COVID-19 affected cases using time series …
The novel coronavirus (2019-nCoV) is a recently emerged human pathogen that has spread widely since January 2020. Initially, the basic reproductive number, R0, was estimated to be 2.2 to 2.7. Here we provide a new estimate of this quantity. We collected extensive individual case reports and estimated key epidemiology parameters, including the incubation period. Integrating these estimates and high-resolution real-time human travel and infection data with mathematical models, we estimated that the number of infected individuals during early epidemic double every 2.4 days, and the R0 value is li…
The response of many governments to the COVID-19 pandemic has involved measures to control within- and between-household transmission, providing motivation to improve understanding of the absolute and relative risks in these contexts. Here, we perform exploratory, residual-based, and transmission-dynamic household analysis of the Office for National Statistics (ONS) COVID-19 Infection Survey (CIS) data from 26 April 2020 to 15 July 2021 in England. This provides evidence for: (i) temporally varying rates of introduction of infection into households broadly following the trajectory of the overa…
During the early stage of the COVID-19 pandemic, many countries implemented non-pharmaceutical interventions (NPIs) to control the transmission of SARS-CoV-2, the causative pathogen of COVID-19. Among those NPIs, quarantine measures were widely adopted and enforced through stay-at-home and shelter-in-place orders. Understanding the effectiveness of quarantine measures can inform decision-making and control planning during the ongoing COVID-19 pandemic and for future disease outbreaks. In this study, we use mathematical models to evaluate the impact of quarantine measures on COVID-19 spread in …
The new coronavirus known as COVID-19 is spread world-wide since December 2019. Without any vaccination or medicine, the means of controlling it are limited to quarantine and social distancing. Here we study the spatio-temporal propagation of the first wave of the COVID-19 virus in China and compare it to other global locations. We provide a comprehensive picture of the spatial propagation from Hubei to other provinces in China in terms of distance, population size, and human mobility and their scaling relations. Since strict quarantine has been usually applied between cities, more insight abo…
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 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…
At the time of this writing, the novel coronavirus (COVID-19) pandemic outbreak has already put tremendous strain on many countries' citizens, resources and economies around the world. Social distancing measures, travel bans, self-quarantines, and business closures are changing the very fabric of societies worldwide. With people forced out of public spaces, much conversation about these phenomena now occurs online, e.g., on social media platforms like Twitter. In this paper, we describe a multilingual coronavirus (COVID-19) Twitter dataset that we have been continuously collecting since Januar…
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 …
As of December 2020, the COVID-19 pandemic has infected over 75 million people, making it the deadliest pandemic in modern history. This study develops a novel compartmental epidemiological model specific to the SARS-CoV-2 virus and analyzes the effect of common preventative measures such as testing, quarantine, social distancing, and vaccination. By accounting for the most prevalent interventions that have been enacted to minimize the spread of the virus, the model establishes a paramount foundation for future mathematical modeling of COVID-19 and other modern pandemics. Specifically, the mod…
[Abridged] Naturally produced droplets from humans (such as those produced by breathing, talking, sneezing, and coughing) include several types of cells (e.g., epithelial cells and cells of the immune system), physiological electrolytes contained in mucous and saliva (e.g. Na+, K+, Cl-), as well as, potentially, several infectious agents (e.g. bacteria, fungi, and viruses). In response to the novel coronavirus SARS-CoV-2 epidemic, which has become a major public health issue worldwide, we provide a concise overview of airborne germ transmission as seen from a physics perspective. We study whet…
To evaluate the effectiveness of the containment on the epidemic spreading of the new Coronavirus disease 2019, we carry on an analysis of the time evolution of the infection in a selected number of different Countries, by considering well-known macroscopic growth laws, the Gompertz law, and the logistic law. We also propose here a generalization of Gompertz law. Our data analysis permits an evaluation of the maximum number of infected individuals. The daily data must be compared with the obtained fits, to verify if the spreading is under control. From our analysis it appears that the spreadin…
During the COVID-19 pandemic, community containment measures have been implemented in different parts of the world. However, despite government recommendations and mandates, a progressive increase in mobility was observed in several sites. This phenomenon is often referred to as "quarantine fatigue". Mathematical models have been used for more than a century to study the dynamics of diseases spread. Since the start of the COVID-19 pandemic, a large number of models have been developed to investigate different aspects of the pandemic. The aim of the present work has been to design and explore a…
Based on the SEIR model and the modeling of urban transportation networks, a general-purpose simulator for the spread of epidemics in Chinese cities is built. The Chinese public transportation system between over 340 prefectural-level cities is modeled as a multi-layer bi-partite network, with layers representing different means of transportation (airlines, railways, sail routes and buses), and nodes divided into two categories (central cities, peripheral cities). At each city, an open-system SEIR model tracks the local spread of the disease, with population in- and out-flow exchanging with th…
We introduce a system of differential equations to assess the impact of (self-)quarantine of symptomatic infectious individuals on disease dynamics. To this end we depart from using the classic bilinear infection process, but remain still within the framework of the mass-action assumption. From the mathematical point of view our model is interesting due to the lack of continuous differentiability at disease free steady states, which implies also that the basic reproductive number cannot be computed following established approaches for certain parameter values. However, we parametrise our mathe…
Ever since the outbreak of the COVID-19 epidemic, various public health control strategies have been proposed and tested against the coronavirus SARS-CoV-2. We study three specific COVID-19 epidemic control models: the susceptible, exposed, infectious, recovered (SEIR) model with vaccination control; the SEIR model with shield immunity control; and the susceptible, un-quarantined infected, quarantined infected, confirmed infected (SUQC) model with quarantine control. We express the control requirement in metric temporal logic (MTL) formulas (a type of formal specification languages) which can …
Public health services are constantly searching for new ways to reduce the spread of infectious diseases, such as public vaccination of asymptomatic individuals, quarantine (isolation) and treatment of symptomatic individuals. Epidemic models have a long history of assisting in public health planning and policy making. In this paper, we introduce epidemic models including variable population size, degree-related imperfect vaccination and quarantine on scale-free networks. More specifically, the models are formulated both on the population with and without permanent natural immunity to infectio…
In this article we propose a compartmental model for the dynamics of Coronavirus Disease 2019 (COVID-19). We take into account the presence of asymptomatic infections and the main policies that have been adopted so far to contain the epidemic: isolation (or social distancing) of a portion of the population, quarantine for confirmed cases and testing. We model isolation by separating the population in two groups: one composed by key-workers that keep working during the pandemic and have a usual contact rate, and a second group consisting of people that are enforced/recommended to stay at home. …
Based on the classical SIR model, we derive a simple modification for the dynamics of epidemics with a known incubation period of infection. The model is described by a system of integro-differential equations. Parameters of our model directly related to epidemiological data. We derive some analytical results, as well as perform numerical simulations. We use the proposed model to analyze COVID-19 epidemic data in Armenia. We propose a strategy: organize a quarantine, and then conduct extensive testing of risk groups during the quarantine, evaluating the percentage of the population among risk …
A mathematical model to calculate the transmissibility of SARS-Cov-2 in Wuhan City was developed and published recently by Tian-Mu Chen et al., Infectious Diseases of Poverty, 2020, https://doi.org/10.1186/s40249-020-00640-3. This paper improves this model in order to study the effect of different scenarios that include actions to contain the pandemic, such as isolation and quarantine of infected and at-risk people. Comparisons made between the different scenarios show that the progress of the infection is found to strongly depend on measures taken in each case. The particular case of Brazil w…
We report a statistical analysis of some highly infected countries by the novel coronavirus (COVID-19). The cumulative infected data were fitted with various growth models (e.g. Logistic equation, Weibull equation and Hill equation) and obtained the power index of top ten highly infected countries. The newly infected data were fitted with Gaussian distribution with the peak at ~40 days for the countries whose infection curves are seem to be saturated. The similarity in growth kinetics of infected people of different countries provides first-hand guidelines to take proper precautions to minimiz…
The COVID-19 pandemic, caused by the novel coronavirus SARS-CoV-2, is currently spreading rapidly throughout the world, causing many deaths and severe economic damage. It is believed that hot and humid conditions do not favor the novel coronavirus, yet this is still under debate due to many uncertainties associated with the COVID-19 data. Here we propose surrogate data tests to examine the preference of this virus to spread under different climate conditions. We find that the disease is significantly (above the 95% confidence level) more common when the temperature is $\sim$10$^\circ$C, the sp…
The new coronavirus (2019-nCoV or SARS-CoV2), inducing the current pandemic disease (COVID-19) and causing pneumoniae in humans, is dramatically increasing in epidemic scale since its first appearance in Wuhan, China, in December 2019. The first infection from epidemic coronaviruses in 2003 fostered the spread of an overwhelming amount of related scientific efforts. The manifold aspects that have been raised, as well as their redundancy offer precious information that has been underexploited and needs to be critically re-evaluated, appropriately used and offered to the whole community, from sc…
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…
The recent spreading of coronavirus made many countries impose restrictions in order to control its dangerous effect on the citizens. We developed a theoretical dynamical model based on compartmental SIR system with additional adjustment taken from Flow network and Markov chain frameworks to illustrate developments and trends based on publicly available data. Based on this Model, code in R was written and fed by stamped publicly available data from authorized governmental websites in Spain and in the Nederlands, to compare trends. Our results show that the 'peak' of infection is already behind…
This paper is based on the observation that, during Covid-19 epidemic, the choice of which individuals should be tested has an important impact on the effectiveness of selective confinement measures. This decision problem is closely related to the problem of optimal sensor selection, which is a very active research subject in control engineering. The goal of this paper is to propose a policy to smartly select the individuals to be tested. The main idea is to model the epidemics as a stochastic dynamic system and to select the individual to be tested accordingly to some optimality criteria, e.g…
University of Macau（澳门大学）；Zhuhai Institutes of Advanced Technology of the Chinese Academy of Sciences（中国科学院珠海先进技术研究院）；Techno India College of Technology（印度Techno印度科技学院）；Universidad Internacional de La Rioja（拉里奥哈国际大学）；University of Granada（格拉纳达大学）
In the advent of the novel coronavirus epidemic since December 2019, governments and authorities have been struggling to make critical decisions under high uncertainty at their best efforts. Composite Monte-Carlo (CMC) simulation is a forecasting method which extrapolates available data which are broken down from multiple correlated/casual micro-data sources into many possible future outcomes by drawing random samples from some probability distributions. For instance, the overall trend and propagation of the infested cases in China are influenced by the temporal-spatial data of the nearby citi…
The temporal growth in the number of deaths in the COVID-19 epidemic is subexponential. Here we show that a piecewise quadratic law provides an excellent fit during the thirty days after the first three fatalities on January 20 and later since the end of March 2020. There is also a brief intermediate period of exponential growth. During the second quadratic growth phase, the characteristic time of the growth is about eight times shorter than in the beginning, which can be understood as the occurrence of separate hotspots. Quadratic behavior can be motivated by peripheral growth when further sp…
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…
This work provides an overview on deterministic and stochastic models that have previously been proposed by us to study the transmission dynamics of the Coronavirus Disease 2019 (COVID-19) in Europe and USA. Briefly, we describe realistic deterministic and stochastic models for the evolution of the COVID-19 pandemic, subject to the lockdown and quarantine measures, which take into account the time-delay for recovery or death processes. Realistic dynamic equations for the entire process have been derived by adopting the so-called "kinetic-type reactions approach". The lockdown and the quarantin…
With the continued spread of coronavirus, the task of forecasting distinctive COVID-19 growth curves in different cities, which remain inadequately explained by standard epidemiological models, is critical for medical supply and treatment. Predictions must take into account non-pharmaceutical interventions to slow the spread of coronavirus, including stay-at-home orders, social distancing, quarantine and compulsory mask-wearing, leading to reductions in intra-city mobility and viral transmission. Moreover, recent work associating coronavirus with human mobility and detailed movement data sugge…
Understanding the number of individuals who have been infected with the novel coronavirus SARS-CoV-2, and the extent to which social distancing policies have been effective at limiting its spread, are critical for effective policy going forward. Here we present estimates of the extent to which confirmed cases in the United States undercount the true number of infections, and analyze how effective social distancing measures have been at mitigating or suppressing the virus. Our analysis uses a Bayesian model of COVID-19 fatalities with a likelihood based on an underlying differential equation mo…
To model the spread of COVID-19 coronavirus in Russian regions and in Moscow, a discrete logistic equation describing the increase in the number of cases is used. To check the adequacy of the mathematical model, the simulation results were compared with the spread of coronavirus in China, in a number of European and Asian countries, and the United States. The parameters of the logistics equation for Russia, Moscow and other large regions were determined in the interval (01.03 - 08.04). A comparative analysis of growth rates of COVID-19 infected population for different countries and regions is…
