In December 2019, a novel coronavirus was found in a seafood wholesale market in Wuhan, China. WHO officially named this coronavirus as COVID-19. Since the first patient was hospitalized on December 12, 2019, China has reported a total of 78,824 confirmed CONID-19 cases and 2,788 deaths as of February 28, 2020. Wuhan's cumulative confirmed cases and deaths accounted for 61.1% and 76.5% of the whole China mainland , making it the priority center for epidemic prevention and control. Meanwhile, 51 countries and regions outside China have reported 4,879 confirmed cases and 79 deaths as of February 28, 2020. COVID-19 epidemic does great harm to people's daily life and country's economic development. This paper adopts three kinds of mathematical models, i.e., Logistic model, Bertalanffy model and Gompertz model. The epidemic trends of SARS were first fitted and analyzed in order to prove the validity of the existing mathematical models. The results were then used to fit and analyze the situation of COVID-19. The prediction results of three different mathematical models are different for different parameters and in different regions. In general, the fitting effect of Logistic model may be the best among the three models studied in this paper, while the fitting effect of Gompertz model may be better than Bertalanffy model. According to the current trend, based on the three models, the total number of people expected to be infected is 49852-57447 in Wuhan,12972-13405 in non-Hubei areas and 80261-85140 in China respectively. The total death toll is 2502-5108 in Wuhan, 107-125 in Non-Hubei areas and 3150-6286 in China respetively. COVID-19 will be over p robably in late-April, 2020 in Wuhan and before late-March, 2020 in other areas respectively.
In this research, we study the propagation patterns of epidemic diseases such as the COVID-19 coronavirus, from a mathematical modeling perspective. The study is based on an extensions of the well-known susceptible-infected-recovered (SIR) family of compartmental models. It is shown how social measures such as distancing, regional lockdowns, quarantine and global public health vigilance, influence the model parameters, which can eventually change the mortality rates and active contaminated cases over time, in the real world. As with all mathematical models, the predictive ability of the model …
The outbreak of novel coronavirus (2019-nCoV) in China has caused a viral epidemic affecting tens of thousands of persons. Though the danger of this epidemic is evident, the statistical analysis of data offered in this paper indicates that the increase in new cases in China will stabilize in the coming days or weeks. Our forecast could serve to evaluate risks and control the evolution of this disease.
This paper deals with the mathematical modeling and numerical simulations related to the coronavirus dynamics. A description is developed based on the framework of susceptible-exposed-infectious-recovered model. Initially, a model verification is carried out calibrating system parameters with data from China, Italy, Iran and Brazil. Afterward, numerical simulations are performed to analyzed different scenarios of COVID-19 in Brazil. Results show the importance of governmental and individual actions to control the number and the period of the critical situations related to the pandemic.
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 …
COVID-19 is a new type of coronavirus disease which is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It originated in China in the month of December 2019 and quickly started to spread within the country. On 31st December 2019, it was first reported to country office of World Health Organization (WHO) in China. Since then, it has spread to most of the countries around the globe. However, there has been a recent rise in trend in believing that it would go away during summer days, which has not yet been properly investigated. In this paper, relationship of daily number o…
In this paper, I study epidemic diffusion in a generalized spatial SEIRD model, where individuals are initially connected in a social or geographical network. As the virus spreads in the network, the structure of interactions between people may endogenously change over time, due to quarantining measures and/or spatial-distancing policies. I explore via simulations the dynamic properties of the co-evolutionary process dynamically linking disease diffusion and network properties. Results suggest that, in order to predict how epidemic phenomena evolve in networked populations, it is not enough to…
In this paper, we develop a probabilistic mathematical model for the spread of coronavirus disease (COVID-19). It takes into account the known special characteristics of this disease such as the existence of infectious undetected cases and the different social and infectiousness conditions of infected people. In particular, it considers the social structure and governmental measures in a country, the fraction of detected cases over the real total infected cases, and the influx of undetected infected people from outside the borders. Although the model is simple and allows a reasonable identific…
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 …
To increase situational awareness and support evidence-based policy-making, we formulated two types of mathematical models for COVID-19 transmission within a regional population. One is a fitting function that can be calibrated to reproduce an epidemic curve with two timescales (e.g., fast growth and slow decay). The other is a compartmental model that accounts for quarantine, self-isolation, social distancing, a non-exponentially distributed incubation period, asymptomatic individuals, and mild and severe forms of symptomatic disease. Using Bayesian inference, we have been calibrating our mod…
After the sudden outbreak of Coronavirus in Wuhan, continuous and rich data of the epidemic has been made public as the vital fact for decision support in control measures and aggressive implementation of containment strategies and plans. With the further growth and spreading of the virus, future resource allocation and planning under updated strategies and measures rely on careful study of the epidemic data and characteristics for accurate prediction and estimation. By using the SIR model and reported data, key parameters are obtained from least sum of squared errors for an accurate predictio…
With the emergence of a new pandemic worldwide, a novel strategy to approach it has emerged. Several initiatives under the umbrella of "open science" are contributing to tackle this unprecedented situation. In particular, the "R Language and Environment for Statistical Computing" offers an excellent tool and ecosystem for approaches focusing on open science and reproducible results. Hence it is not surprising that with the onset of the pandemic, a large number of R packages and resources were made available for researches working in the pandemic. In this paper, we present an R package that all…
We have learned to live with many potentially deadly viruses for which there is no vaccine, no immunity, and no cure. We do not live in constant fear of these viruses, instead, we have learned how to outsmart them and reduce the harm they cause. A new mathematical model that combines the spread of diseases that do not confer immunity together with the evolution of human behaviors indicates that we may be able to fight new diseases with the same type of strategy we use to fight viruses like HIV.
We developed a mathematical model to describe the transmission of new coronavirus in the São Paulo State, Brazil. The model divided a community in subpopulations comprised by young and elder persons, in order to take into account higher risk of fatality among elder persons with severe CoViD-19. From data collected in the São Paulo State, we estimated the transmission and additional mortality rates, from which we calculated the basic reproduction number R0. From estimated parameters, estimation of the deaths due to CoViD-19 was three times lower than those found in literature. Considering isola…
Since the end of 2019 an outbreak of a new strain of coronavirus, called 2019--nCoV, is reported from China and later other parts of the world. Since January 21, WHO reports daily data on confirmed cases and deaths from both China and other countries. In this work we present some discrete and continuous models to discribe the disease dynamics in China and estimate the needed epidemiological parameters. Good agreement with the current dynamics has be found for both a discrete transmission model and a slightly modified SIR-model.
Human movement decisions during Coronavirus Disease 2019
International Institute for Zoonosis Control, Hokkaido University（国际动物传染病控制研究所，北海道大学）；Faculty of Environmental Earth Science, Hokkaido University（环境地球科学学院，北海道大学）；Recruit Co., Ltd（recruit株式会社）；Department of Biology, Faculty of Science, Kyushu University（理学部生物学系，九州大学）
The rapid transmission of the highly contagious novel coronavirus has been represented through several data-guided approaches across targeted geographies, in an attempt to understand when the pandemic will be under control and imposed lockdown measures can be relaxed. However, these epidemiological models predominantly based on training data employing number of cases and fatalities are limited in that they do not account for the spatiotemporal population dynamics that principally contributes to the disease spread. Here, a stochastic cellular automata enabled predictive model is presented that …
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 …
Amrita Vishwa Vidyapeetham（阿姆里塔维什瓦维迪亚皮塔姆）；Amrita School of Engineering（阿姆里塔工程学院）；Center for Computational Engineering and Networking (CEN)（计算工程与网络中心）
In this paper, we have applied the logistic growth regression model and genetic algorithm to predict the number of coronavirus infected cases that can be expected in upcoming days in India and also estimated the final size and its peak time of the coronavirus epidemic in India.
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 novel coronavirus, SARS-CoV-2, and the disease it causes, COVID-19 was declared a pandemic on March 11, 2020 by the World Health Organization. Since then, the disease has spread all over the world, with the United States becoming the country with the highest number of cases. Governments around the world have undertaken varying degrees of public safety measures, including recommendations and ad campaigns for improved hygiene practices, enacting social distancing requirements and limiting large public gatherings, and stay-at-home orders and lockdowns. In the United States, while the response…
Mathematical models of SARS-CoV-2 spread are used for guiding the design of mitigation steps aimed at containing and decelerating the contagion, and at identifying impending breaches of health care system surge capacity. The challenges of having only lacunary information about daily new infections are compounded by the geographic heterogeneity of the population. To address this problem, we propose to account for the differences between rural and urban settings using network-based, distributed models where the spread of the pandemic is described in distinct local cohorts with nested SEIR models…
Since the beginning of March 2020, the cumulative numbers of cases of infection with the novel coronavirus SARS-CoV-2 in Germany have been reported on a daily basis. The reports originate from national laws, according to which positive test findings must be submitted to the Federal Health Authorities, the Robert Koch Institute, via the local health authorities. Since an enormous number of unreported cases can be expected, the question of how widespread the disease has been in the population cannot be answered based on these administrative reports. Using mathematical modeling, however, estimate…
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 …
Epidemic is a rapid and wide spread of infectious disease threatening many lives and economy damages. It is important to fore-tell the epidemic lifetime so to decide on timely and remedic actions. These measures include closing borders, schools, suspending community services and commuters. Resuming such curfews depends on the momentum of the outbreak and its rate of decay. Being able to accurately forecast the fate of an epidemic is an extremely important but difficult task. Due to limited knowledge of the novel disease, the high uncertainty involved and the complex societal-political factors …
In December 2019, a novel coronavirus (SARS-CoV-2) has been identified to cause acute respiratory disease in humans. An outbreak of this disease has been reported in mainland China with the city of Wuhan as the recognized epicenter. The disease has also been exported to other countries, including the Philippines, but the level of spread is still under control (as of 08 February 2020). To describe and predict the dynamics of the disease, several preliminary mathematical models are formulated by various international study groups. Here, the insights that can be drawn from these models are discus…
A mathematical model is proposed for quantitative description of the outbreak of novel coronavirus COVID-19 in China. Although the model is relatively simple, the comparison with the public data shows that an exact solution solution of the model (with the correctly-specified parameters) leads to the results, which are in good agreement with the measured data. Prediction of the total number of the COVID-19 cases is discussed and an example is presented using the measured data in Austria.
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 …
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…
Objectives.--To estimate the basic reproduction number of the Wuhan novel coronavirus (2019-nCoV). Methods.--Based on the susceptible-exposed-infected-removed (SEIR) compartment model and the assumption that the infectious cases with symptoms occurred before January 25, 2020 are resulted from free propagation without intervention, we estimate the basic reproduction number of 2019-nCoV according to the reported confirmed cases and suspected cases, as well as the theoretical estimated number of infected cases by other research teams, together with some epidemiological determinants learned from t…
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…
An outbreak of respiratory disease caused by a novel coronavirus is ongoing from December 2019. As of July 22, 2020, it has caused an epidemic outbreak with more than 15 million confirmed infections and above 6 hundred thousand reported deaths worldwide. During this period of an epidemic when human-to-human transmission is established and reported cases of coronavirus disease 2019 (COVID-19) are rising worldwide, investigation of control strategies and forecasting are necessary for health care planning. In this study, we propose and analyze a compartmental epidemic model of COVID-19 to predict…
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…
Koya University（科亚大学）；Salahaddin University-Erbil（萨拉赫丁大学埃尔比勒分校）；University of Wolverhampton（伍尔弗汉普顿大学）；Ulster University（阿尔斯特大学）；Howard University（霍华德大学）；Manchester Metropolitan University（曼彻斯特城市大学）
Coronaviruses are a famous family of viruses that cause illness in both humans and animals. The new type of coronavirus COVID-19 was firstly discovered in Wuhan, China. However, recently, the virus has widely spread in most of the world and causing a pandemic according to the World Health Organization (WHO). Further, nowadays, all the world countries are striving to control the COVID-19. There are many mechanisms to detect coronavirus including clinical analysis of chest CT scan images and blood test results. The confirmed COVID-19 patient manifests as fever, tiredness, and dry cough. Particul…
Novel coronavirus-19 (2019-nCoV or COVID-19) is by far the most dangerous coronavirus ever identified for the third time in the three decades capable of infecting not only the animals but also the humans across the globe. Nearly 6000 deaths have been recorded due mainly to COVID-19 outbreak worldwide and more than 50% of these deaths appeared to have evolved from China where the virus was thought to originate. The endemicity of COVID-19 dramatically surpassed severe acute respiratory syndrome coronavirus (SARS-CoV) and Middle East respiratory syndrome coronavirus (MERS-CoV) that were so far di…
COVID-19, a novel coronavirus, is currently a major worldwide threat. It has infected more than a million people globally leading to hundred-thousands of deaths. In such grave circumstances, it is very important to predict the future infected cases to support prevention of the disease and aid in the healthcare service preparation. Following that notion, we have developed a model and then employed it for forecasting future COVID-19 cases in India. The study indicates an ascending trend for the cases in the coming days. A time series analysis also presents an exponential increase in the number o…
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…
The coronavirus disease 2019 (COVID-19) pandemic is changing and impacting lives on a global scale. In this paper, we introduce a mean-field game model in controlling the propagation of epidemics on a spatial domain. The control variable, the spatial velocity, is first introduced for the classical disease models, such as the SIR model. For this proposed model, we provide fast numerical algorithms based on proximal primal-dual methods. Numerical experiments demonstrate that the proposed model illustrates how to separate infected patients in a spatial domain effectively.
This work is a trial in which we propose SIR model and machine learning tools to analyze the coronavirus pandemic in the real world. Based on the public data from \cite{datahub}, we estimate main key pandemic parameters and make predictions on the inflection point and possible ending time for the real world and specifically for Senegal. The coronavirus disease 2019, by World Health Organization, rapidly spread out in the whole China and then in the whole world. Under optimistic estimation, the pandemic in some countries will end soon, while for most part of countries in the world (US, Italy, e…
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 outbreaks of Coronavirus Disease 2019 (COVID-19) have impacted the world significantly. Modeling the trend of infection and real-time forecasting of cases can help decision making and control of the disease spread. However, data-driven methods such as recurrent neural networks (RNN) can perform poorly due to limited daily samples in time. In this work, we develop an integrated spatiotemporal model based on the epidemic differential equations (SIR) and RNN. The former after simplification and discretization is a compact model of temporal infection trend of a region while the latter models t…
In March of 2020, many U.S. state governments encouraged or mandated restrictions on social interactions to slow the spread of COVID-19, the disease caused by the novel coronavirus SARS-CoV-2 that has spread to nearly 180 countries. Estimating the effectiveness of these social-distancing strategies is challenging because surveillance of COVID-19 has been limited, with tests generally being prioritized for high-risk or hospitalized cases according to temporally and regionally varying criteria. Here we show that reductions in mobility across U.S. counties with at least 100 confirmed cases of COV…
The novel coronavirus and its deadly outbreak have posed grand challenges to human society: as of March 26, 2020, there have been 85,377 confirmed cases and 1,293 reported deaths in the United States; and the World Health Organization (WHO) characterized coronavirus disease (COVID-19) - which has infected more than 531,000 people with more than 24,000 deaths in at least 171 countries - a global pandemic. A growing number of areas reporting local sub-national community transmission would represent a significant turn for the worse in the battle against the novel coronavirus, which points to an u…
Since December 2019, A novel coronavirus (2019-nCoV) has been breaking out in China, which can cause respiratory diseases and severe pneumonia. Mathematical and empirical models relying on the epidemic situation scale for forecasting disease outbreaks have received increasing attention. Given its successful application in the evaluation of infectious diseases scale, we propose a Susceptible-Undiagnosed-Infected-Removed (SUIR) model to offer the effective prediction, prevention, and control of infectious diseases. Our model is a modified susceptible-infected-recovered (SIR) model that injects u…
Tremendous effort has been given to the development of diagnostic tests, preventive vaccines, and therapeutic medicines for coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Much of this development has been based on the reference genome collected on January 5, 2020. Based on the genotyping of 6156 genome samples collected up to April 24, 2020, we report that SARS-CoV-2 has had 4459 alarmingly mutations which can be clustered into five subtypes. We introduce mutation ratio and mutation $h$-index to characterize the protein conservativen…
The year 2020 has seen an unprecedented COVID-19 pandemic due to the outbreak of a novel strain of coronavirus in 180 countries. In a desperate effort to discover new drugs and vaccines for COVID-19, many scientists are working around the clock. Their valuable time and effort may benefit from computer-based mining of a large volume of health science literature that is a treasure trove of information. In this paper, we have developed a graph-based model using abstracts of 10,683 scientific articles to find key information on three topics: transmission, drug types, and genome research related to…
The coronavirus pandemic has rapidly evolved into an unprecedented crisis. The susceptible-infectious-removed (SIR) model and its variants have been used for modeling the pandemic. However, time-independent parameters in the classical models may not capture the dynamic transmission and removal processes, governed by virus containment strategies taken at various phases of the epidemic. Moreover, very few models account for possible inaccuracies of the reported cases. We propose a Poisson model with time-dependent transmission and removal rates to account for possible random errors in reporting …
Faced with the 2020 SARS-CoV2 epidemic, public health officials have been seeking models that could be used to predict not only the number of new cases but also the levels of hospitalisation, critical care and deaths. In this paper we present a stochastic compartmental model capable of real-time monitoring and forecasting of the pandemic incorporating multiple streams of real-world data, reported cases, testing intensity, deaths, hospitalisations and critical care occupancy. Model parameters are estimated via a Bayesian particle filtering technique. The model successfully tracks the key variab…
Governments around the world have implemented preventive measures against the spread of the coronavirus disease (COVID-19). In this study, we consider a multivariate discrete-time Markov model to analyze the propagation of COVID-19 across 33 provincial regions in China. This approach enables us to evaluate the effect of mobility restriction policies on the spread of the disease. We use data on daily human mobility across regions and apply the Bayesian framework to estimate the proposed model. The results show that the spread of the disease in China was predominately driven by community transmi…
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…
Mathematical models have been used to understand the spread patterns of infectious diseases such as Coronavirus Disease 2019 (COVID-19). The transmission component of the models can be modelled in an age-dependent manner via introducing contact matrix for the population, which describes the contact rates between the age groups. Since social contact patterns vary from country to country, we can compare and group the countries using the corresponding contact matrices. In this paper, we present a framework for clustering countries based on their contact matrices with respect to an underlying epid…
