A decision-support framework to optimize border control for global outbreak mitigation

Artificial Intelligence for Neurosurgery : Current State and Future Directions

Artificial intelligence (AI) is a field of computer science that equips machines with human-like intelligence and enables them to learn, reason, and solve problems when presented with data in various formats. Neurosurgery is often at the forefront of innovative and disruptive technologies, which have similarly altered the course of acute and chronic diseases. In diagnostic imaging, such as X-rays, computed tomography, and magnetic resonance imaging, AI is used to analyze images. The use of robots in the field of neurosurgery is also increasing. In neurointensive care units, AI is used to analyze data and provide care to critically ill patients. Moreover, AI can be used to predict a patient's prognosis. Several AI applications have already been introduced in the field of neurosurgery, and many more are expected in the near future. Ultimately, it is our responsibility to keep pace with this evolution to provide meaningful outcomes and personalize each patient's care. Rather than blindly relying on AI in the future, neurosurgeons should gain a thorough understanding of it and use it to enhance their patient care.

United by Contagion: How Can China Improve Its Capabilities of Port Infectious Disease Prevention and Control?

The rapid development of the social economy and science and technology has led to more frequent transnational movements of people, goods and vehicles. At the same time, various cross-border risks have significantly increased. The rapid global spread and continuous mutation of Coronavirus Disease 2019 (COVID-19) have again exposed the international community’s extreme vulnerability to major transnational public health emergencies. China started a “war against the epidemic” with tight quarantine regulations and border restrictions on people, vehicles and international goods. However, it also revealed the weaknesses in and incapacity for disease prevention and control at ports in terms of obstructed performance of the whole chain of public agencies, incompatible laws and regulations, lack of key technologies, and difficulties in international cooperation. Combined with persuasive data, this paper systematically illustrates how transnational infectious diseases lead humans to be “united by contagion”. On this basis, this paper makes a targeted analysis of the deficiencies of port epidemic prevention and control in China’s fight against COVID-19 and suggests corresponding countermeasures and reflections.

A symbiosis between cellular automata and dynamic weighted multigraph with application on virus spread modeling

The pattern of coronavirus spread at different geographical scales verifies that travel or shipment by air, sea or road are potential to transmit viruses from one location to somewhere far away in a very short time. Simulation and analysis of such a situation requires the development of models that support long distance transmission of viruses. Cellular Automata (CA) are a family of spatiotemporal computational models frequently employed in analysis of biomedical systems. A CA consists of a topological combination of units called cells as well as a transition function that propagates the configuration of cells locally and step by step. In this paper, we first present some patterns that show the local interaction between CA cells is not sufficient for virus spread modeling, especially at large spatial scales. Then, we generalize the concept of CA by providing a symbiosis between the neighborhood relationship of cells and the transmission channels represented by a dynamic weighted multigraph. Furthermore, we characterize the capabilities of the proposed modeling tool in simulation of the virus spread, and estimating the risk control during the movement restrictions and related health protocols. Finally, we simulate the coronavirus outbreak in the five study areas including three states and two countries. Our experiments using the proposed model verify that the proposed model is capable of formulating different ways of virus transmission, including long-distance transmission, and supports high-precision simulation of the pandemic.

TLQP: Early-stage transportation lock-down and quarantine problem

The advent of COVID-19 is a sensible reminder of the vulnerability of our society to pandemics. We need to be better prepared for finding ways to stem such outbreaks. Except from social distancing and wearing face masks, restricting the movement of people is one important measure necessary to control the spread. Such decisions on the lock-down/reduction of movement should be made in an informed way and, accordingly, modeled as an optimization problem. We propose the Early-stage Transportation Lock-down and Quarantine Problem (TLQP), which can help to decide which parts of the transportation infrastructure of a country should be restricted in early stages. On top of the network-based Susceptible-Exposed-Infectious-Recovered (SEIR) model, we establish a decision recommendation framework, which considers the lock-down of cross-border traffic, internal traffic, and movement inside individual populations. The combinatorial optimization problem aims to find the best set of actions which minimize the social cost of a lock-down. Given the inherent intractability of this problem, we develop a highly-efficient heuristic based on the Effective Distance (ED) path and the Cost-Effective Lazy Forward (CELF) algorithm. We perform and report experiments on the global spread of COVID-19 and show how individual countries may protect their population by taking appropriate measures against the threatening pandemic. We believe that our study contributes to the orchestration of measures for dealing with current and future epidemic outbreaks.

A Full-Scale Agent-Based Model to Hypothetically Explore the Impact of Lockdown, Social Distancing, and Vaccination During the COVID-19 Pandemic in Lombardy, Italy: Model Development

BACKGROUND

The COVID-19 outbreak, an event of global concern, has provided scientists the opportunity to use mathematical modeling to run simulations and test theories about the pandemic.

OBJECTIVE

The aim of this study was to propose a full-scale individual-based model of the COVID-19 outbreak in Lombardy, Italy, to test various scenarios pertaining to the pandemic and achieve novel performance metrics.

METHODS

The model was designed to simulate all 10 million inhabitants of Lombardy person by person via a simple agent-based approach using a commercial computer. In order to obtain performance data, a collision detection model was developed to enable cluster nodes in small cells that can be processed fully in parallel. Within this collision detection model, an epidemic model based mostly on experimental findings about COVID-19 was developed.

RESULTS

The model was used to explain the behavior of the COVID-19 outbreak in Lombardy. Different parameters were used to simulate various scenarios relating to social distancing and lockdown. According to the model, these simple actions were enough to control the virus. The model also explained the decline in cases in the spring and simulated a hypothetical vaccination scenario, confirming, for example, the herd immunity threshold computed in previous works.

CONCLUSIONS

The model made it possible to test the impact of people's daily actions (eg, maintaining social distance) on the epidemic and to investigate interactions among agents within a social network. It also provided insight on the impact of a hypothetical vaccine.

Managing borders during public health emergencies of international concern: a proposed typology of cross-border health measures

BACKGROUND

The near universal adoption of cross-border health measures during the COVID-19 pandemic worldwide has prompted significant debate about their effectiveness and compliance with international law. The number of measures used, and the range of measures applied, have far exceeded previous public health emergencies of international concern. However, efforts to advance research, policy and practice to support their effective use has been hindered by a lack of clear and consistent definition.

RESULTS

Based on a review of existing datasets for cross-border health measures, such as the Oxford Coronavirus Government Response Tracker and World Health Organization Public Health and Social Measures, along with analysis of secondary and grey literature, we propose six categories to define measures more clearly and consistently - policy goal, type of movement (travel and trade), adopted by public or private sector, level of jurisdiction applied, stage of journey, and degree of restrictiveness. These categories are then brought together into a proposed typology that can support research with generalizable findings and comparative analyses across jurisdictions. Addressing the current gaps in evidence about travel measures, including how different jurisdictions apply such measures with varying effects, in turn, enhances the potential for evidence-informed decision-making based on fuller understanding of policy trade-offs and externalities. Finally, through the adoption of standardized terminology and creation of an agreed evidentiary base recognized across jurisdictions, the typology can support efforts to strengthen coordinated global responses to outbreaks and inform future efforts to revise the WHO International Health Regulations (2005).

CONCLUSIONS

The widespread use of cross-border health measures during the COVID-19 pandemic has prompted significant reflection on available evidence, previous practice and existing legal frameworks. The typology put forth in this paper aims to provide a starting point for strengthening research, policy and practice.

Travel-related control measures to contain the COVID-19 pandemic: an evidence map

OBJECTIVES

To comprehensively map the existing evidence assessing the impact of travel-related control measures for containment of the SARS-CoV-2/COVID-19 pandemic.

DESIGN

Rapid evidence map.

DATA SOURCES

MEDLINE, Embase and Web of Science, and COVID-19 specific databases offered by the US Centers for Disease Control and Prevention and the WHO.

ELIGIBILITY CRITERIA

We included studies in human populations susceptible to SARS-CoV-2/COVID-19, SARS-CoV-1/severe acute respiratory syndrome, Middle East respiratory syndrome coronavirus/Middle East respiratory syndrome or influenza. Interventions of interest were travel-related control measures affecting travel across national or subnational borders. Outcomes of interest included infectious disease, screening, other health, economic and social outcomes. We considered all empirical studies that quantitatively evaluate impact available in Armenian, English, French, German, Italian and Russian based on the team's language capacities.

DATA EXTRACTION AND SYNTHESIS

We extracted data from included studies in a standardised manner and mapped them to a priori and (one) post hoc defined categories.

RESULTS

We included 122 studies assessing travel-related control measures. These studies were undertaken across the globe, most in the Western Pacific region (n=71). A large proportion of studies focused on COVID-19 (n=59), but a number of studies also examined SARS, MERS and influenza. We identified studies on border closures (n=3), entry/exit screening (n=31), travel-related quarantine (n=6), travel bans (n=8) and travel restrictions (n=25). Many addressed a bundle of travel-related control measures (n=49). Most studies assessed infectious disease (n=98) and/or screening-related (n=25) outcomes; we found only limited evidence on economic and social outcomes. Studies applied numerous methods, both inferential and descriptive in nature, ranging from simple observational methods to complex modelling techniques.

CONCLUSIONS

We identified a heterogeneous and complex evidence base on travel-related control measures. While this map is not sufficient to assess the effectiveness of different measures, it outlines aspects regarding interventions and outcomes, as well as study methodology and reporting that could inform future research and evidence synthesis.

Simplified model on the timing of easing the lockdown

Lockdown procedures have been proven successful in mitigating the spread of the viruses in this COVID-19 pandemic, but they also have devastating impact on the economy. We use a modified Susceptible-Infectious-Recovered-Deceased model with time dependent infection rate to simulate how the infection is spread under lockdown. The economic cost due to the loss of workforce and incurred medical expenses is evaluated with a simple model. We find the best strategy, meaning the smallest economic cost for the entire course of the pandemic, is to keep the strict lockdown as long as possible.

A dynamic pandemic model evaluating reopening strategies amid COVID-19

Among over 200 COVID-19 affected countries, some are fighting to "flatten the curve", while some others are considering reopening after lockdown. It remains unclear how different reopening strategies obstruct the local virus containment and impact the economy. We develop a model with travelers across heterogeneous epicenters. A low-risk area attempts to safely reopen utilizing internal policies, such as social distancing and contact tracing, and external policies, including capacity quota, quarantine, and tests. Simulations based on the COVID-19 scenario show that external policies differ in efficacy. They can substitute each other and complement internal policies. Simultaneous relaxation of both channels may lead to a new wave of COVID-19 and large economic costs. This work highlights the importance of quantitative assessment prior to implementing reopening strategies.

Outbreak dynamics of COVID-19 in China and the United States

On March 11, 2020, the World Health Organization declared the coronavirus disease 2019, COVID-19, a global pandemic. In an unprecedented collective effort, massive amounts of data are now being collected worldwide to estimate the immediate and long-term impact of this pandemic on the health system and the global economy. However, the precise timeline of the disease, its transmissibility, and the effect of mitigation strategies remain incompletely understood. Here we integrate a global network model with a local epidemic SEIR model to quantify the outbreak dynamics of COVID-19 in China and the United States. For the outbreak in China, in [Formula: see text] provinces, we found a latent period of 2.56 ± 0.72 days, a contact period of 1.47 ± 0.32 days, and an infectious period of 17.82 ± 2.95 days. We postulate that the latent and infectious periods are disease-specific, whereas the contact period is behavior-specific and can vary between different provinces, states, or countries. For the early stages of the outbreak in the United States, in [Formula: see text] states, we adopted the disease-specific values from China and found a contact period of 3.38 ± 0.69 days. Our network model predicts that-without the massive political mitigation strategies that are in place today-the United States would have faced a basic reproduction number of 5.30 ± 0.95 and a nationwide peak of the outbreak on May 10, 2020 with 3 million infections. Our results demonstrate how mathematical modeling can help estimate outbreak dynamics and provide decision guidelines for successful outbreak control. We anticipate that our model will become a valuable tool to estimate the potential of vaccination and quantify the effect of relaxing political measures including total lockdown, shelter in place, and travel restrictions for low-risk subgroups of the population or for the population as a whole.

Information technology in emergency management of COVID-19 outbreak

Emergency management of the emerging infectious disease outbreak is critical for public health threats. Currently, control of the COVID-19 outbreak is an international concern and has become a crucial challenge in many countries. This article reviews significant information technologyIT) applications in emergency management of COVID-19 by considering the prevention/mitigation, preparedness, response, and recovery phases of the crisis. This review was conducted using MEDLINE PubMed), Embase, IEEE, and Google Scholar. Expert opinions were collected to show existence gaps, useful technologies for each phase of emergency management, and future direction. Results indicated that various IT-based systems such as surveillance systems, artificial intelligence, computational methods, Internet of things, remote sensing sensor, online service, and GIS geographic information system) could have different outbreak management applications, especially in response phases. Information technology was applied in several aspects, such as increasing the accuracy of diagnosis, early detection, ensuring healthcare providers' safety, decreasing workload, saving time and cost, and drug discovery. We categorized these applications into four core topics, including diagnosis and prediction, treatment, protection, and management goals, which were confirmed by five experts. Without applying IT, the control and management of the crisis could be difficult on a large scale. For reducing and improving the hazard effect of disaster situations, the role of IT is inevitable. In addition to the response phase, communities should be considered to use IT capabilities in prevention, preparedness, and recovery phases. It is expected that IT will have an influential role in the recovery phase of COVID-19. Providing IT infrastructure and financial support by the governments should be more considered in facilitating IT capabilities.

COVID-19: Data-Driven Mean-Field-Type Game Perspective

In this article, a class of mean-field-type games with discrete-continuous state spaces is considered. We establish Bellman systems which provide sufficiency conditions for mean-field-type equilibria in state-and-mean-field-type feedback form. We then derive unnormalized master adjoint systems (MASS). The methodology is shown to be flexible enough to capture multi-class interaction in epidemic propagation in which multiple authorities are risk-aware atomic decision-makers and individuals are risk-aware non-atomic decision-makers. Based on MASS, we present a data-driven modelling and analytics for mitigating Coronavirus Disease 2019 (COVID-19). The model integrates untested cases, age-structure, decision-making, gender, pre-existing health conditions, location, testing capacity, hospital capacity, and a mobility map of local areas, including in-cities, inter-cities, and internationally. It is shown that the data-driven model can capture most of the reported data on COVID-19 on confirmed cases, deaths, recovered, number of testing and number of active cases in 66+ countries. The model also reports non-Gaussian and non-exponential properties in 15+ countries.

Big data, machine learning, and artificial intelligence: a field guide for neurosurgeons

Big data has transformed into a trend phrase in healthcare and neurosurgery, becoming a pervasive and inescapable phrase in everyday life. The upsurge in big data applications is a direct consequence of the drastic boom in information technology as well as the growing number of internet-connected devices called the Internet of Things in healthcare. Compared with business, marketing, and other sectors, healthcare applications are lagging due to a lack of technical knowledge among healthcare workers, technological limitations in acquiring and analyzing the data, and improper governance of healthcare big data. Despite these limitations, the medical literature is flooded with big data-related articles, and most of these are filled with abstruse terminologies such as machine learning, artificial intelligence, artificial neural network, and algorithm. Many of the recent articles are restricted to neurosurgical registries, creating a false impression that big data is synonymous with registries. Others advocate that the utilization of big data will be the panacea to all healthcare problems and research in the future. Without a proper understanding of these principles, it becomes easy to get lost without the ability to differentiate hype from reality. To that end, the authors give a brief narrative of big data analysis in neurosurgery and review its applications, limitations, and the challenges it presents for neurosurgeons and healthcare professionals naive to this field. Awareness of these basic concepts will allow neurosurgeons to understand the literature regarding big data, enabling them to make better decisions and deliver personalized care.

Data-driven modeling of COVID-19-Lessons learned

Understanding the outbreak dynamics of COVID-19 through the lens of mathematical models is an elusive but significant goal. Within only half a year, the COVID-19 pandemic has resulted in more than 19 million reported cases across 188 countries with more than 700,000 deaths worldwide. Unlike any other disease in history, COVID-19 has generated an unprecedented volume of data, well documented, continuously updated, and broadly available to the general public. Yet, the precise role of mathematical modeling in providing quantitative insight into the COVID-19 pandemic remains a topic of ongoing debate. Here we discuss the lessons learned from six month of modeling COVID-19. We highlight the early success of classical models for infectious diseases and show why these models fail to predict the current outbreak dynamics of COVID-19. We illustrate how data-driven modeling can integrate classical epidemiology modeling and machine learning to infer critical disease parameters-in real time-from reported case data to make informed predictions and guide political decision making. We critically discuss questions that these models can and cannot answer and showcase controversial decisions around the early outbreak dynamics, outbreak control, and exit strategies. We anticipate that this summary will stimulate discussion within the modeling community and help provide guidelines for robust mathematical models to understand and manage the COVID-19 pandemic. EML webinar speakers, videos, and overviews are updated at https://imechanica.org/node/24098.

Is it safe to lift COVID-19 travel bans? The Newfoundland story

A key strategy to prevent a local outbreak during the COVID-19 pandemic is to restrict incoming travel. Once a region has successfully contained the disease, it becomes critical to decide when and how to reopen the borders. Here we explore the impact of border reopening for the example of Newfoundland and Labrador, a Canadian province that has enjoyed no new cases since late April, 2020. We combine a network epidemiology model with machine learning to infer parameters and predict the COVID-19 dynamics upon partial and total airport reopening, with perfect and imperfect quarantine conditions. Our study suggests that upon full reopening, every other day, a new COVID-19 case would enter the province. Under the current conditions, banning air travel from outside Canada is more efficient in managing the pandemic than fully reopening and quarantining 95% of the incoming population. Our study provides quantitative insights of the efficacy of travel restrictions and can inform political decision making in the controversy of reopening.

Is it safe to lift COVID-19 travel bans? The Newfoundland story

A key strategy to prevent a local outbreak during the COVID-19 pandemic is to restrict incoming travel. Once a region has successfully contained the disease, it becomes critical to decide when and how to reopen the borders. Here we explore the impact of border reopening for the example of Newfoundland and Labrador, a Canadian province that has enjoyed no new cases since late April, 2020. We combine a network epidemiology model with machine learning to infer parameters and predict the COVID-19 dynamics upon partial and total airport reopening, with perfect and imperfect quarantine conditions. Our study suggests that upon full reopening, every other day, a new COVID-19 case would enter the province. Under the current conditions, banning air travel from outside Canada is more efficient in managing the pandemic than fully reopening and quarantining 95% of the incoming population. Our study provides quantitative insights of the efficacy of travel restrictions and can inform political decision making in the controversy of reopening.

Outbreak dynamics of COVID-19 in Europe and the effect of travel restrictions

For the first time in history, on March 17, 2020, the European Union closed all its external borders in an attempt to contain the spreading of the coronavirus 2019, COVID-19. Throughout two past months, governments around the world have implemented massive travel restrictions and border control to mitigate the outbreak of this global pandemic. However, the precise effects of travel restrictions on the outbreak dynamics of COVID-19 remain unknown. Here we combine a global network mobility model with a local epidemiology model to simulate and predict the outbreak dynamics and outbreak control of COVID-19 across Europe. We correlate our mobility model to passenger air travel statistics and calibrate our epidemiology model using the number of reported COVID-19 cases for each country. Our simulations show that mobility networks of air travel can predict the emerging global diffusion pattern of a pandemic at the early stages of the outbreak. Our results suggest that an unconstrained mobility would have significantly accelerated the spreading of COVID-19, especially in Central Europe, Spain, and France. Ultimately, our network epidemiology model can inform political decision making and help identify exit strategies from current travel restrictions and total lockdown.

Outbreak dynamics of COVID-19 in Europe and the effect of travel restrictions

For the first time in history, on March 17, 2020, the European Union closed all its external borders in an attempt to contain the spreading of the coronavirus 2019, COVID-19. Throughout two past months, governments around the world have implemented massive travel restrictions and border control to mitigate the outbreak of this global pandemic. However, the precise effects of travel restrictions on the outbreak dynamics of COVID-19 remain unknown. Here we combine a global network mobility model with a local epidemiology model to simulate and predict the outbreak dynamics and outbreak control of COVID-19 across Europe. We correlate our mobility model to passenger air travel statistics and calibrate our epidemiology model using the number of reported COVID-19 cases for each country. Our simulations show that mobility networks of air travel can predict the emerging global diffusion pattern of a pandemic at the early stages of the outbreak. Our results suggest that an unconstrained mobility would have significantly accelerated the spreading of COVID-19, especially in Central Europe, Spain, and France. Ultimately, our network epidemiology model can inform political decision making and help identify exit strategies from current travel restrictions and total lockdown.

Utility of Artificial Intelligence Amidst the COVID 19 Pandemic: A Review

The term machine learning refers to a collection of tools used for identifying patterns in data. As opposed to traditional methods of pattern identification, machine learning tools relies on artificial intelligence to map out patters from large amounts of data, can self-improve as and when new data becomes available and is quicker in accomplishing these tasks. This review describes various techniques of machine learning that have been used in the past in the prediction, detection and management of infectious diseases, and how these tools are being brought into the battle against COVID-19. In addition, we also discuss their applications in various stages of the pandemic, the advantages, disadvantages and possible pit falls.

Outbreak dynamics of COVID-19 in Europe and the effect of travel restrictions

For the first time in history, on March 17, 2020, the European Union closed all its external borders in an attempt to contain the spreading of the coronavirus 2019, COVID-19. Throughout two past months, governments around the world have implemented massive travel restrictions and border control to mitigate the outbreak of this global pandemic. However, the precise effects of travel restrictions on the outbreak dynamics of COVID-19 remain unknown. Here we combine a global network mobility model with a local epidemiology model to simulate and predict the outbreak dynamics and outbreak control of COVID-19 across Europe. We correlate our mobility model to passenger air travel statistics and calibrate our epidemiology model using the number of reported COVID-19 cases for each country. Our simulations show that mobility networks of air travel can predict the emerging global diffusion pattern of a pandemic at the early stages of the outbreak. Our results suggest that an unconstrained mobility would have significantly accelerated the spreading of COVID-19, especially in Central Europe, Spain, and France. Ultimately, our network epidemiology model can inform political decision making and help identify exit strategies from current travel restrictions and total lockdown.

Multiple Epidemic Wave Model of the COVID-19 Pandemic: Modeling Study

BACKGROUND

Intervention measures have been implemented around the world to mitigate the spread of the coronavirus disease (COVID-19) pandemic. Understanding the dynamics of the disease spread and the effectiveness of the interventions is essential in predicting its future evolution.

OBJECTIVE

The aim of this study is to simulate the effect of different social distancing interventions and investigate whether their timing and stringency can lead to multiple waves (subepidemics), which can provide a better fit to the wavy behavior observed in the infected population curve in the majority of countries.

METHODS

We have designed and run agent-based simulations and a multiple wave model to fit the infected population data for many countries. We have also developed a novel Pandemic Response Index to provide a quantitative and objective way of ranking countries according to their COVID-19 response performance.

RESULTS

We have analyzed data from 18 countries based on the multiple wave (subepidemics) hypothesis and present the relevant parameters. Multiple waves have been identified and were found to describe the data better. The effectiveness of intervention measures can be inferred by the peak intensities of the waves. Countries imposing fast and stringent interventions exhibit multiple waves with declining peak intensities. This result strongly corroborated with agent-based simulations outcomes. We also provided an estimate of how much lower the number of infections could have been if early and strict intervention measures had been taken to stop the spread at the first wave, as actually happened for a handful of countries. A novel index, the Pandemic Response Index, was constructed, and based on the model's results, an index value was assigned to each country, quantifying in an objective manner the country's response to the pandemic.

CONCLUSIONS

Our results support the hypothesis that the COVID-19 pandemic can be successfully modeled as a series of epidemic waves (subepidemics) and that it is possible to infer to what extent the imposition of early intervention measures can slow the spread of the disease.

Outbreak dynamics of COVID-19 in China and the United States

On March 11, 2020, the World Health Organization declared the coronavirus disease 2019, COVID-19, a global pandemic. In an unprecedented collective effort, massive amounts of data are now being collected worldwide to estimate the immediate and long-term impact of this pandemic on the health system and the global economy. However, the precise timeline of the disease, its transmissibility, and the effect of mitigation strategies remain incompletely understood. Here we integrate a global network model with a local epidemic SEIR model to quantify the outbreak dynamics of COVID-19 in China and the United States. For the outbreak in China, in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=30$$\end{document}n=30 provinces, we found a latent period of 2.56 ± 0.72 days, a contact period of 1.47 ± 0.32 days, and an infectious period of 17.82 ± 2.95 days. We postulate that the latent and infectious periods are disease-specific, whereas the contact period is behavior-specific and can vary between different provinces, states, or countries. For the early stages of the outbreak in the United States, in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=50$$\end{document}n=50 states, we adopted the disease-specific values from China and found a contact period of 3.38 ± 0.69 days. Our network model predicts that—without the massive political mitigation strategies that are in place today—the United States would have faced a basic reproduction number of 5.30 ± 0.95 and a nationwide peak of the outbreak on May 10, 2020 with 3 million infections. Our results demonstrate how mathematical modeling can help estimate outbreak dynamics and provide decision guidelines for successful outbreak control. We anticipate that our model will become a valuable tool to estimate the potential of vaccination and quantify the effect of relaxing political measures including total lockdown, shelter in place, and travel restrictions for low-risk subgroups of the population or for the population as a whole.

A Review of Coronavirus Disease-2019 (COVID-19)

There is a new public health crises threatening the world with the emergence and spread of 2019 novel coronavirus (2019-nCoV) or the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The virus originated in bats and was transmitted to humans through yet unknown intermediary animals in Wuhan, Hubei province, China in December 2019. There have been around 96,000 reported cases of coronavirus disease 2019 (COVID-2019) and 3300 reported deaths to date (05/03/2020). The disease is transmitted by inhalation or contact with infected droplets and the incubation period ranges from 2 to 14 d. The symptoms are usually fever, cough, sore throat, breathlessness, fatigue, malaise among others. The disease is mild in most people; in some (usually the elderly and those with comorbidities), it may progress to pneumonia, acute respiratory distress syndrome (ARDS) and multi organ dysfunction. Many people are asymptomatic. The case fatality rate is estimated to range from 2 to 3%. Diagnosis is by demonstration of the virus in respiratory secretions by special molecular tests. Common laboratory findings include normal/ low white cell counts with elevated C-reactive protein (CRP). The computerized tomographic chest scan is usually abnormal even in those with no symptoms or mild disease. Treatment is essentially supportive; role of antiviral agents is yet to be established. Prevention entails home isolation of suspected cases and those with mild illnesses and strict infection control measures at hospitals that include contact and droplet precautions. The virus spreads faster than its two ancestors the SARS-CoV and Middle East respiratory syndrome coronavirus (MERS-CoV), but has lower fatality. The global impact of this new epidemic is yet uncertain.

Mathematical Modeling and Forecasting of COVID-19 in Moscow and Novosibirsk Region

We investigate inverse problems of finding unknown parameters of mathematical models SEIR-HCD and SEIR-D of COVID-19 spread with additional information about the number of detected cases, mortality, self-isolation coefficient, and tests performed for the city of Moscow and Novosibirsk region since 23.03.2020. In SEIR-HCD the population is divided into seven groups, and in SEIR-D into five groups with similar characteristics and transition probabilities depending on the specific region of interest. An identifiability analysis of SEIR-HCD is made to reveal the least sensitive unknown parameters as related to the additional information. The parameters are corrected by minimizing some objective functionals which is made by stochastic methods (simulated annealing, differential evolution, and genetic algorithm). Prognostic scenarios for COVID-19 spread in Moscow and in Novosibirsk region are developed, and the applicability of the models is analyzed.

Mathematical Modeling of the Wuhan COVID-2019 Epidemic and Inverse Problems

Mathematical models for transmission dynamics of the novel COVID-2019 coronavirus, an outbreak of which began in December, 2019, in Wuhan are considered. To control the epidemiological situation, it is necessary to develop corresponding mathematical models. Mathematical models of COVID-2019 spread described by systems of nonlinear ordinary differential equations (ODEs) are overviewed. Some of the coefficients and initial data for the ODE systems are unknown or their averaged values are specified. The problem of identifying model parameters is reduced to the minimization of a quadratic objective functional. Since the ODEs are nonlinear, the solution of the inverse epidemiology problems can be nonunique, so approaches for analyzing the identifiability of inverse problems are described. These approaches make it possible to establish which of the unknown parameters (or their combinations) can be uniquely and stably recovered from available additional information. For the minimization problem, methods are presented based on a combination of global techniques (covering methods, nature-like algorithms, multilevel gradient methods) and local techniques (gradient methods and the Nelder–Mead method).