Mathematical modeling of COVID-19 in 14.8 million individuals in Bahia, Brazil

Modeling the impact of hospital beds and vaccination on the dynamics of an infectious disease

The unprecedented scale and rapidity of dissemination of re-emerging and emerging infectious diseases impose new challenges for regulators and health authorities. To curb the dispersal of such diseases, proper management of healthcare facilities and vaccines are core drivers. In the present work, we assess the unified impact of healthcare facilities and vaccination on the control of an infectious disease by formulating a mathematical model. To formulate the model for any region, we consider four classes of human population; namely, susceptible, infected, hospitalized, and vaccinated. It is assumed that the increment in number of beds in hospitals is continuously made in proportion to the number of infected individuals. To ensure the occurrence of transcritical, saddle-node and Hopf bifurcations, the conditions are derived. The normal form is obtained to show the existence of Bogdanov-Takens bifurcation. To validate the analytically obtained results, we have conducted some numerical simulations. These results will be useful to public health authorities for planning appropriate health care resources and vaccination programs to diminish prevalence of infectious diseases.

Clinical Severity of SARS-CoV-2 Variants during COVID-19 Vaccination: A Systematic Review and Meta-Analysis

Due to the variation in the SARS-CoV-2 virus, COVID-19 exhibits significant variability in severity. This presents challenges for governments in managing the allocation of healthcare resources and prioritizing health interventions. Clinical severity is also a critical statistical parameter for researchers to quantify the risks of infectious disease, model the transmission of COVID-19, and provide some targeted measures to control the pandemic. To obtain more accurate severity estimates, including confirmed case-hospitalization risk, confirmed case-fatality risk, hospitalization-fatality risk, and hospitalization-ICU risk, we conducted a systematic review and meta-analysis on the clinical severity (including hospitalization, ICU, and fatality risks) of different variants during the period of COVID-19 mass vaccination and provided pooled estimates for each clinical severity metric. All searches were carried out on 1 February 2022 in PubMed for articles published from 1 January 2020 to 1 February 2022. After identifying a total of 3536 studies and excluding 3523 irrelevant studies, 13 studies were included. The severity results show that the Delta and Omicron variants have the highest (6.56%, 0.46%, 19.63%, and 9.06%) and lowest severities (1.51%, 0.04%, 6.01%, and 3.18%), respectively, according to the four clinical severity metrics. Adults over 65 have higher severity levels for all four clinical severity metrics.

Predictive dynamical modeling and stability of the equilibria in a discrete fractional difference COVID-19 epidemic model

The SARSCoV-2 virus, also known as the coronavirus-2, is the consequence of COVID-19, a severe acute respiratory syndrome. Droplets from an infectious individual are how the pathogen is transmitted from one individual to another and occasionally, these particles can contain toxic textures that could also serve as an entry point for the pathogen. We formed a discrete fractional-order COVID-19 framework for this investigation using information and inferences from Thailand. To combat the illnesses, the region has implemented mandatory vaccination, interpersonal stratification and mask distribution programs. As a result, we divided the vulnerable people into two groups: those who support the initiatives and those who do not take the influence regulations seriously. We analyze endemic problems and common data while demonstrating the threshold evolution defined by the fundamental reproductive quantity R 0 . Employing the mean general interval, we have evaluated the configuration value systems in our framework. Such a framework has been shown to be adaptable to changing pathogen populations over time. The Picard Lindelöf technique is applied to determine the existence-uniqueness of the solution for the proposed scheme. In light of the relationship between the R 0 and the consistency of the fixed points in this framework, several theoretical conclusions are made. Numerous numerical simulations are conducted to validate the outcome.

Mathematical Modeling Evaluates How Vaccinations Affected the Course of COVID-19 Disease Progression

The regulation policies implemented, the characteristics of vaccines, and the evolution of the virus continue to play a significant role in the progression of the SARS-CoV-2 pandemic. Numerous research articles have proposed using mathematical models to predict the outcomes of different scenarios, with the aim of improving awareness and informing policy-making. In this work, we propose an expansion to the classical SEIR epidemiological model that is designed to fit the complex epidemiological data of COVID-19. The model includes compartments for vaccinated, asymptomatic, hospitalized, and deceased individuals, splitting the population into two branches based on the severity of progression. In order to investigate the impact of the vaccination program on the spread of COVID-19 in Greece, this study takes into account the realistic vaccination program implemented in Greece, which includes various vaccination rates, different dosages, and the administration of booster shots. It also examines for the first time policy scenarios at crucial time-intervention points for Greece. In particular, we explore how alterations in the vaccination rate, immunity loss, and relaxation of measures regarding the vaccinated individuals affect the dynamics of COVID-19 spread. The modeling parameters revealed an alarming increase in the death rate during the dominance of the delta variant and before the initiation of the booster shot program in Greece. The existing probability of vaccinated people becoming infected and transmitting the virus sets them as catalytic players in COVID-19 progression. Overall, the modeling observations showcase how the criticism of different intervention measures, the vaccination program, and the virus evolution has been present throughout the various stages of the pandemic. As long as immunity declines, new variants emerge, and vaccine protection in reducing transmission remains incompetent; monitoring the complex vaccine and virus evolution is critical to respond proactively in the future.

Mathematical modeling and investigation on the role of demography and contact patterns in social distancing measures effectiveness in COVID-19 dissemination

In this article, we investigate the importance of demography and contact patterns in determining the spread of COVID-19 and to the effectiveness of social distancing policies. We investigate these questions proposing an augmented epidemiological model with an age-structured model, with the population divided into susceptible (S), exposed (E), asymptomatic infectious (A), hospitalized (H), symptomatic infectious (I) and recovered individuals (R), to simulate COVID-19 dissemination. The simulations were carried out using six combinations of four types of isolation policies (work restrictions, isolation of the elderly, community distancing and school closures) and four representative fictitious countries generated over alternative demographic transition stage patterns (aged developed, developed, developing and least developed countries). We concluded that the basic reproduction number depends on the age profile and the contact patterns. The aged developed country had the lowest basic reproduction number ($R0=1.74$) due to the low contact rate among individuals, followed by the least developed country ($R0=2.00$), the developing country ($R0=2.43$) and the developed country ($R0=2.64$). Because of these differences in the basic reproduction numbers, the same intervention policies had higher efficiencies in the aged and least developed countries. Of all intervention policies, the reduction in work contacts and community distancing were the ones that produced the highest decrease in the $R0$ value, prevalence, maximum hospitalization demand and fatality rate. The isolation of the elderly was more effective in the developed and aged developed countries. The school closure was the less effective intervention policy, though its effects were not negligible in the least developed and developing countries.

Uncertainty quantification in mechanistic epidemic models via cross-entropy approximate Bayesian computation

This paper proposes a data-driven approximate Bayesian computation framework for parameter estimation and uncertainty quantification of epidemic models, which incorporates two novelties: (i) the identification of the initial conditions by using plausible dynamic states that are compatible with observational data; (ii) learning of an informative prior distribution for the model parameters via the cross-entropy method. The new methodology's effectiveness is illustrated with the aid of actual data from the COVID-19 epidemic in Rio de Janeiro city in Brazil, employing an ordinary differential equation-based model with a generalized SEIR mechanistic structure that includes time-dependent transmission rate, asymptomatics, and hospitalizations. A minimization problem with two cost terms (number of hospitalizations and deaths) is formulated, and twelve parameters are identified. The calibrated model provides a consistent description of the available data, able to extrapolate forecasts over a few weeks, making the proposed methodology very appealing for real-time epidemic modeling.

A new method for spatio-temporal transmission prediction of COVID-19

COVID-19 is the most serious public health event of the 21st century and has had a huge impact across the world. The spatio-temporal pattern analysis and simulation of epidemic spread have become the focus of current research. LSTM model has made a lot of achievements in the prediction of infectious diseases by virtue of its advantages in time prediction, but lacks the spatial expression. CA model plays an important role in epidemic spatial propagation modeling due to its unique evolution characteristics from local to global. However, no existing studies of CA have considered long-term dependence due to the impact of time changes on the evolution of the epidemic, and few have modeled using location data from actual diagnosed patients. Therefore, we proposed a LSTM-CA model to solve above mentioned problems. Base on the advantages of LSTM in temporal level and CA in spatial level, LSTM and CA are integrated from the spatio-temporal perspective of geography based on the fine-grained characteristics of epidemic data. The method divides the study area into regular grids, simulates the spatial interactions between neighborhood cells with the help of CA model, and extracts the parameters affecting the transition probability in CA with the help of LSTM model to assist evolution. Simulations are conducted in Python 3.4 to model the propagation of COVID-19 between Feb, 6 to Mar 20, 2020 in China. Experimental results show that, LSTM-CA performs a higher statistical accuracy than LSTM and spatial accuracy than CA, which could demonstrate the effectiveness of the proposed model. This method could be universal for the temporal and spatial transmission of major public health events. Especially in the early stage of the epidemic, we can quickly understand its development trend and cycle, so as to provide an important reference for epidemic prevention and control and public sentiment counseling.

Profile of COVID-19 in Brazil-risk factors and socioeconomic vulnerability associated with disease outcome: retrospective analysis of population-based registers

OBJECTIVES

To classify the most up-to-date factors associated with COVID-19 disease outcomes in Brazil.

DESIGN

Retrospective study.

SETTING

Nationwide Brazilian COVID-19 healthcare registers.

PARTICIPANTS

We used healthcare data of individuals diagnosed with mild/moderate (n=70 056 602) or severe (n=2801 380) COVID-19 disease in Brazil between 26 February 2020 and 15 November 2021.

MAIN OUTCOME MEASURES

Risk of hospitalisation and mortality affected by demographic, clinical and socioeconomic variables were estimated. The impacts of socioeconomic inequalities on vaccination rates, cases and deaths were also evaluated.

RESULTS

15.6 million SARS-CoV-2 infection cases and 584 761 COVID-19-related deaths occurred in Brazil between 26 February 2020 and 15 November 2021. Overall, men presented a higher odds of death than women (OR=1.14, 95% CI 1.13 to 1.15), but postpartum patients admitted to hospital wards were at increased odds of dying (OR=1.23, 95% CI 1.13 to 1.34) compared with individuals without reported comorbidities. Death in younger age groups was notably higher in most deprived municipalities and also among individuals <40 years belonging to indigenous backgrounds compared with white patients, as shown by descriptive analysis. Ethnic/racial backgrounds exhibited a continuum of decreasing survival chances of mixed-race (OR=1.11, 95% CI 1.10 to 1.12), black (OR=1.34, 95% CI 1.32 to 1.36) and indigenous (OR=1.42, 95% CI 1.31 to 1.54) individuals, while those in most deprived municipalities also presented an increased odds of death (OR=1.38, 95% CI 1.36 to 1.40). Deprivation levels also affect the prompt referral of patients to adequate care. Our results show that the odds of death of individuals hospitalised for less than 4 days is more than double that of patients with close-to-average hospital stays (OR=2.07, 95% CI 2.05 to 2.10). Finally, negative vaccination status also increased the odds of dying from the disease (OR=1.29, 95% CI 1.28 to 1.31).

CONCLUSIONS

The data provide evidence that the patterns of COVID-19 mortality in Brazil are influenced by both individual-level health and social risk factors, as well as municipality-level deprivation. In addition, these data suggest that there may be inequalities in the timely provision of appropriate healthcare that are related to municipality-level deprivation.

Mental health among healthcare workers during the prolonged COVID-19 pandemic: A cross-sectional survey in Jilin Province in China

Background

The prolonged COVID-19 pandemic has seriously impacted the mental health of healthcare workers. This study aimed to explore the mental health status of healthcare workers, compare the differences in mental health between physicians and nurses, and verify the impact of risk perception on mental health in the long-term COVID-19 pandemic in Jilin Province, China.

Methods

A stratified random sample was used to conduct an on-site questionnaire survey in December 2020 to measure the mental health status, risk perceptions, and demographic characteristics of healthcare workers in Jilin Province, China. A total of 3,383 participants completed the questionnaire survey, of which 3,373 were valid questionnaires.

Results

A total of 23.6% (n = 795) of participants had symptoms of depression, 27.4% (n = 923) had symptoms of anxiety, and 16.3% (n = 551) had symptoms of stress. Physicians reported significantly higher rates of depression and anxiety than nurses (p = 0.023, p = 0.013, respectively). There was no significant difference in the proportion of participants with stress between physicians and nurses (p = 0.474). Multivariate logistic regression results showed that healthcare workers who had a high level of risk perception were more likely to have symptoms of depression (AOR = 4.12, p < 0.001), anxiety (AOR = 3.68, p < 0.001), and stress (AOR = 4.45, p < 0.001) after controlling for other variables.

Conclusion

At least one in six healthcare workers experienced mental health problems, and physicians were more likely than nurses to suffer from depression during the prolonged COVID-19 epidemic. Risk perception was highly predictive of depression, anxiety, and stress symptoms in medical staff. Public health interventions are needed to mitigate the long-term psychological impact of the COVID-19 pandemic.

Identification of the effects of COVID-19 on patients with pulmonary fibrosis and lung cancer: a bioinformatics analysis and literature review

Coronavirus disease 2019 (COVID-19) poses a serious threat to human health and life. The effective prevention and treatment of COVID-19 complications have become crucial to saving patients’ lives. During the phase of mass spread of the epidemic, a large number of patients with pulmonary fibrosis and lung cancers were inevitably infected with the SARS-CoV-2 virus. Lung cancers have the highest tumor morbidity and mortality rates worldwide, and pulmonary fibrosis itself is one of the complications of COVID-19. Idiopathic lung fibrosis (IPF) and various lung cancers (primary and metastatic) become risk factors for complications of COVID-19 and significantly increase mortality in patients. Therefore, we applied bioinformatics and systems biology approaches to identify molecular biomarkers and common pathways in COVID-19, IPF, colorectal cancer (CRC) lung metastasis, SCLC and NSCLC. We identified 79 DEGs between COVID-19, IPF, CRC lung metastasis, SCLC and NSCLC. Meanwhile, based on the transcriptome features of DSigDB and common DEGs, we identified 10 drug candidates. In this study, 79 DEGs are the common core genes of the 5 diseases. The 10 drugs were found to have positive effects in treating COVID-19 and lung cancer, potentially reducing the risk of pulmonary fibrosis.

Estimating the effective reproduction number for heterogeneous models using incidence data

The effective reproduction number, R ( t ) , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of R ( t ) , using incidence data, rely on the generation interval distribution, g(τ), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain g(τ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.

Estimating the effective reproduction number for heterogeneous models using incidence data

The effective reproduction number, R ( t ) , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of R ( t ) , using incidence data, rely on the generation interval distribution, g(τ), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain g(τ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.

Estimating the effective reproduction number for heterogeneous models using incidence data

The effective reproduction number, R ( t ) , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of R ( t ) , using incidence data, rely on the generation interval distribution, g(τ), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain g(τ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.

Enhancing resilience in construction against infectious diseases using stochastic multi-agent approach

To recover from the adverse impacts of COVID-19 on construction and to avoid further losses to the industry in future pandemics, the resilience of construction industry needs to be enhanced against infectious diseases. Currently, there is a gap for modelling frameworks to simulate the spread of infectious diseases in construction projects at micro-level and to test interventions' effectiveness for data-informed decision-making. Here, this gap is addressed by developing a simulation framework using stochastic agent-based modelling, which enables construction researchers and practitioners to simulate and limit the spread of infectious diseases in construction projects. This is specifically important, since the results of a building project case-study reveals that, in comparison to the general population, infectious diseases may spread faster among construction workers and fatalities can be significantly higher. The proposed framework motivates future research on micro-level modelling of infectious diseases and efforts for intervening the spread of diseases in construction projects.

Disease spreading modeling and analysis: a survey

MOTIVATION

The control of the diffusion of diseases is a critical subject of a broad research area, which involves both clinical and political aspects. It makes wide use of computational tools, such as ordinary differential equations, stochastic simulation frameworks and graph theory, and interaction data, from molecular to social granularity levels, to model the ways diseases arise and spread. The coronavirus disease 2019 (COVID-19) is a perfect testbench example to show how these models may help avoid severe lockdown by suggesting, for instance, the best strategies of vaccine prioritization.

RESULTS

Here, we focus on and discuss some graph-based epidemiological models and show how their use may significantly improve the disease spreading control. We offer some examples related to the recent COVID-19 pandemic and discuss how to generalize them to other diseases.

Reframing the environment in data-intensive health sciences

In this paper, we analyse the relation between the use of environmental data in contemporary health sciences and related conceptualisations and operationalisations of the notion of environment. We consider three case studies that exemplify a different selection of environmental data and mode of data integration in data-intensive epidemiology. We argue that the diversification of data sources, their increase in scale and scope, and the application of novel analytic tools have brought about three significant conceptual shifts. First, we discuss the EXPOsOMICS project, an attempt to integrate genomic and environmental data which suggests a reframing of the boundaries between external and internal environments. Second, we explore the MEDMI platform, whose efforts to combine health, environmental and climate data instantiate a reframing and expansion of environmental exposure. Third, we illustrate how extracting epidemiological insights from extensive social data collected by the CIDACS institute yields innovative attributions of causal power to environmental factors. Identifying these shifts highlights the benefits and opportunities of new environmental data, as well as the challenges that such tools bring to understanding and fostering health. It also emphasises the constraints that data selection and accessibility pose to scientific imagination, including how researchers frame key concepts in health-related research.

A new comparative study on the general fractional model of COVID-19 with isolation and quarantine effects

A generalized version of fractional models is introduced for the COVID-19 pandemic, including the effects of isolation and quarantine. First, the general structure of fractional derivatives and integrals is discussed; then the generalized fractional model is defined from which the stability results are derived. Meanwhile, a set of real clinical observations from China is considered to determine the parameters and compute the basic reproduction number, i.e., R0≈6.6361. Additionally, an efficient numerical technique is applied to simulate the new model and provide the associated numerical results. Based on these simulations, some figures and tables are presented, and the data of reported cases from China are compared with the numerical findings in both classical and fractional frameworks. Our comparative study indicates that a particular case of general fractional formula provides a better fit to the real data compared to the other classical and fractional models. There are also some other key parameters to be examined that show the health of society when they come to eliminate the disease.

Characterizing stages of COVID-19 epidemics: a nonlinear physics perspective based on amplitude equations

The relevant dynamics underlying COVID-19 waves is described from an amplitude space perspective. To this end, the amplitude dynamics of infected populations is considered in different stages of epidemic waves. Eigenvectors and their corresponding amplitudes are derived analytically for low-dimensional models and by means of computational methods for high-dimensional models. It is shown that the amplitudes of all eigenvectors as functions of time can be tracked through the diverse stages of COVID-19 waves featuring jumps at the stage boundaries. In particular, it is shown that under certain circumstances the initial, outbreak stage and the final, subsiding stage of an epidemic wave are primarily determined by the unstable eigenvector of the initial stage and its corresponding remnant vector of the final stage. The corresponding amplitude captures most of the dynamics of the emerging and subsiding epidemics such that the problem at hand effectively becomes one dimensional leading to a dramatic reduction of the complexity of the problem at hand. Explicitly demonstrated for the first-wave COVID-19 epidemics of the year 2020 in the state of New York and Pakistan are given.

SARS-coronavirus-2 infections: biological instabilities characterized by order parameters

A four-variable virus dynamics TIIV model was considered that involves infected cells in an eclipse phase. The state space description of the model was transferred into an amplitude space description which is the appropriate general, nonlinear physics framework to describe instabilities. In this context, the unstable eigenvector or order parameter of the model was determined. Subsequently, a model-based analysis of viral load data from eight symptomatic COVID-19 patients was conducted. For all patients, it was found that the initial SARS-CoV-2 infection evolved along the respective patient-specific order parameter, as expected by theoretical considerations. The order parameter amplitude that described the initial virus multiplication showed doubling times between 30 minutes and 3 hours. Peak viral loads of patients were linearly related to the amplitudes of the patient order parameters. Finally, it was found that the patient order parameters determined qualitatively and quantitatively the relationships between the increases in virus-producing infected cells and infected cells in the eclipse phase. Overall, the study echoes the 40 years old suggestion by Mackey and Glass to consider diseases as instabilities.

Asymptomatic and pre-symptomatic infection in Coronavirus Disease 2019 pandemic

With the presence of Coronavirus Disease 2019 (COVID-19) asymptomatic infections detected, their proportion, transmission potential, and other aspects such as immunity and related emerging challenges have attracted people's attention. We have found that based on high-quality research, asymptomatic infections account for at least one-third of the total cases, whereas based on systematic review and meta-analysis, the proportion is about one-fifth. Evaluating the true transmission potential of asymptomatic cases is difficult but critical, since it may affect national policies in response to COVID-19. We have summarized the current evidence and found, compared with symptomatic cases, the transmission capacity of asymptomatic individuals is weaker, even though they have similar viral load and relatively short virus shedding duration. As the outbreak progresses, asymptomatic infections have also been found to develop long COVID-19. In addition, the role of asymptomatic infection in COVID-19 remains to be further revealed as the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants continue to emerge. Nevertheless, as asymptomatic infections transmit the SARS-CoV-2 virus silently, they still pose a substantial threat to public health. Therefore, it is essential to conduct screening to obtain more knowledge about the asymptomatic infections and to detect them as soon as possible; meanwhile, management of them is also a key point in the fight against COVID-19 community transmission. The different management of asymptomatic infections in various countries are compared and the experience in China is displayed in detail.

Understanding the uneven spread of COVID-19 in the context of the global interconnected economy

The worldwide spread of the COVID-19 pandemic is a complex and multivariate process differentiated across countries, and geographical distance is acceptable as a critical determinant of the uneven spreading. Although social connectivity is a defining condition for virus transmission, the network paradigm in the study of the COVID-19 spatio-temporal spread has not been used accordingly. Toward contributing to this demand, this paper uses network analysis to develop a multidimensional methodological framework for understanding the uneven (cross-country) spread of COVID-19 in the context of the globally interconnected economy. The globally interconnected system of tourism mobility is modeled as a complex network and studied within the context of a three-dimensional (3D) conceptual model composed of network connectivity, economic openness, and spatial impedance variables. The analysis reveals two main stages in the temporal spread of COVID-19, defined by the cutting-point of the 44th day from Wuhan. The first describes the outbreak in Asia and North America, the second stage in Europe, South America, and Africa, while the outbreak in Oceania intermediates. The analysis also illustrates that the average node degree exponentially decays as a function of COVID-19 emergence time. This finding implies that the highly connected nodes, in the Global Tourism Network (GTN), are disproportionally earlier infected by the pandemic than the other nodes. Moreover, countries with the same network centrality as China are early infected on average by COVID-19. The paper also finds that network interconnectedness, economic openness, and transport integration are critical determinants in the early global spread of the pandemic, and it reveals that the spatio-temporal patterns of the worldwide spreading of COVID-19 are more a matter of network interconnectivity than of spatial proximity.

Modeling the COVID-19 Epidemic With Multi-Population and Control Strategies in the United States

As of January 19, 2021, the cumulative number of people infected with coronavirus disease-2019 (COVID-19) in the United States has reached 24,433,486, and the number is still rising. The outbreak of the COVID-19 epidemic has not only affected the development of the global economy but also seriously threatened the lives and health of human beings around the world. According to the transmission characteristics of COVID-19 in the population, this study established a theoretical differential equation mathematical model, estimated model parameters through epidemiological data, obtained accurate mathematical models, and adopted global sensitivity analysis methods to screen sensitive parameters that significantly affect the development of the epidemic. Based on the established precise mathematical model, we calculate the basic reproductive number of the epidemic, evaluate the transmission capacity of the COVID-19 epidemic, and predict the development trend of the epidemic. By analyzing the sensitivity of parameters and finding sensitive parameters, we can provide effective control strategies for epidemic prevention and control. After appropriate modifications, the model can also be used for mathematical modeling of epidemics in other countries or other infectious diseases.

Assessing vaccination priorities for different ages and age-specific vaccination strategies of COVID-19 using an SEIR modelling approach

In the past year, the global epidemic situation is still not optimistic, showing a trend of continuous expansion. With the research and application of vaccines, there is an urgent need to develop some optimal vaccination strategies. How to make a reasonable vaccination strategy to determine the priority of vaccination under the limited vaccine resources to control the epidemic and reduce human casualties? We build a dynamic model with vaccination which is extended the classical SEIR model. By fitting the epidemic data of three countries—China, Brazil, Indonesia, we have evaluated age-specific vaccination strategy for the number of infections and deaths. Furthermore, we have evaluated the impact of age-specific vaccination strategies on the number of the basic reproduction number. At last, we also have evaluated the different age structure of the vaccination priority. It shows that giving priority to vaccination of young people can control the number of infections, while giving priority to vaccination of the elderly can greatly reduce the number of deaths in most cases. Furthermore, we have found that young people should be mainly vaccinated to reduce the number of infections. When the emphasis is on reducing the number of deaths, it is important to focus vaccination on the elderly. Simulations suggest that appropriate age-specific vaccination strategies can effectively control the epidemic, both in terms of the number of infections and deaths.

The Organic Turn: Coping With Pandemic and Non-pandemic Challenges by Integrating Evidence-, Theory-, Experience-, and Context-Based Knowledge in Advising Health Policy

The COVID-19 pandemic has posed an extraordinary challenge for public health and health policy. Questions have arisen concerning the main strategies to cope with this situation and the lessons to be learned from the pandemic. This conceptual paper aims to clarify these questions via sociological concepts. Regarding coping strategies used during the pandemic, there is a strong tendency for health policymakers to rely on expert knowledge rather than on evidence-based knowledge. This has caused the evidence-based healthcare community to respond to urgent demands for advice by rapidly processing new knowledge. Nonetheless, health policymakers still mainly rely on experts in making policy decisions. Our sociological analysis of this situation identified three lessons for coping with pandemic and non-pandemic health challenges: (1) the phenomenon of accelerating knowledge processing could be interpreted from the organizational innovation perspective as a shift from traditional mechanistic knowledge processing to more organic forms of knowledge processing. This can be described as an "organic turn." (2) The return of experts is part of this organic turn and shows that experts provide both evidence-based knowledge as well as theoretical, experiential, and contextual knowledge. (3) Experts can use theory to expeditiously provide advice at times when there is limited evidence available and to provide complexity-reducing orientation for decisionmakers at times where knowledge production leads to an overload of knowledge; thus, evidence-based knowledge should be complemented by theory-based knowledge in a structured two-way interaction to obtain the most comprehensive and valid recommendations for health policy.

Social stress drives the multi-wave dynamics of COVID-19 outbreaks

The dynamics of epidemics depend on how people's behavior changes during an outbreak. At the beginning of the epidemic, people do not know about the virus, then, after the outbreak of epidemics and alarm, they begin to comply with the restrictions and the spreading of epidemics may decline. Over time, some people get tired/frustrated by the restrictions and stop following them (exhaustion), especially if the number of new cases drops down. After resting for a while, they can follow the restrictions again. But during this pause the second wave can come and become even stronger then the first one. Studies based on SIR models do not predict the observed quick exit from the first wave of epidemics. Social dynamics should be considered. The appearance of the second wave also depends on social factors. Many generalizations of the SIR model have been developed that take into account the weakening of immunity over time, the evolution of the virus, vaccination and other medical and biological details. However, these more sophisticated models do not explain the apparent differences in outbreak profiles between countries with different intrinsic socio-cultural features. In our work, a system of models of the COVID-19 pandemic is proposed, combining the dynamics of social stress with classical epidemic models. Social stress is described by the tools of sociophysics. The combination of a dynamic SIR-type model with the classical triad of stages of the general adaptation syndrome, alarm-resistance-exhaustion, makes it possible to describe with high accuracy the available statistical data for 13 countries. The sets of kinetic constants corresponding to optimal fit of model to data were found. These constants characterize the ability of society to mobilize efforts against epidemics and maintain this concentration over time and can further help in the development of management strategies specific to a particular society.

Assessing the impact of non-pharmaceutical interventions (NPI) on the dynamics of COVID-19: A mathematical modelling study of the case of Ethiopia

The World Health Organization (WHO) declared COVID-19 a pandemic on March 11, 2020 and by November 14, 2020 there were 53.3M confirmed cases and 1.3M reported deaths in the world. In the same period, Ethiopia reported 102K cases and 1.5K deaths. Effective public health preparedness and response to COVID-19 requires timely projections of the time and size of the peak of the outbreak. Currently, Ethiopia under the COVAX facility has begun vaccinating high risk populations but due to vaccine supply shortages and the absence of an effective treatment, the implementation of NPIs (non-pharmaceutical interventions), like hand washing, wearing face coverings or social distancing, still remain the most effective methods of controlling the pandemic as recommended by WHO. This study proposes a modified Susceptible Exposed Infected and Recovered (SEIR) model to predict the number of COVID-19 cases at different stages of the disease under the implementation of NPIs at different adherence levels in both urban and rural settings of Ethiopia. To estimate the number of cases and their peak time, 30 different scenarios were simulated. The results indicated that the peak time of the pandemic is different in urban and rural populations of Ethiopia. In the urban population, under moderate implementation of three NPIs the pandemic will be expected to reach its peak in December, 2020 with 147,972 cases, of which 18,100 are symptomatic and 957 will require admission to an Intensive Care Unit (ICU). Among the implemented NPIs, increasing the coverage of wearing masks by 10% could reduce the number of new cases on average by one-fifth in urban-populations. Varying the coverage of wearing masks in rural populations minimally reduces the number of cases. In conclusion, the models indicate that the projected number of hospital cases during the peak time is higher than the Ethiopian health system capacity. To contain symptomatic and ICU cases within the health system capacity, the government should pay attention to the strict implementation of the existing NPIs or impose additional public health measures.

Asymptomatic individuals can increase the final epidemic size under adaptive human behavior

Infections produced by non-symptomatic (pre-symptomatic and asymptomatic) individuals have been identified as major drivers of COVID-19 transmission. Non-symptomatic individuals, unaware of the infection risk they pose to others, may perceive themselves-and be perceived by others-as not presenting a risk of infection. Yet, many epidemiological models currently in use do not include a behavioral component, and do not address the potential consequences of risk misperception. To study the impact of behavioral adaptations to the perceived infection risk, we use a mathematical model that incorporates the behavioral decisions of individuals, based on a projection of the system's future state over a finite planning horizon. We found that individuals' risk misperception in the presence of non-symptomatic individuals may increase or reduce the final epidemic size. Moreover, under behavioral response the impact of non-symptomatic infections is modulated by symptomatic individuals' behavior. Finally, we found that there is an optimal planning horizon that minimizes the final epidemic size.

How Important Is Behavioral Change during the Early Stages of the COVID-19 Pandemic? A Mathematical Modeling Study

How important is the speed and intensity of behavioral change due to government policies, such as enhanced social distancing or lockdown, when an emerging infectious disease occurs? In this study, we introduce a deterministic SEIR model considering the behavior-changed susceptible group to investigate the effect of the speed and intensity of behavioral change on the transmission dynamics of COVID-19. We used epidemiological data from South Korea and Italy for the simulation study, because South Korea and Italy were the first countries to report an outbreak of COVID-19 after China and the prevention and response policy of each government were similar during the first outbreak of COVID-19. Simulation results showed that it took approximately twenty fewer days in Korea than in Italy until 90% of susceptible individuals changed their behavior during the first outbreak. It was observed that the behavior-changed susceptible individuals reduced the COVID-19 transmission rate by up to 93% in Korea and 77% in Italy. Furthermore, if the intensity and speed of behavioral change in Italy were the same as in Korea, the expected number of cumulative confirmed cases would have been reduced by approximately 95%, from 210,700 to 10,700, until the end of the lockdown period. We assumed that behavioral change is influenced by the number of confirmed cases and does not take into account social and cultural differences, as well as the state of the healthcare system, between the two countries. Our mathematical modeling showed how important the high intensity and fast speed of behavioral change to reduce the number of confirmed cases in the early period of an epidemic are.

A review of mathematical model-based scenario analysis and interventions for COVID-19

Mathematical model-based analysis has proven its potential as a critical tool in the battle against COVID-19 by enabling better understanding of the disease transmission dynamics, deeper analysis of the cost-effectiveness of various scenarios, and more accurate forecast of the trends with and without interventions. However, due to the outpouring of information and disparity between reported mathematical models, there exists a need for a more concise and unified discussion pertaining to the mathematical modeling of COVID-19 to overcome related skepticism. Towards this goal, this paper presents a review of mathematical model-based scenario analysis and interventions for COVID-19 with the main objectives of (1) including a brief overview of the existing reviews on mathematical models, (2) providing an integrated framework to unify models, (3) investigating various mitigation strategies and model parameters that reflect the effect of interventions, (4) discussing different mathematical models used to conduct scenario-based analysis, and (5) surveying active control methods used to combat COVID-19.

Differential evolution and particle swarm optimization against COVID-19

COVID-19 disease, which highly affected global life in 2020, led to a rapid scientific response. Versatile optimization methods found their application in scientific studies related to COVID-19 pandemic. Differential Evolution (DE) and Particle Swarm Optimization (PSO) are two metaheuristics that for over two decades have been widely researched and used in various fields of science. In this paper a survey of DE and PSO applications for problems related with COVID-19 pandemic that were rapidly published in 2020 is presented from two different points of view: 1. practitioners seeking the appropriate method to solve particular problem, 2. experts in metaheuristics that are interested in methodological details, inter comparisons between different methods, and the ways for improvement. The effectiveness and popularity of DE and PSO is analyzed in the context of other metaheuristics used against COVID-19. It is found that in COVID-19 related studies: 1. DE and PSO are most frequently used for calibration of epidemiological models and image-based classification of patients or symptoms, but applications are versatile, even interconnecting the pandemic and humanities; 2. reporting on DE or PSO methodological details is often scarce, and the choices made are not necessarily appropriate for the particular algorithm or problem; 3. mainly the basic variants of DE and PSO that were proposed in the late XX century are applied, and research performed in recent two decades is rather ignored; 4. the number of citations and the availability of codes in various programming languages seems to be the main factors for choosing metaheuristics that are finally used.

A simple mathematical model for the evaluation of the long first wave of the COVID-19 pandemic in Brazil

We propose herein a mathematical model to predict the COVID-19 evolution and evaluate the impact of governmental decisions on this evolution, attempting to explain the long duration of the pandemic in the 26 Brazilian states and their capitals well as in the Federative Unit. The prediction was performed based on the growth rate of new cases in a stable period, and the graphics plotted with the significant governmental decisions to evaluate the impact on the epidemic curve in each Brazilian state and city. Analysis of the predicted new cases was correlated with the total number of hospitalizations and deaths related to COVID-19. Because Brazil is a vast country, with high heterogeneity and complexity of the regional/local characteristics and governmental authorities among Brazilian states and cities, we individually predicted the epidemic curve based on a specific stable period with reduced or minimal interference on the growth rate of new cases. We found good accuracy, mainly in a short period (weeks). The most critical governmental decisions had a significant temporal impact on pandemic curve growth. A good relationship was found between the predicted number of new cases and the total number of inpatients and deaths related to COVID-19. In summary, we demonstrated that interventional and preventive measures directly and significantly impact the COVID-19 pandemic using a simple mathematical model. This model can easily be applied, helping, and directing health and governmental authorities to make further decisions to combat the pandemic.

Assessing the Spatio-temporal Spread of COVID-19 via Compartmental Models with Diffusion in Italy, USA, and Brazil

The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments based on qualitative characteristics, with different assumptions about the nature and rate of transfer across compartments. Though most commonly formulated as ordinary differential equation models, in which the compartments depend only on time, recent works have also focused on partial differential equation (PDE) models, incorporating the variation of an epidemic in space. Such research on PDE models within a Susceptible, Infected, Exposed, Recovered, and Deceased framework has led to promising results in reproducing COVID-19 contagion dynamics. In this paper, we assess the robustness of this modeling framework by considering different geometries over more extended periods than in other similar studies. We first validate our code by reproducing previously shown results for Lombardy, Italy. We then focus on the U.S. state of Georgia and on the Brazilian state of Rio de Janeiro, one of the most impacted areas in the world. Our results show good agreement with real-world epidemiological data in both time and space for all regions across major areas and across three different continents, suggesting that the modeling approach is both valid and robust.

Analysis of Delayed Vaccination Regimens: A Mathematical Modeling Approach

The first round of vaccination against coronavirus disease 2019 (COVID-19) began in early December of 2020 in a few countries. There are several vaccines, and each has a different efficacy and mechanism of action. Several countries, for example, the United Kingdom and the USA, have been able to develop consistent vaccination programs where a great percentage of the population has been vaccinated (May 2021). However, in other countries, a low percentage of the population has been vaccinated due to constraints related to vaccine supply and distribution capacity. Countries such as the USA and the UK have implemented different vaccination strategies, and some scholars have been debating the optimal strategy for vaccine campaigns. This problem is complex due to the great number of variables that affect the relevant outcomes. In this article, we study the impact of different vaccination regimens on main health outcomes such as deaths, hospitalizations, and the number of infected. We develop a mathematical model of COVID-19 transmission to focus on this important health policy issue. Thus, we are able to identify the optimal strategy regarding vaccination campaigns. We find that for vaccines with high efficacy (>70%) after the first dose, the optimal strategy is to delay inoculation with the second dose. On the other hand, for a low first dose vaccine efficacy, it is better to use the standard vaccination regimen of 4 weeks between doses. Thus, under the delayed second dose option, a campaign focus on generating a certain immunity in as great a number of people as fast as possible is preferable to having an almost perfect immunity in fewer people first. Therefore, based on these results, we suggest that the UK implemented a better vaccination campaign than that in the USA with regard to time between doses. The results presented here provide scientific guidelines for other countries where vaccination campaigns are just starting, or the percentage of vaccinated people is small.

A control framework to optimize public health policies in the course of the COVID-19 pandemic

The SARS-CoV-2 pandemic triggered substantial economic and social disruptions. Mitigation policies varied across countries based on resources, political conditions, and human behavior. In the absence of widespread vaccination able to induce herd immunity, strategies to coexist with the virus while minimizing risks of surges are paramount, which should work in parallel with reopening societies. To support these strategies, we present a predictive control system coupled with a nonlinear model able to optimize the level of policies to stop epidemic growth. We applied this system to study the unfolding of COVID-19 in Bahia, Brazil, also assessing the effects of varying population compliance. We show the importance of finely tuning the levels of enforced measures to achieve SARS-CoV-2 containment, with periodic interventions emerging as an optimal control strategy in the long-term.

Analysis of Key Factors of a SARS-CoV-2 Vaccination Program: A Mathematical Modeling Approach

The administration of vaccines against the coronavirus disease 2019 (COVID-19) started in early December of 2020. Currently, there are only a few approved vaccines, each with different efficacies and mechanisms of action. Moreover, vaccination programs in different regions may vary due to differences in implementation, for instance, simply the availability of the vaccine. In this article, we study the impact of the pace of vaccination and the intrinsic efficacy of the vaccine on prevalence, hospitalizations, and deaths related to the SARS-CoV-2 virus. Then we study different potential scenarios regarding the burden of the COVID-19 pandemic in the near future. We construct a compartmental mathematical model and use computational methodologies to study these different scenarios. Thus, we are able to identify some key factors to reach the aims of the vaccination programs. We use some metrics related to the outcomes of the COVID-19 pandemic in order to assess the impact of the efficacy of the vaccine and the pace of the vaccine inoculation. We found that both factors have a high impact on the outcomes. However, the rate of vaccine administration has a higher impact in reducing the burden of the COVID-19 pandemic. This result shows that health institutions need to focus on increasing the vaccine inoculation pace and create awareness in the population about the importance of COVID-19 vaccines.

Assessing the nationwide impact of COVID-19 mitigation policies on the transmission rate of SARS-CoV-2 in Brazil

COVID-19 is now identified in almost all countries in the world, with poorer regions being particularly more disadvantaged to efficiently mitigate the impacts of the pandemic. In the absence of efficient therapeutics or large-scale vaccination, control strategies are currently based on non-pharmaceutical interventions, comprising changes in population behavior and governmental interventions, among which the prohibition of mass gatherings, closure of non-essential establishments, quarantine and movement restrictions. In this work we analyzed the effects of 707 governmental interventions published up to May 22, 2020, and population adherence thereof, on the dynamics of COVID-19 cases across all 27 Brazilian states, with emphasis on state capitals and remaining inland cities. A generalized SEIR (Susceptible, Exposed, Infected and Removed) model with a time-varying transmission rate (TR), that considers transmission by asymptomatic individuals, is presented. We analyze the effect of both the extent of enforced measures across Brazilian states and population movement on the changes in the TR and effective reproduction number. The social mobility reduction index, a measure of population movement, together with the stringency index, adapted to incorporate the degree of restrictions imposed by governmental regulations, were used in conjunction to quantify and compare the effects of varying degrees of policy strictness across Brazilian states. Our results show that population adherence to social distance recommendations plays an important role for the effectiveness of interventions and represents a major challenge to the control of COVID-19 in low- and middle-income countries.

Assessing the nationwide impact of COVID-19 mitigation policies on the transmission rate of SARS-CoV-2 in Brazil

COVID-19 is now identified in almost all countries in the world, with poorer regions being particularly more disadvantaged to efficiently mitigate the impacts of the pandemic. In the absence of efficient therapeutics or large-scale vaccination, control strategies are currently based on non-pharmaceutical interventions, comprising changes in population behavior and governmental interventions, among which the prohibition of mass gatherings, closure of non-essential establishments, quarantine and movement restrictions. In this work we analyzed the effects of 707 governmental interventions published up to May 22, 2020, and population adherence thereof, on the dynamics of COVID-19 cases across all 27 Brazilian states, with emphasis on state capitals and remaining inland cities. A generalized SEIR (Susceptible, Exposed, Infected and Removed) model with a time-varying transmission rate (TR), that considers transmission by asymptomatic individuals, is presented. We analyze the effect of both the extent of enforced measures across Brazilian states and population movement on the changes in the TR and effective reproduction number. The social mobility reduction index, a measure of population movement, together with the stringency index, adapted to incorporate the degree of restrictions imposed by governmental regulations, were used in conjunction to quantify and compare the effects of varying degrees of policy strictness across Brazilian states. Our results show that population adherence to social distance recommendations plays an important role for the effectiveness of interventions and represents a major challenge to the control of COVID-19 in low- and middle-income countries.

Performance of Fuzzy Multi-Criteria Decision Analysis of Emergency System in COVID-19 Pandemic. An Extensive Narrative Review

The actual coronavirus disease 2019 (COVID-19) pandemic has led to the limit of emergency systems worldwide, leading to the collapse of health systems, police, first responders, as well as other areas. Various ways of dealing with this world crisis have been proposed from many aspects, with fuzzy multi-criteria decision analysis being a method that can be applied to a wide range of emergency systems and professional groups, aiming to confront several associated issues and challenges. The purpose of this critical review was to discuss the basic principles, present current applications during the first pandemic wave, and propose future implications of this methodology. For this purpose, both primary sources, such as scientific articles, and secondary ones, such as bibliographic indexes, web pages, and databases, were used. The main search engines were PubMed, SciELO, and Google Scholar. The method was a systematic literature review of the available literature regarding the performance of the fuzzy multi-criteria decision analysis of emergency systems in the COVID-19 pandemic. The results of this study highlight the importance of the fuzzy multi-criteria decision analysis method as a beneficial tool for healthcare workers and first responders’ emergency professionals to face this pandemic as well as to manage the created uncertainty and its related risks.

SEIR order parameters and eigenvectors of the three stages of completed COVID-19 epidemics: with an illustration for Thailand January to May 2020

By end of October 2020, the COVID-19 pandemic has taken a tragic toll of 1150 000 lives and this number is expected to increase. Despite the pandemic is raging in most parts of the world, in a few countries COVID-19 epidemics subsided due to successful implementations of intervention measures. A unifying perspective of the beginnings, middle stages, and endings of such completed COVID-19 epidemics is developed based on the order parameter and eigenvalue concepts of nonlinear physics, in general, and synergetics, in particular. To this end, a standard susceptible-exposed-infected-recovered (SEIR) epidemiological model is used. It is shown that COVID-19 epidemic outbreaks follow a suitably defined SEIR order parameter. Intervention measures switch the eigenvalue of the order parameter from a positive to a negative value, and in doing so, stabilize the COVID-19 disease-free state. The subsiding of COVID-19 epidemics eventually follows the remnant of the order parameter of the infection dynamical system. These considerations are illustrated for the COVID-19 epidemic in Thailand from January to May 2020. The decay of effective contact rates throughout the three epidemic stages is demonstrated. Evidence for the sign-switching of the dominant eigenvalue is given and the order parameter and its stage-3 remnant are identified. The presumed impacts of interventions measures implemented in Thailand are discussed in this context.

Adaptive Human Behavior in Epidemics: the Impact of Risk Misperception on the Spread of Epidemics

Infections produced by pre-symptomatic and asymptomatic (non-symptomatic) individuals have been identified as major drivers of COVID-19 transmission. Non-symptomatic individuals unaware of the infection risk they pose to others, may perceive themselves --and being perceived by others-- as not representing risk of infection. Yet many epidemiological models currently in use do not include a behavioral component, and do not address the potential consequences of risk misperception. To study the impact of behavioral adaptations to the perceived infection risk, we use a mathematical model that incorporates individuals' behavioral decisions based on a projection of the future system's state over a finite planning horizon. We found that individuals' risk misperception in the presence of asymptomatic individuals may increase or reduce the final epidemic size. Moreover, under behavioral response the impact of asymptomatic infections is modulated by symptomatic individuals' behavior. Finally, we found that there is an optimal planning horizon that minimizes the final epidemic size.

Impact of environmental transmission and contact rates on Covid-19 dynamics: A simulation study

The emergence of the COVID-19 pandemic has been a major social and economic challenge globally. Infections from infected surfaces have been identified as drivers of Covid-19 transmission, but many epidemiological models do not include an environmental component to account for indirect transmission. We formulate a deterministic Covid-19 model with both direct and indirect transmissions. The computed basic reproduction number R 0 represents the average number of secondary direct human-to-human infections, and the average number of secondary indirect infections from the environment. Using Partial Rank Correlation Coefficient, we compute sensitivity indices of the basic reproductive number R 0 . As expected, the most significant parameter to reduce initial disease transmission is the natural death rate of pathogens in the environment. Variation of the basic reproduction number for different values of direct and indirect transmissions are numerically investigated. Decreasing the effective direct human-to-human contact rate and indirect transmission from human-to-environment will decrease the spread of the disease as R 0 decreases and vice versa. Since the effective contact rate often accounted for as a factor of the force of infection and other interventions measures such as treatment rate are prominent features of infectious diseases, we consider several functional forms of the incidence function, and numerically investigate their potential impact on the long-term dynamics of the disease. Simulations results revealed some differences for the time and infection to reach its peak. Thus, the choice of the functional form of the force of infection should mainly be influenced by the specifics of the prevention measures being implemented.