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In this work, we developed, validated, and analysed the behaviour of a compartmental model of COVID-19 transmission in Saudi Arabia. The population was structured into four classes: susceptible (S), exposed (E), infectious (I), and removed (R) individuals. This SEIR model assumes a bilinear incidence rate and a nonlinear recovery rate that depends on the quality of health services. The model also considers a treatment function and incorporates the effect of fear due to the disease. We derived the expression of the basic reproduction number and the equilibrium points of the model and demonstrated that when the reproduction number is less than one, the disease-free equilibrium is stable, and the model predicts a backward bifurcation. We further found that when the reproduction number is larger than one, the model predicts stable periodic behaviour. Finally, we used numerical simulations with parameter values fitted to Saudi Arabia to analyse the effects of the model parameters on the model-predicted dynamic behaviours. [ABSTRACT FROM AUTHOR]

This paper is concerned with solving the problem of identifying the control vector problem for a fractional multi-order system of nonlinear ordinary differential equations (ODEs). We describe a quasilinearization approach, based on minimization of a quadratic functional, to compute the values of the unknown parameter vector. Numerical algorithm combining the method with appropriate fractional derivative approximation on graded mesh is applied to SIS and SEIR problems to illustrate the efficiency and accuracy. Tikhonov regularization is implemented to improve the convergence. Results from computations, both with noisy-free and noisy data, are provided and discussed. Simulations with real data are also performed. [ABSTRACT FROM AUTHOR]

In recent years, social media has emerged as an important channel for the dissemination of destination branding. Despite the fact that the dissemination of information through social media enables a broader audience to become acquainted with destinations, the dissemination process of trending events exhibits variances. Consequently, the precise impact of the underlying mechanisms that govern the spread of information on the efficacy of disseminating destination brand trending events remains ambiguous. In an endeavor to bridge this gap, an improved SEIR model was developed in this research to investigate the dynamic dissemination mechanisms and influencing factors of destination trending events within social media. The model was applied to simulate the diffusion mechanism of destinations' trending events. The results show that during the dissemination process of destination trending events on social media, the proportion of users affected at different stages influences the ultimate effectiveness of information propagation. In light of these insights, this research proposes a social media trending event dissemination strategy to aid in enhancing the propagation efficiency of destination brands through existing resources. [ABSTRACT FROM AUTHOR]

With the development of the healthcare industry, the demand for medical services and protective equipment is boosted, causing the generation rate of infectious medical waste to increase rapidly. Therefore, it is of utmost importance for decision makers to effectively predict the potential risks and propose corresponding solutions. This paper investigates the reverse logistics network optimization for medical waste under the conditions of an uncertain proposal demand. Firstly, a prediction model of medical waste based on the SEIR epidemiological dynamics is constructed, in which both routine and public health emergency scenarios are simultaneously considered. Secondly, a bi-objective location-routing optimization model for a medical waste reverse logistics network is proposed, by simultaneously optimizing the total economic cost and potential risk throughout the entire logistics process. Subsequently, an NSGA-II algorithm is designed for a model solution in response to the model's characteristics. The epidemiological dynamics-based prediction model is validated by the real case to be scientifically effective in predicting the amount of generated medical waste with a mean absolute percentage error (MAPE) of 18.08%. The constructed reverse logistics network model and the NSGA II algorithm provide a medical waste process center location, transportation routing, and vehicle selection solutions for both routine and emergency public health cases of Xi'an city with large, medium, and small scales. The above results indicate that the research scheme proposed in this paper could significantly reduce the medical waste logistics-related risks and costs and provide decision makers with more safe and reliable logistical solutions. [ABSTRACT FROM AUTHOR]

In this research, we present the first steps toward developing a data-driven agent-based model (ABM) specifically designed for simulating infectious disease dynamics in Greece. Amidst the ongoing COVID-19 pandemic caused by SARS-CoV-2, this research holds significant importance as it can offer valuable insights into disease transmission patterns and assist in devising effective intervention strategies. To the best of our knowledge, no similar study has been conducted in Greece. We constructed a prototype ABM that utilizes publicly accessible data to accurately represent the complex interactions and dynamics of disease spread in the Greek population. By incorporating demographic information and behavioral patterns, our model captures the specific characteristics of Greece, enabling accurate and context-specific simulations. By using our proposed ABM, we aim to assist policymakers in making informed decisions regarding disease control and prevention. Through the use of simulations, policymakers have the opportunity to explore different scenarios and predict the possible results of various intervention measures. These may include strategies like testing approaches, contact tracing, vaccination campaigns, and social distancing measures. Through these simulations, policymakers can assess the effectiveness and feasibility of these interventions, leading to the development of well-informed strategies aimed at reducing the impact of infectious diseases on the Greek population. This study is an initial exploration toward understanding disease transmission patterns and a first step towards formulating effective intervention strategies for Greece. [ABSTRACT FROM AUTHOR]

Pharmaceuticals play a critical role in the eradication of infectious diseases. Effective pharmaceutical inventory management is important for controlling epidemics since medical resources such as pharmaceuticals, medical staff, and hospitals are limited. In this study, a novel epidemiological model is proposed to evaluate the resource requirements for pharmaceuticals and is applied to analyze different pharmaceutical inventory management strategies. We formulate the relationship between the number of infected individuals and the risk of infection to account for virus mutation. Evolutionary game theory is integrated into an epidemiological model to represent human behavioral choices. The proposed model can be developed to forecast the demand for pharmaceuticals and analyze how human behavior affects the demand of pharmaceuticals. This study found that making people aware of the risk of disease has a positive impact on both reducing the number of infections and managing the pharmaceutical inventory. The main contribution of this study is to enhance areas of research in pharmaceutical inventory management. This study revealed that the correct recognition of the risk of disease leads to appropriate pharmaceutical management. There are a few studies on the application of infectious disease models to inventory control problems. This study provides clues toward proper pharmaceutical management. [ABSTRACT FROM AUTHOR]

In construction engineering safety management, the problem of construction workers' unsafe behavior (CWUB) has always been a focus for researchers as well as practice managers. Currently, most studies focus on the influencing factors and mechanisms of (CWUB), with less attention given to the dissemination process and control effects of CWUB. Therefore, this paper aims to investigate a safety control detection system for the transmission process. The heterogeneous cellular automaton (CA) has advantages in constructing such a system as it can reflect the interactive processes of construction workers from micro to macro, local to global, and consider the heterogeneity of individuals and space, satisfying unequal interaction probabilities between individuals and spatial variations in characteristics. The SEIR model accurately categorizes construction workers and visually represents the changing quantities of different state groups at each stage. It effectively describes the process of CWUB transmission among construction workers. Based on the aforementioned foundation, a safety control and monitoring system was proposed for the implementation stages of the project. Finally, the control detection system is simulated to assess its effectiveness. Simulation results closely align with reality, showing a continuous decrease in susceptible individuals, a peak followed by a rapid decline in latent and infected individuals, and a steady increase in immune individuals. To control CWUB transmission, it is crucial to enhance immunity against unsafe behaviors, reduce the rate of immunity conversion, and shorten the disease cycle caused by such behaviors. This research has practical implications for construction projects. [ABSTRACT FROM AUTHOR]

This paper establishes a novel fractional-order version of a recently expanded form of the Susceptible-Exposed-Infectious-Recovery (SEIR) Mpox model. This model is investigated by means of demonstrating some significant findings connected with the stability analysis and the vaccination impact, as well. In particular, we analyze the fractional-order Mpox model in terms of its invariant region, boundedness of solution, equilibria, basic reproductive number, and its elasticity. In accordance with an effective vaccine, we study the progression and dynamics of the Mpox disease in compliance with various scenarios of the vaccination ratio through the proposed fractional-order Mpox model. Accordingly, several numerical findings of the proposed model are depicted with the use of two numerical methods; the Fractional Euler Method (FEM) and Modified Fractional Euler Method (MFEM). Such findings demonstrate the influence of the fractional-order values coupled with the vaccination rate on the dynamics of the established disease model. [ABSTRACT FROM AUTHOR]

For solving first-order linear and nonlinear differential equations, a new two-stage implicit–explicit approach is given. The scheme's first stage, or predictor stage, is implicit, while the scheme's second stage is explicit. The first stage of the proposed scheme is an extended form of the existing Runge–Kutta scheme. The scheme's stability and consistency are also offered. In two phases, the technique achieves third-order accuracy. The method is applied to the SEIR epidemic model with a convex incidence rate. The local stability is also examined. The technique is evaluated compared to existing Euler and nonstandard finite difference methods. In terms of accuracy, the produced plots show that the suggested scheme outperforms the existing Euler and nonstandard finite difference methods. Furthermore, a neural network technique is being considered to map the relationship between time and the amount of susceptible, exposed, and infected people. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This work presents a new polymorphic, reusable, and comprehensive mathematical model for COVID-19 epidemic transition cycle dynamics. This model has the following characteristics: (1) The core SEIR model includes asymptomatic and symptomatic infections; (2) the symptomatic infection is a multi-variant; (3) the recovery stage provides a partial feed to the symptomatic infection; and (4) the symptomatic and asymptomatic stages have additional feed streams from the protected stage. The proposed formalisation template is a canonical way to achieve different models for the underlying health control environment. This template approach endows the model with polymorphic and reusable capability across different scenarios. To verify the model's reliability and validity, this work utilised two sets of initial conditions: date range and COVID-19 data for Canada and Saudi Arabia. [ABSTRACT FROM AUTHOR]

Nowadays, a lot of research papers are concentrating on the diffusion dynamics of infectious diseases, especially the most recent one: COVID-19. The primary goal of this work is to explore the stability analysis of a new version of the S E I R model formulated with incommensurate fractional-order derivatives. In particular, several existence and uniqueness results of the solution of the proposed model are derived by means of the Picard–Lindelöf method. Several stability analysis results related to the disease-free equilibrium of the model are reported in light of computing the so-called basic reproduction number, as well as in view of utilising a certain Lyapunov function. In conclusion, various numerical simulations are performed to confirm the theoretical findings. [ABSTRACT FROM AUTHOR]

Due to insufficient epidemic detection and control, untimely government interventions, and high epidemic prevention costs in the early stages of the epidemic outbreak, the spread of the epidemic may become out of control and pose a great threat to human society. This paper optimized and improved the traditional Susceptible-Exposed-Infectious-Removed (SEIR) model for investigating epidemic control and public health emergency management. Using the Corona Virus Disease 2019 (COVID-19) outbreak as an example, this paper simulates and analyzes the development of an epidemic outbreak during various periods with the optimized SEIR model, to explore the emergency control capacity of conventional medical control measures, such as large-scale outbreak testing capacity, hospital admission capacity, or daily protection of key personnel, and analyze the government's emergency management strategies to achieve low-cost epidemic control. The model developed in this study and the results of its analysis demonstrate the differences in outbreak emergency control capacity under different conditions and different implementation strategies. A low-cost local outbreak emergency management strategy and the timing of the government's resumption of work and school are discussed on this basis. [ABSTRACT FROM AUTHOR]

In 2020, coronavirus (COVID-19) was declared a global pandemic and it remains prevalent today. A necessity to model the transmission of the virus has emerged as a result of COVID-19's exceedingly contagious characteristics and its rapid propagation throughout the world. Assessing the incidence of infection could enable policymakers to identify measures to halt the pandemic and gauge the required capacity of healthcare centers. Therefore, modeling the susceptibility, exposure, infection, and recovery in relation to the COVID-19 pandemic is crucial for the adoption of interventions by regulatory authorities. Fundamental factors, such as the infection rate, mortality rate, and recovery rate, must be considered in order to accurately represent the behavior of the pandemic using mathematical models. The difficulty in creating a mathematical model is in identifying the real model variables. Parameters might vary significantly across models, which can result in variations in the simulation results because projections primarily rely on a particular dataset. The purpose of this work was to establish a susceptible–exposed–infected–recovered (SEIR) model describing the propagation of the COVID-19 outbreak throughout the Kingdom of Saudi Arabia (KSA). The goal of this study was to derive the essential COVID-19 epidemiological factors from actual data. System dynamics modeling and design of experiment approaches were used to determine the most appropriate combination of epidemiological parameters and the influence of COVID-19. This study investigates how epidemiological variables such as seasonal amplitude, social awareness impact, and waning time can be adapted to correctly estimate COVID-19 scenarios such as the number of infected persons on a daily basis in KSA. This model can also be utilized to ascertain how stress (or hospital capacity) affects the percentage of hospitalizations and the number of deaths. Additionally, the results of this study can be used to establish policies or strategies for monitoring or restricting COVID-19 in Saudi Arabia. [ABSTRACT FROM AUTHOR]

In the context of the rapid development of new media such as network citizen journalism, it is of great theoretical and practical significance to use the online public opinion to supervise sewage discharge enterprises' emission governance behaviors and improve the social opinion supervision mechanism. This paper considers the dynamic characteristics of the spread process of public opinion and the game process of social supervision on corporate pollution control; constructs a tripartite evolutionary game model of the local government, sewage discharge enterprises, and the public by coupling the susceptible–exposed–infected–removed (SEIR) model and the evolutionary game model; and discusses the influence laws of public opinion spread on the tripartite evolutionary game. The results show that (1) the public with higher influence or authority has a more significant restraint effect to restrain the pollution control behavior of the local government and pollutant companies by using online public opinion supervision. (2) Increasing the probability of transforming a latent person into a supervisor and the topic derivative rate or reducing the probability of a supervisor's self-healing can increase the peak value of supervisors, expand the scope of social public opinion, and improve the effectiveness of public opinion supervision. (3) The relatively high authenticity of public opinion supervision makes public opinion supervision a substitute for local government supervision, but it has a relatively strong inhibitory effect on the over-standard pollutant discharge behavior of sewage discharge enterprises. These conclusions can provide a reference for improving the social supervision mechanism of pollution control in the era of network citizen journalism. [ABSTRACT FROM AUTHOR]

During the height of the COVID-19 epidemic, production lagged and enterprises could not deliver goods on time, which will bring considerable risks to the supply chain system. Modeling risk diffusion in supply chain networks is important for prediction and control. To study the influence of uncertain information on risk diffusion in a dynamic network, this paper constructs a dynamic evolution model based on a hypernetwork to study risk diffusion and control under uncertain information. First, a dynamic evolution model is constructed to represent the network topology, which includes the addition of links, rewiring of links, entry of nodes, and the exit of outdated nodes that obey the aging principle. Then, the risk diffusion scale is discussed with the Microscopic Markovian Chain Approach (MMCA), and the risk threshold is analyzed. Finally, the consistency of Monte Carlo (MC) simulation and MMCA is verified by MATLAB, and the influence of each parameter on the risk diffusion scale and risk threshold is tested. The results show that reducing the cooperation and production during the risk period, declining the attenuation factor, enhancing the work efficiency of the official media, and increasing the probability of the exit of outdated nodes in the supply chain networks will increase the risk threshold and restrain the risk diffusion. [ABSTRACT FROM AUTHOR]

With the transmission of the COVID-19 epidemic at home and abroad, this paper considers the spread process in China, improves the classic epidemic SEIR model, and establishes a multistage time-delay control model (MTCM) for COVID-19 transmission. The MTCM divides the spread of COVID-19 into three periods: the outbreak period, the control period and the steady period. The classical SEIR model, the improved SEQIR model and the SEQIR Ⅱ model correspond to the three periods. The classical SEIR model was adopted for the outbreak period and yielded results that were consistent with the observed early propagation of COVID-19 transmission. In the control period, adding isolation measures and a time delay to the MTCM and adjusting the rates yielded a better simulation effect. In the steady period, the focus of consideration is the number of new patients, population movement (in-migration and out-migration of the population) and patient classification (symptomatic and asymptomatic patients). The MCTM was used for simulation, and the comparison results revealed that the simulated data of the MCTM (improved SEQIR model) and the actual data are similar in the control period. The control policy of isolation measures is effective. New infections, population flow and patients with symptomatic or asymptomatic symptoms are more consistent with the steady period characteristics. The multi-stage time-delay control model for COVID-19 transmission provides theoretical methods and good prevention and control measures for future epidemic policy formulation. [ABSTRACT FROM AUTHOR]

In real life, individuals play an important role in the social networking system. When an epidemic breaks out the individual's recovery rate depends heavily on the social network in which he or she lives. For this reason, in this paper a nonlinear coupling dynamic model on the hyper network was built. The upper layer is the dynamic social network under the hypernetwork vision, and the lower layer is the physical contact layer. Thus, the dynamic evolutionary coupling mechanism between the social network and epidemic transmission was established. At the same time, this paper deduced the evolution process of the dynamic system according to the Markov chain method. The probability equation of the dynamic evolution process was determined, and the threshold of epidemic spread on the non-uniform network was obtained. In addition, numerical simulations verified the correctness of the theory and the validity of the model. The results show that an individual's recovery state will be affected by the individual's social ability and the degree of information forgetting. Finally, suitable countermeasures are suggested to suppress the pandemic from spreading in response to the coupling model's affecting factors. [ABSTRACT FROM AUTHOR]

Background: Comprehensive and evidence-based countermeasures against emerging infectious diseases have become increasingly important in recent years. COVID-19 and many other infectious diseases are spread by human movement and contact, but complex transportation networks in the 21st century make it difficult to predict disease spread in rapidly changing situations. It is especially challenging to estimate the network of infection transmission in countries where traffic and human movement data infrastructure is not yet developed. Methods: In this study, we devised a method utilizing an ordinary and partial differential equations-based mathematical model and a modified mathematical optimization method to estimate the network of transmission of COVID-19 from the time series data of its infection and applied it to determine its spread across areas in Japan. Furthermore, utilizing the estimated human mobility network, we predicted the spread of infection using the Tokyo Olympics as a model. Findings: We incorporated the effects of soft lockdowns, such as the declaration of a state of emergency, and changes in the infection network due to government-sponsored travel promotion, and revealed that the estimated effective distance captured human mobility changing dynamically in the different stages of the pandemic. The model predicted that the Tokyo Olympic and Paralympic Games would increase the number of infected cases in the host prefectures by up to 80%. Interpretation: The models used in this study are available online, and our data-driven infection network models are scalable, whether it be at the level of a city, town, country, or continent, and applicable anywhere in the world, as long as the time-series data of infections per region is available. These estimations of effective distance and the depiction of infectious disease networks based on actual infection data are expected to be useful in devising data-driven countermeasures against emerging infectious diseases worldwide. [ABSTRACT FROM AUTHOR]

The behavioral choices and speculative psychology of the participants in medical waste disposal can lead to the evolution of the medical waste disposal crisis, which has a great impact on and represents a potential threat to environmental safety as well as public health. This study constructs the SEIR evolutionary game model based on the theory of propagation dynamics and evolutionary game and explores the game relationship between local governments and medical waste disposal enterprises. Then it analyzes the propagation threshold and evolutionary path of medical institutions' speculative psychology under different behavioral decisions of both subjects and explores the process and law of system evolution to a benign stable state and conducts a multi-situated simulation analysis. The results showed that the number of infected states in medical institutions varies in a positive direction with the propagation threshold of their speculative psychology, and when the propagation threshold is greater than 1, the speculative psychology of medical institutions will spread widely in the system. The "strict regulation and high-quality disposal" behavior of local governments and disposal enterprises could effectively eliminate the speculative psychology of medical institutions, the number of infected medical institutions could gradually evolve to 0, then the further evolution of the medical waste disposal crisis could be prevented. The formation of an integrated, coordinated, and mutually constraining crisis governance mechanism should improve the government's regulatory capacity and efficiency, develop attractive and deterrent reward and punishment policies to guide disposal enterprises to high-quality disposal, and contribute to the compliant disposal of medical waste in medical institutions. [ABSTRACT FROM AUTHOR]

This article develops a detailed epidemiological multi-factor model, the K-susceptible–exposed–infected–removed (K-SEIR) model, and several simpler sub-models as its building blocks. The general model enables us to account for all the relevant COVID-19 features, its disparate impact on different population groups, and interactions within and between the groups. It also includes the availability (or lack thereof) of spare hospital beds and intensive care units (ICU) to accommodate the pent-up demand due to the pandemic. We use the most recent hospitalization and mortality data to calibrate the model. Since our model is multi-factor, we can use it to simulate and analyze the consequences of the sheltering-in-place for each specific group and compare the lives saved and lost due to this measure. We show that in countries with well-developed healthcare systems and a population willing to abide by suitable containment and mitigation procedures, the sheltering in place of the entire community is excessive and harmful when considered holistically. At the same time, sealing nursing homes as thoroughly as possible to avoid high infection and mortality rates is an absolute necessity. [ABSTRACT FROM AUTHOR]

Currently, the spread of COVID-19 is running at a constant pace. The current situation is not so alarming, but every pandemic has a history of three waves. Two waves have been seen, and now expecting the third wave. Compartmental models are one of the methods that predict the severity of a pandemic. An enhanced SEIR model is expected to predict the new cases of COVID-19. The proposed model has an additional compartment of vaccination. This proposed model is the SEIRV model that predicts the severity of COVID-19 when the population is vaccinated. The proposed model is simulated with three conditions. The first condition is when social distancing is not incorporated, while the second condition is when social distancing is included. The third one condition is when social distancing is combined when the population is vaccinated. The result shows an epidemic growth rate of about 0.06 per day, and the number of infected people doubles every 10.7 days. Still, with imparting social distancing, the proposed model obtained the value of R0 is 1.3. Vaccination of infants and kids will be considered as future work. [ABSTRACT FROM AUTHOR]

Ever since the World Health Organization gave the name COVID-19 to the coronavirus pneumonia disease, much of the world has been severely impact by the pandemic socially and economically. In this paper, the mathematical modeling and stability analyses in terms of the susceptible–exposed–infected–removed (SEIR) model with a nonlinear incidence rate, along with media interaction effects, are presented. The sliding mode control methodology is used to design a robust closed loop control of the epidemiological system, where the property of symmetry in the Lyapunov function plays a vital role in achieving the global asymptotic stability in the output. Two policies are considered: the first considers only the governmental interaction, the second considers only the vaccination policy. Numerical simulations of the control algorithms are then evaluated. [ABSTRACT FROM AUTHOR]

COVID-19 has threatened human lives. Countries have implemented various interventions such as vaccination, mask-wearing, body temperature screening, and isolation. However, the effectiveness of single and combined interventions has not yet been accurately analyzed. In this study, an improved SEIR model considering both real human indoor close contact behaviors and susceptibility to COVID-19 was established. Taking Hong Kong as an example, a quantitative assessment of the relationship between the efficiency of single and combined interventions and implementation time and intensity was carried out. The results showed that the infection risk (one-hour close contact with an infected person) of COVID-19 of students, workers, and non-workers/non-students was 3.1%, 8.7%, and 13.6%, respectively. Workplace closures were more effective among built environment interventions. If mask-wearing was mandatorily required in schools, workplaces, supermarkets, shopping centers, and public transport, COVID-19 could not be totally restricted. Workers should be prioritized for vaccination, followed by non-workers/non-students and students. Among all interventions, reducing close contact rate and increasing vaccination rate were better interventions. There was no COVID-19 outbreak (basic reproduction number R0 = 1) if the close contact reduction rate was 59.9% or the vaccination rate reached 89.5%. The results may provide scientific support for COVID-19 prevention and control. [ABSTRACT FROM AUTHOR]

Is it possible that the origin of Mycobacterium tuberculosis (Mtb) infection was around 70,000 years before the common era? At that time Homo sapiens was just another primate species with discrete growth and a very low-density geographic occupation. Therefore, it is difficult to understand the origin of a highly virulent obligate human pathogen. We have designed a new SEIR model (TBSpectr) that allows the differentiation of smear-positive and -negative tuberculosis. The model reconciles currently accepted growth rates for the Middle Paleolithic (0.003%/year) and Neolithic (0.1%/year). The obtained data link the origin of Mtb infection in the Middle Paleolithic to the induction of smear-negative TB, and reveal that its persistence required interrelations among hunter–gatherer groups, while the risk of human extinction was negligible. It also highlights the number of people infected per case and the fast progression to disease for Mtb infection maintenance, as well as the link between poor health in the Neolithic with the increased incidence of more severe forms of TB (smear-positive). In conclusion, our data support the origin of TB as a well-tolerated, highly persistent disease, even in low-density populations, showing the difficulty of its eradication and highlighting the necessity for providing better health conditions to humans to reduce its severity. [ABSTRACT FROM AUTHOR]

The global COVID-19 pandemic has taken a heavy toll on health, social, and economic costs since the end of 2019. Predicting the spread of a pandemic is essential to developing effective intervention policies. Since the beginning of this pandemic, many models have been developed to predict its pathways. However, the majority of these models assume homogeneous dynamics over the geographic space, while the pandemic exhibits substantial spatial heterogeneity. In addition, spatial interaction among territorial entities and variations in their magnitude impact the pandemic dynamics. In this study, we used a spatial extension of the SEIR-type epidemiological model to simulate and predict the 4-week number of COVID-19 cases in the Charlotte-Concord-Gastonia Metropolitan Statistical Area (MSA), USA. We incorporated a variety of covariates, including mobility, pharmaceutical, and non-pharmaceutical interventions, demographics, and weather data to improve the model's predictive performance. We predicted the number of COVID-19 cases for up to four weeks in the 10 counties of the studied MSA simultaneously over the time period 29 March 2020 to 13 March 2021, and compared the results with the reported number of cases using the root-mean-squared error (RMSE) metric. Our results highlight the importance of spatial heterogeneity and spatial interactions among locations in COVID-19 pandemic modeling.

The current novel Coronavirus Disease 2019 (COVID-19) is a multistage epidemic consisting of multiple rounds of alternating outbreak and containment periods that cannot be modeled with a conventional single-stage Suspected-Exposed-Infectious-Removed (SEIR) model. Seasonality and control measures could be the two most important driving factors of the multistage epidemic. Our goal is to formulate and incorporate the influences of seasonality and control measures into an epidemic model and interpret how these two factors interact to shape the multistage epidemic curves. New confirmed cases will be collected daily from seven Northern Hemisphere countries and five Southern Hemisphere countries from March 2020 to March 2021 to fit and validate the modified model. Results show that COVID-19 is a seasonal epidemic and that epidemic curves can be clearly distinguished in the two hemispheres. Different levels of control measures between different countries during different seasonal periods have different influences on epidemic transmission. Seasonality alone cannot cause the baseline reproduction number R 0 to fall below one and control measures must be taken. A superposition of a high level of seasonality and a low level of control measures can lead to a dramatically rapid increase in reported cases.

COVID-19 vaccinations have been administered quickly in the USA. However, a surprisingly large number of Americans are unwilling to get vaccinated. Without enough people getting vaccinated, the pandemic will not end. The longer the pandemic persists, the more opportunities exist for more virulent strains to emerge. This model looks at the effects of people's behavior in containing and ending the COVID-19 pandemic in the USA. Human behavior adds several feedback loops to the standard SEIR model. Comparisons are made between cases with and without behavior loops, with reduced adherence to the recommended or mandated masks and social distancing, with and without the vaccine, and the effects of an early mask mandate termination. The results suggest human behavior must be accounted for in epidemiology models and that removing masks before enough vaccine are administered not only puts those vaccinated at risk, but allows the disease to readily spread again. [ABSTRACT FROM AUTHOR]

We consider a scenario where the pandemic infection rate is inversely proportional to the power of the distance between the infected region and the non-infected region. In our study, we analyze the case where the exponent of the distance is 2, which is in accordance with Reilly's law of retail gravitation. One can test for infection but such tests are costly so one seeks to determine the region of infection while performing few tests. Our goal is to find a boundary region of minimal size that contains all infected areas. We discuss efficient algorithms and provide the asymptotic bound of the testing cost and simulation results for this problem. [ABSTRACT FROM AUTHOR]

From the end of 2020, different vaccines against COVID-19 have been approved, offering a glimmer of hope and relief worldwide. However, in late 2020, new cases of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) started to re-surge, worsened by the emergence of highly infectious variants. To study this scenario, we extend the Susceptible-Exposed-Infectious-Removed model with lockdown measures used in our previous work with the inclusion of new lineages and mass vaccination campaign. We estimate model parameters using the Bayesian method Conditional Robust Calibration in two case studies: Italy and the Umbria region, the Italian region being worse affected by the emergence of variants. We then use the model to explore the dynamics of COVID-19, given different vaccination paces and a policy of gradual reopening. Our findings confirm the higher reproduction number of Umbria and the increase of transmission parameters due to the presence of new variants. The results illustrate the importance of preserving population-wide interventions, especially during the beginning of vaccination. Finally, under the hypothesis of waning immunity, the predictions show that a seasonal vaccination with a constant rate would probably be necessary to control the epidemic. [ABSTRACT FROM AUTHOR]

Epidemic spreading causes severe challenges to the global public health system, and global and local interventions are considered an effective way to contain such spreading, including school closures (local), border control (global), etc. However, there is little study on comparing the efficiency of global and local interventions on epidemic spreading. Here, we develop a new model based on the Susceptible-Exposed-Infectious-Recovered (SEIR) model with an additional compartment called "quarantine status". We simulate various kinds of outbreaks and interventions. Firstly, we predict, consistent with previous studies, interventions reduce epidemic spreading to 16% of its normal level. Moreover, we compare the effect of global and local interventions and find that local interventions are more effective than global ones. We then study the relationships between incubation period and interventions, finding that early implementation of rigorous intervention significantly reduced the scale of the epidemic. Strikingly, we suggest a Pareto optimal in the intervention when resources were limited. Finally, we show that combining global and local interventions is the most effective way to contain the pandemic spreading if initially infected individuals are concentrated in localized regions. Our work deepens our understandings of the role of interventions on the pandemic, and informs an actionable strategy to contain it.

Mathematical models of the spread of epidemic diseases are studied, paying special attention to networks. We treat the Susceptible-Infected-Recovered (SIR) model and the Susceptible-Exposed-Infectious-Recovered (SEIR) model described by differential equations. We perform microscopic numerical simulations for corresponding epidemic models on networks. Comparing a random network and a scale-free network for the spread of the infection, we emphasize the role of hubs in a scale-free network. We also present a simple derivation of the exact solution of the SIR model. [ABSTRACT FROM AUTHOR]

We investigate the impact of the delay in compulsory mask wearing on the spread of COVID-19 in the community, set in the Singapore context. By using modified SEIR-based compartmental models, we focus on macroscopic population-level analysis of the relationships between the delay in compulsory mask wearing and the maximum infection, through a series of scenario-based analysis. Our analysis suggests that collective masking can meaningfully reduce the transmission of COVID-19 in the community, but only if implemented within a critical time window of approximately before 80-100 days delay after the first infection is detected, coupled with strict enforcement to ensure compliance throughout the duration. We also identify a delay threshold of about 100 days that results in masking enforcement having little significant impact on the Maximum Infected Values. The results therefore highlight the necessity for rapid implementation of compulsory mask wearing to curb the spread of the pandemic.

In this paper, an extended SEIR model with a vaccination compartment is proposed to simulate the novel coronavirus disease (COVID-19) spread in Saudi Arabia. The model considers seven stages of infection: susceptible (S), exposed (E), infectious (I), quarantined (Q), recovered (R), deaths (D), and vaccinated (V). Initially, a mathematical analysis is carried out to illustrate the non-negativity, boundedness, epidemic equilibrium, existence, and uniqueness of the endemic equilibrium, and the basic reproduction number of the proposed model. Such numerical models can be, however, subject to various sources of uncertainties, due to an imperfect description of the biological processes governing the disease spread, which may strongly limit their forecasting skills. A data assimilation method, mainly, the ensemble Kalman filter (EnKF), is then used to constrain the model outputs and its parameters with available data. We conduct joint state-parameters estimation experiments assimilating daily data into the proposed model using the EnKF in order to enhance the model's forecasting skills. Starting from the estimated set of model parameters, we then conduct short-term predictions in order to assess the predicability range of the model. We apply the proposed assimilation system on real data sets from Saudi Arabia. The numerical results demonstrate the capability of the proposed model in achieving accurate prediction of the epidemic development up to two-week time scales. Finally, we investigate the effect of vaccination on the spread of the pandemic. [ABSTRACT FROM AUTHOR]

The wide dissemination of false information and the frequent occurrence of extreme speeches on online social platforms have become increasingly prominent, which impact on the harmony and stability of society. In order to solve the problems in the dissemination and polarization of public opinion over online social platforms, it is necessary to conduct in-depth research on the formation mechanism of the dissemination and polarization of public opinion. This article appends individual communicating willingness and forgetting effects to the Susceptible-Exposed-Infected-Recovered (SEIR) model to describe individual state transitions; secondly, it introduces three heterogeneous factors describing the characteristics of individual differences in the Jager-Amblard (J-A) model, namely: Individual conformity, individual conservative degree, and inter-individual relationship strength in order to reflect the different roles of individual heterogeneity in the opinions interaction; thirdly, it integrates the improved SEIR model and J-A model to construct the SEIR-JA model to study the formation mechanism of public opinion dissemination and polarization. Transmission parameters and polarization parameters are simulated and analyzed. Finally, a public opinion event from the pricing of China's self-developed COVID-19 vaccine are used, and related Weibo comment data about this event are also collected so as to verify the rationality and effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Simple Summary: In the absence of vaccines and antiviral therapies against COVID-19, non-pharmaceutical interventions represent the only weapon to fight this new coronavirus. In this context, mathematical models are an important tool for supporting the study of spread and transmission of this disease and to understand how restrictive measures could control the epidemic. In the current study, we adopt a new mathematical model representing the dynamics of COVID-19. We estimate model parameters with a new Bayesian method while using the public Italian data, in order to reproduce the pandemic evolution for Italy and one of its regions, Umbria. Once the model is calibrated, we also apply an algorithm, called Conditional Robustness Analysis. This algorithm allows for us to understand the influence of epidemiological parameters and non-pharmaceutical interventions on the number of hospitalized patients. This pipeline of analysis provides a quantitative explanation of the number of underestimated positive cases during the first wave of the epidemic and of the impact of lock-down measures on the hospitalization capacity. Moreover, the calibrated model is quite accurate for making updated estimations of the epidemic evolution. This study started from the request of providing predictions on hospitalization and Intensive Care Unit (ICU) rates that are caused by COVID-19 for the Umbria region in Italy. To this purpose, we propose the application of a computational framework to a SEIR-type (Susceptible, Exposed, Infected, Removed) epidemiological model describing the different stages of COVID-19 infection. The model discriminates between asymptomatic and symptomatic cases and it takes into account possible intervention measures in order to reduce the probability of transmission. As case studies, we analyze not only the epidemic situation in Umbria but also in Italy, in order to capture the evolution of the pandemic at a national level. First of all, we estimate model parameters through a Bayesian calibration method, called Conditional Robust Calibration (CRC), while using the official COVID-19 data of the Italian Civil Protection. Subsequently, Conditional Robustness Analysis (CRA) on the calibrated model is carried out in order to quantify the influence of epidemiological and intervention parameters on the hospitalization rates. The proposed pipeline properly describes the COVID-19 spread during the lock-down phase. It also reveals the underestimation of new positive cases and the need of promptly isolating asymptomatic and presymptomatic cases. The results emphasize the importance of the lock-down timeliness and provide accurate predictions on the current evolution of the pandemic. [ABSTRACT FROM AUTHOR]

Simple Summary: There is a large variety of data available about the coronavirus pandemic, but we still lack data about some important factors. Who is likely to infect whom and under what conditions and how long after becoming infected? These factors are the essence of transmission dynamics. Two groups using identical complex models can be expected to make different predictions simply because they make different choices for such transmission parameters in the model. A policy setter has no way to choose between their predictions. Simple models are not good for assessing contact tracing and detecting asymptomatic carriers, and do not replace agent-based models. However, we explain how simple models can be used to answer complex questions by adding what we call satellite equations, addressing questions involving age groups, death rates, and likelihood of transmission to nursing homes and to uninfected, isolated populations. Simple models are ideal for showing policy setters who are not mathematically sophisticated the kinds of interventions that are needed to achieve public goals. As the coronavirus pandemic spreads across the globe, people are debating policies to mitigate its severity. Many complex, highly detailed models have been developed to help policy setters make better decisions. However, the basis of these models is unlikely to be understood by non-experts. We describe the advantages of simple models for COVID-19. We say a model is "simple" if its only parameter is the rate of contact between people in the population. This contact rate can vary over time, depending on choices by policy setters. Such models can be understood by a broad audience, and thus can be helpful in explaining the policy decisions to the public. They can be used to evaluate the outcomes of different policies. However, simple models have a disadvantage when dealing with inhomogeneous populations. To augment the power of a simple model to evaluate complicated situations, we add what we call "satellite" equations that do not change the original model. For example, with the help of a satellite equation, one could know what his/her chance is of remaining uninfected through the end of an epidemic. Satellite equations can model the effects of the epidemic on high-risk individuals, death rates, and nursing homes and other isolated populations. To compare simple models with complex models, we introduce our "slightly complex" Model J. We find the conclusions of simple and complex models can be quite similar. However, for each added complexity, a modeler may have to choose additional parameter values describing who will infect whom under what conditions, choices for which there is often little rationale but that can have big impacts on predictions. Our simulations suggest that the added complexity offers little predictive advantage. [ABSTRACT FROM AUTHOR]

At the beginning of 2020, the global outbreak of the novel coronavirus COVID-19 posed a huge challenge to the governance capabilities of public health in various countries. In this paper, the SEIR model is used to fit the number of confirmed cases in each province in China, and the reduction rate of the basic reproduction number is used to measure the actual score of the control effect of COVID-19. The potential capacity of prevention and control of epidemics, in theory, is constructed, and we use the difference between theoretical ability and actual score to measure the ability of governance of public health. We found that there were significant differences between actual effect and theoretical ability in various regions, and governance capabilities were an important reason leading to this difference, which was not consistent with the level of economic development. The balance of multiple objectives, the guiding ideology of emphasizing medical treatment over prevention, the fragmentation of the public health system, and the insufficiency of prevention and control ability in primary public health systems seriously affected the government's ability to respond to public health emergencies.

Temperature response curves under diurnal oscillating temperatures differ from those under constant conditions for all stages of the Phytophthora infestans infection cycle on potatoes. We developed a mechanistic model (BLIGHTSIM) with an hourly time step to simulate late blight under fluctuating environmental conditions and predict late blight epidemics in potato fields. BLIGHTSIM is a modified susceptible (S), latent (L), infectious (I) and removed (R) compartmental model with hourly temperature and relative humidity as driving variables. The model was calibrated with growth chamber data covering one infection cycle and validated with field data from Ecuador. The model provided a good fit to all data sets evaluated. There was a significant interaction between average temperature and amplitude in their effects on the area under the disease progress curve (AUDPC) as predicted from growth chamber data on a single infection cycle. BLIGHTSIM can be incorporated in a potato growth model to study effects of diurnal temperature range on late blight impact under climate change scenarios. [ABSTRACT FROM AUTHOR]

The outbreak of coronavirus disease 2019 (COVID-19) was identified in Wuhan, China, in December 2019. As of 17 April 2020, more than 2 million cases of COVID-19 have been reported worldwide. Northern Italy is one of the world's centers of active coronavirus cases. In this study, we predicted the spread of COVID-19 and its burden on hospital care under different conditions of social distancing in Lombardy and Emilia-Romagna, the two regions of Italy most affected by the epidemic. To do this, we used a Susceptible-Exposed-Infectious-Recovered (SEIR) deterministic model, which encompasses compartments relevant to public health interventions such as quarantine. A new compartment L was added to the model for isolated infected population, i.e., individuals tested positives that do not need hospital care. We found that in Lombardy restrictive containment measures should be prolonged at least until early July to avoid a resurgence of hospitalizations; on the other hand, in Emilia-Romagna the number of hospitalized cases could be kept under a reasonable amount with a higher contact rate. Our results suggest that territory-specific forecasts under different scenarios are crucial to enhance or take new containment measures during the epidemic. [ABSTRACT FROM AUTHOR]

Ongoing outbreak of pneumonia caused by novel coronavirus (2019-nCoV) began in December 2019 in Wuhan, China, and the number of new patients continues to increase. Even though it began to spread to many other parts of the world, such as other Asian countries, the Americas, Europe, and the Middle East, the impact of secondary outbreaks caused by exported cases outside China remains unclear. We conducted simulations to estimate the impact of potential secondary outbreaks in a community outside China. Simulations using stochastic SEIR model were conducted, assuming one patient was imported to a community. Among 45 possible scenarios we prepared, the worst scenario resulted in the total number of persons recovered or removed to be 997 (95% CrI 990–1000) at day 100 and a maximum number of symptomatic infectious patients per day of 335 (95% CrI 232–478). Calculated mean basic reproductive number (R0) was 6.5 (Interquartile range, IQR 5.6–7.2). However, better case scenarios with different parameters led to no secondary cases. Altering parameters, especially time to hospital visit. could change the impact of a secondary outbreak. With these multiple scenarios with different parameters, healthcare professionals might be able to better prepare for this viral infection. [ABSTRACT FROM AUTHOR]

Since the emergence of the first cases in Wuhan, China, the novel coronavirus (2019-nCoV) infection has been quickly spreading out to other provinces and neighboring countries. Estimation of the basic reproduction number by means of mathematical modeling can be helpful for determining the potential and severity of an outbreak and providing critical information for identifying the type of disease interventions and intensity. A deterministic compartmental model was devised based on the clinical progression of the disease, epidemiological status of the individuals, and intervention measures. The estimations based on likelihood and model analysis show that the control reproduction number may be as high as 6.47 (95% CI 5.71–7.23). Sensitivity analyses show that interventions, such as intensive contact tracing followed by quarantine and isolation, can effectively reduce the control reproduction number and transmission risk, with the effect of travel restriction adopted by Wuhan on 2019-nCoV infection in Beijing being almost equivalent to increasing quarantine by a 100 thousand baseline value. It is essential to assess how the expensive, resource-intensive measures implemented by the Chinese authorities can contribute to the prevention and control of the 2019-nCoV infection, and how long they should be maintained. Under the most restrictive measures, the outbreak is expected to peak within two weeks (since 23 January 2020) with a significant low peak value. With travel restriction (no imported exposed individuals to Beijing), the number of infected individuals in seven days will decrease by 91.14% in Beijing, compared with the scenario of no travel restriction. [ABSTRACT FROM AUTHOR]

Western countries are experiencing surges in COVID-19 cases and deaths due to increasing public transportation during holiday seasons. This study aimed to explore whether mainland China will face an epidemic rebound during the Spring Festival holiday, when millions of Chinese people travel across the country, and investigate which nucleic acid testing (NAT) strategy is optimal to contain the epidemic. A microsimulation model was used to simulate SARS-CoV-2 transmission among railway travelers and evaluated the effects of various NAT strategies. An extended susceptible-exposed-infectious-recovered (SEIR) model was built to forecast local transmission during the Spring Festival period under different scenarios of testing strategies. The total number of infections, testing burden, and medical expenditure were calculated to devise an optimal strategy during the Spring Festival travel rush. Assuming the daily incidence of 20 per 10 million persons, our model simulated that there would be 97 active infections on the day of travel among 10 million railway passengers without NAT and symptom screening. Pre-travel testing could reduce the number of active infections. Compared with no NAT, testing passengers from risk tier 2-4 regions 3 days before travelling could significantly reduce the risk of transmission, and it is more economical and efficient than testing for all passengers.

The coronavirus COVID-19 has recently started to spread rapidly in Malaysia. The number of total infected cases has increased to 3662 on 05 April 2020, leading to the country being placed under lockdown. As the main public concern is whether the current situation will continue for the next few months, this study aims to predict the epidemic peak using the Susceptible-Exposed-Infectious-Recovered (SEIR) model, with incorporation of the mortality cases. The infection rate was estimated using the Genetic Algorithm (GA), while the Adaptive Neuro-Fuzzy Inference System (ANFIS) model was used to provide short-time forecasting of the number of infected cases. The results show that the estimated infection rate is 0.228 ± 0.013, while the basic reproductive number is 2.28 ± 0.13. The epidemic peak of COVID-19 in Malaysia could be reached on 26 July 2020, with an uncertain period of 30 days (12 July-11 August). Possible interventions by the government to reduce the infection rate by 25% over two or three months would delay the epidemic peak by 30 and 46 days, respectively. The forecasting results using the ANFIS model show a low Normalized Root Mean Square Error (NRMSE) of 0.041; a low Mean Absolute Percentage Error (MAPE) of 2.45%; and a high coefficient of determination (R 2 ) of 0.9964. The results also show that an intervention has a great effect on delaying the epidemic peak and a longer intervention period would reduce the epidemic size at the peak. The study provides important information for public health providers and the government to control the COVID-19 epidemic.