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It is crucial to capture the actual infection scale of communicable diseases. However, the official case numbers cannot equal to actual infection scale in society, because a large number of asymptomatic individuals are not recognized. To deal with this challenge, this paper takes COVID-19 as the object, and develops an improved SEIR dynamics model to estimate its actual infection scale. Generalized to the circumstances in this work, we improve the classical SEIR model by considering three implicit factors: self-recovered asymptomatic individuals, recovered individuals, and deceased individuals. The dynamics process inside the improved model is expressed using mathematical formulas, and the parameter estimation scheme is given accordingly. To evaluate the estimation effect of the proposal, we employ pandemic data from 10 representative countries to build experimental scenario. The results obtained through model fitting demonstrate that the estimated actual infection scale is approximately 10–30 times higher than the reported average “newly confirmed cases”. Furthermore, our findings reveal a noteworthy negative correlation between the transmission coefficient and vaccination rate, confirming the beneficial role of vaccination in mitigating COVID-19 spreading. [ABSTRACT FROM AUTHOR]

During the COVID-19 pandemic, over one thousand papers were published on "Susceptible- Exposed-Infectious-Removed" (SEIR) epidemic computational models. The English word "exposed" in its vernacular and public health usage means a state of having been in contact with an infectious individual, but not necessarily infected. In contrast, the term "exposed" in SEIR modeling usage typically stands for a state of already being infected but not yet being infectious to others, a state more properly termed "latently infected." In public health language, "exposed" means possibly infected, yet in SEIR modeling language, "exposed" means already infected. This paper retraces the conceptual and mathematical origins of this terminological disconnect and concludes that epidemic modelers should consider using the "SLIR" notational short-hand (L for Latent) instead of SEIR. [ABSTRACT FROM AUTHOR]

Since the early days of the coronavirus (COVID-19) outbreak in Wuhan, China, Saudi Arabia started to implement several preventative measures starting with the imposition of travel restrictions to and from China. Due to the rapid spread of COVID-19, and with the first confirmed case in Saudi Arabia in March 2019, more strict measures, such as international travel restriction, and suspension or cancellation of major events, social gatherings, prayers at mosques, and sports competitions, were employed. These non-pharmaceutical interventions aim to reduce the extent of the epidemic due to the implications of international travel and mass gatherings on the increase in the number of new cases locally and globally. Since this ongoing outbreak is the first of its kind in the modern world, the impact of suspending mass gatherings on the outbreak is unknown and difficult to measure. We use a stratified SEIR epidemic model to evaluate the impact of Umrah, a global Muslim pilgrimage to Mecca, on the spread of the COVID-19 pandemic during the month of Ramadan, the peak of the Umrah season. The analyses shown in the paper provide insights into the effects of global mass gatherings such as Hajj and Umrah on the progression of the COVID-19 pandemic locally and globally. [ABSTRACT FROM AUTHOR]

Tuberculosis (TB) is a highly contagious disease caused by Mycobacterium tuberculosis, which has historically resulted in numerous fatalities. The analysis of TB is conducted through mathematical models featuring differential equations that describe the dynamics of epidemic spread, as well as its control and prevention. This paper presents the SEIR + D model of TB. According to this model, the total population is divided into five compartments: susceptible, exposed, infected, recovered, and deceased. This paper evaluates the rates (such as transmission rate, incubation rate, etc.) at which individuals transition from one compartment to another under various scenarios. [ABSTRACT FROM AUTHOR]

Basic Susceptible-Exposed-Infectious-Removed (SEIR) models of COVID-19 dynamics tend to be excessively pessimistic due to high basic reproduction values, which result in overestimations of cases of infection and death. We propose an extended SEIR model and daily data of COVID-19 cases in the U.S. and the seven largest European countries to forecast possible pandemic dynamics by investigating the effects of infection vulnerability stratification and measures on preventing the spread of infection. We assume that (i) the number of cases would be underestimated at the beginning of a new virus pandemic due to the lack of effective diagnostic methods and (ii) people more susceptible to infection are more likely to become infected; whereas during the later stages, the chances of infection among others will be reduced, thereby potentially leading to pandemic cessation. Based on infection vulnerability stratification, we demonstrate effects brought by the fraction of infected persons in the population at the start of pandemic deceleration on the cumulative fraction of the infected population. We interestingly show that moderate and long-lasting preventive measures are more effective than more rigid measures, which tend to be eventually loosened or abandoned due to economic losses, delay the peak of infection and fail to reduce the total number of cases. Our calculations relate the pandemic's second wave to high seasonal fluctuations and a low vulnerability stratification coefficient. Our characterisation of basic reproduction dynamics indicates that second wave of the pandemic is likely to first occur in Germany, Spain, France, and Italy, and a second wave is also possible in the U.K. and the U.S. Our findings show that even if the total elimination of the virus is impossible, the total number of infected people can be reduced during the deceleration stage. [ABSTRACT FROM AUTHOR]

During the COVID-19 pandemic, over one thousand papers were published on “Susceptible-Exposed-Infectious-Removed” (SEIR) epidemic computational models. The English word “exposed” in its vernacular and public health usage means a state of having been in contact with an infectious individual, but not necessarily infected. In contrast, the term “exposed” in SEIR modeling usage typically stands for a state of already being infected but not yet being infectious to others, a state more properly termed “latently infected.” In public health language, “exposed” means possibly infected, yet in SEIR modeling language, “exposed” means already infected. This paper retraces the conceptual and mathematical origins of this terminological disconnect and concludes that epidemic modelers should consider using the “SLIR” notational short-hand (L for Latent) instead of SEIR.

Abstract The E/S (exposed/susceptible) ratio is analyzed in the SEIR model. The ratio plays a key role in understanding epidemic dynamics during the 2014–2016 Ebola outbreak in Sierra Leone and Guinea. The maximum value of the ratio occurs immediately before or after the time-dependent reproduction number (R t ) equals 1, depending on the initial susceptible population (S(0)). It is demonstrated that transmission rate curves corresponding to various incubation periods intersect at a single point referred to as the Cross Point (CP). At this point, the E/S ratio reaches an extremum, signifying a critical shift in transmission dynamics and aligning with the time when R t approaches 1. By plotting transmission rate curves, β(t), for any two arbitrary incubation periods and tracking their intersections, we can trace CP over time. CP serves as an indicator of epidemic status, especially when R t is close to 1. It provides a practical means of monitoring epidemics without prior knowledge of the incubation period. Through a case study, we estimate the transmission rate and reproduction number, identifying CP and R t = 1 while examining the E/S ratio across various values of S(0).

Abstract Current global COVID-19 booster scheduling strategies mainly focus on vaccinating high-risk populations at predetermined intervals. However, these strategies overlook key data: the direct insights into individual immunity levels from active serological testing and the indirect information available either through sample-based sero-surveillance, or vital demographic, location, and epidemiological factors. Our research, employing an age-, risk-, and region-structured mathematical model of disease transmission—based on COVID-19 incidence and vaccination data from Israel between 15 May 2020 and 25 October 2021—reveals that a more comprehensive strategy integrating these elements can significantly reduce COVID-19 hospitalizations without increasing existing booster coverage. Notably, the effective use of indirect information alone can considerably decrease COVID-19 cases and hospitalizations, without the need for additional vaccine doses. This approach may also be applicable in optimizing vaccination strategies for other infectious diseases, including influenza.

A recent paper (Zhang R, Yu X. Traveling waves for a four‐compartment lattice epidemic system with exposed class and standard incidence. Math Meth Appl Sci. 2022; 45: 113‐136) presented a four‐compartment lattice epidemic system with exposed class and standard incidence. The authors studied the existence and non‐existence of traveling wave solutions of this system. However, the limit behavior of R$$ R $$‐component of traveling wave solutions is still open. In this paper, we solve this open problem and establish the boundedness of traveling wave solutions by analysis technique. Meanwhile, we study the non‐existence of traveling wave solutions with non‐positive wave velocity. [ABSTRACT FROM AUTHOR]

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]

Background: The most commonly used mathematical model for analyzing disease spread is the Susceptible-Exposed-InfectedRecovered (SEIR) model. Moreover, the dynamics of the SEIR model depend on several factors, such as the parameter values. Objective: This study aimed to compare two optimization methods, namely genetic algorithm (GA) and particle swarm optimization (PSO), in estimating the SEIR model parameter values, such as the infection, transition, recovery, and death rates. Methods: GA and PSO algorithms were compared to estimate parameter values of the SEIR model. The fitness value was calculated from the error between the actual data of cumulative positive COVID-19 cases and the numerical data of cases from the solution of the SEIR COVID-19 model. Furthermore, the numerical solution of the COVID-19 model was calculated using the fourth-order Runge-Kutta algorithm (RK-4), while the actual data were obtained from the cumulative dataset of positive COVID-19 cases in the province of Jakarta, Indonesia. Two datasets were then used to compare the success of each algorithm, namely, Dataset 1, representing the initial interval for the spread of COVID-19, and Dataset 2, representing an interval where there was a high increase in COVID-19 cases. Results: Four parameters were estimated, namely the infection rate, transition rate, recovery rate, and death rate, due to disease. In Dataset 1, the smallest error of GA method, namely 8.9%, occurred when the value of = 0.5, while the numerical error of PSO was 7.5%. In Dataset 2, the smallest error of GA method, namely 31.21%, occurred when = 0.5, while the numerical error of PSO was 3.46%. Conclusion: Based on the parameter estimation results for Datasets 1 and 2, PSO had better fitting results than GA. This showed PSO was more robust to the provided datasets and could better adapt to the trends of the COVID-19 epidemic. [ABSTRACT FROM AUTHOR]

The E/S (exposed/susceptible) ratio is analyzed in the SEIR model. The ratio plays a key role in understanding epidemic dynamics during the 2014–2016 Ebola outbreak in Sierra Leone and Guinea. The maximum value of the ratio occurs immediately before or after the time-dependent reproduction number (Rt) equals 1, depending on the initial susceptible population (S(0)). It is demonstrated that transmission rate curves corresponding to various incubation periods intersect at a single point referred to as the Cross Point (CP). At this point, the E/S ratio reaches an extremum, signifying a critical shift in transmission dynamics and aligning with the time when Rt approaches 1. By plotting transmission rate curves, β(t), for any two arbitrary incubation periods and tracking their intersections, we can trace CP over time. CP serves as an indicator of epidemic status, especially when Rt is close to 1. It provides a practical means of monitoring epidemics without prior knowledge of the incubation period. Through a case study, we estimate the transmission rate and reproduction number, identifying CP and Rt = 1 while examining the E/S ratio across various values of S(0). [ABSTRACT FROM AUTHOR]

In this study, the infiltration model was established to study the early warning of pulmonary tuberculosis data in Xiamen public hospitals. Based on the gender characteristics of residents in Xiamen, a percolation model was established to analyze the transmission rates of diseases under different contact types. In addition, the calculation method of the percolation threshold is discussed, and the model is verified by a simulation experiment. The results show that the model can predict the spread of epidemic situations well. The early warning value and relevant preventive measures were obtained by simulating the spread of tuberculosis under different exposure numbers. Bond percolation analysis was used to predict the proportion of the eventually infected population, this threshold of percolation was the basic regeneration number of tuberculosis, and the tuberculosis infection situation was effectively predicted. [ABSTRACT FROM AUTHOR]

Current global COVID-19 booster scheduling strategies mainly focus on vaccinating high-risk populations at predetermined intervals. However, these strategies overlook key data: the direct insights into individual immunity levels from active serological testing and the indirect information available either through sample-based sero-surveillance, or vital demographic, location, and epidemiological factors. Our research, employing an age-, risk-, and region-structured mathematical model of disease transmission—based on COVID-19 incidence and vaccination data from Israel between 15 May 2020 and 25 October 2021—reveals that a more comprehensive strategy integrating these elements can significantly reduce COVID-19 hospitalizations without increasing existing booster coverage. Notably, the effective use of indirect information alone can considerably decrease COVID-19 cases and hospitalizations, without the need for additional vaccine doses. This approach may also be applicable in optimizing vaccination strategies for other infectious diseases, including influenza. [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 this article, we present a Distributionally Robust Markov Decision Process (DRMDP) approach for addressing the dynamic epidemic control problem. The Susceptible-Exposed-Infectious-Recovered (SEIR) model is widely used to represent the stochastic spread of infectious diseases, such as COVID-19. Although the Markov Decision Process (MDP) offers a mathematical framework for identifying optimal actions, such as vaccination and transmission-reducing intervention, to combat disease spread calculated using the SEIR model. However, uncertainties in these scenarios demand a more robust approach that is less reliant on error-prone assumptions. The primary objective of our study is to introduce a new DRMDP framework that allows for an ambiguous distribution of transition dynamics. Specifically, we consider the worst-case distribution of these transition probabilities within a decision-dependent ambiguity set. To overcome the computational complexities associated with policy determination, we propose an efficient Real-Time Dynamic Programming (RTDP) algorithm that is capable of computing optimal policies based on the reformulated DRMDP model in an accurate, timely, and scalable manner. Comparative analysis against the classic MDP model demonstrates that the DRMDP achieves a lower proportion of infections and susceptibilities at a reduced cost. [ABSTRACT FROM AUTHOR]

Helicobacter pylori (H. pylori), a bacterium that has captured the attention of researchers for over a century, is well-known for its association with peptic ulcer and gastric cancer. Despite a decline in its prevalence to improved hygienic conditions and effective curative and preventive measures, H. pylori still persists in various communities and continues to spread, maintaining its global presence in both developing and developed nations. Persistent efforts in scientific research have led to the discovery of diverse management options to combat this pathogen. In this article, we direct our attention to the global prevalence of H. pylori infection, delve into the factors contributing to its transmission, and explore prevention methods. Through the study's findings, we gain valuable insights into how these factors influence H. pylori infection rates. In addition, we study the local and global stability and the numerical solution for the models. [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]

Mathematical modelling based on the compartmental Susceptible – Exposed – Infected - Recovered (SEIR) model is proposed in this paper to study the pandemic outbreak. In addition, simulations from both the deterministic approach as well as the stochastic approach are implemented to validate the present study. Among each state, the transitions between different categories are simulated by using various graph models including the complete graph, the steady Erdos-Renyi graph, as well as the varying Erdos-Renyi graph. The related parameters for the SEIR model are chosen from available literature and the effect of some other factors such as the inflow or outflow of travellers in a city as well as the impact of vaccination rate is explored. Furthermore, the difference between the simulation results coming from the deterministic SEIR model and the stochastic SEIR one is examined to check the availability of the present simulation. It is found that, the stochastic simulation based on the complete graph is more consistent with the deterministic SEIR model.

This study focuses on the cutting-edge field of epidemic modeling, providing a comprehensive investigation of a third-order two-stage numerical approach combined with neural network simulations for the SEIR (Susceptible-Exposed-Infectious-Removed) epidemic model. An explicit numerical scheme is proposed in this work for dealing with both linear and nonlinear boundary value problems. The scheme is built on two grid points, or two time levels, and is third-order. The main advantage of the scheme is its order of accuracy in two stages. Third-order precision is not only not provided by most existing explicit numerical approaches in two phases, but it also necessitates the computation of an additional derivative of the dependent variable. The proposed scheme's consistency and stability are also examined and presented. Nonlinear SEIR (susceptible-exposed-infected-recovered) models are used to implement the scheme. The scheme is compared with the non-standard finite difference and forward Euler methods that are already in use. The graph shows that the plan is more accurate than non-standard finite difference and forward Euler methods that are already in use. The solution obtained is then looked at through the lens of the neural network. The neural network is trained using an optimization approach known as the Levenberg-Marquardt backpropagation (LMB) algorithm. The mean square error across the total number of iterations, error histograms, and regression plots are the various graphs that can be created from this process. This work conducts thorough evaluations to not only identify the strengths and weaknesses of the suggested approach but also to examine its implications for public health intervention. The results of this study make a valuable contribution to the continuously developing field of epidemic modeling. They emphasize the importance of employing modern numerical techniques and machine learning algorithms to enhance our capacity to predict and effectively control infectious diseases. Doi: 10.28991/ESJ-2024-08-01-023 Full Text: PDF

This paper explores the impact of various distancing measures on the spread of infectious diseases, focusing on the spread of COVID-19 in the Moroccan population as a case study. Contact matrices, generated through a social force model, capture population interactions within distinct activity locations and age groups. These matrices, tailored for each distancing scenario, have been incorporated into an SEIR model. The study models the region as a network of interconnected activity locations, enabling flexible analysis of the effects of different distancing measures within social contexts and between age groups. Additionally, the method assesses the influence of measures targeting potential superspreaders (i.e., agents with a very high contact rate) and explores the impact of inter-activity location flows, providing insights beyond scalar contact rates or survey-based contact matrices. The results suggest that implementing intra-activity location distancing measures significantly reduces in the number of infected individuals relative to the act of imposing restrictions on individuals with a high contact rate in each activity location. The combination of both measures proves more advantageous. On a regional scale, characterized as a network of interconnected activity locations, restrictions on the movement of individuals with high contact rates was found to result in a $ 2 \% $ reduction, while intra-activity location-based distancing measures was found to achieve a $ 44 \% $ reduction. The combination of these two measures yielded a $ 48\% $ reduction.

Epidemiologists have used the timing of the peak of an epidemic to guide public health interventions. By determining the expected peak time, they can allocate resources effectively and implement measures such as quarantine, vaccination, and treatment at the right time to mitigate the spread of the disease. The peak time also provides valuable information for those modeling the spread of the epidemic and making predictions about its future trajectory. In this study, we analyze the time needed for an epidemic to reach its peak by presenting a straightforward analytical expression. Utilizing two epidemiological models, the first is a generalized $ SEIR $ model with two classes of latent individuals, while the second incorporates a continuous age structure for latent infections. We confirm the conjecture that the peak occurs at approximately $ T\sim(\ln N)/\lambda $, where $ N $ is the population size and $ \lambda $ is the largest eigenvalue of the linearized system in the first model or the unique positive root of the characteristic equation in the second model. Our analytical results are compared to numerical solutions and shown to be in good agreement.

In this work, we investigate the transmission dynamics of the Zika virus, considering both a compartmental model involving humans and mosquitoes and an extended model that introduces a non-human primate (monkey) as a second reservoir host. The novelty of our approach lies in the later generalization of the model using a fractional time derivative. The significance of this study is underscored by its contribution to understanding the complex dynamics of Zika virus transmission. Unlike previous studies, we incorporate a non-human primate reservoir host into the model, providing a more comprehensive representation of the disease spread. Our results reveal the importance of utilizing a nonstandard finite difference (NSFD) scheme to simulate the disease's dynamics accurately. This NSFD scheme ensures the positivity of the solution and captures the correct asymptotic behavior, addressing a crucial limitation of standard solvers like the Runge-Kutta Fehlberg method (ode45). The numerical simulations vividly demonstrate the advantages of our approach, particularly in terms of positivity preservation, offering a more reliable depiction of Zika virus transmission dynamics. From these findings, we draw the conclusion that considering a non-human primate reservoir host and employing an NSFD scheme significantly enhances the accuracy and reliability of modeling Zika virus transmission. Researchers and policymakers can use these insights to develop more effective strategies for disease control and prevention.

AbstractVaccines suppress the increased spread of infectious diseases or the number of severe cases. Considerable research and development yielded several vaccines against coronavirus disease 2019 (COVID-19). To contain the disease, governments have run vaccination campaigns and implemented restrictions depending on vaccination status. Ensuring the stability of vaccine supply with increased and/or seasonal demand has thus become critical. However, determination of the required vaccine supply is difficult due to variations in virus mutations, their impacts on the disease, and vaccine efficacy. In this work, we developed a mathematical model to consider the effect of vaccination on the infection numbers, taking COVID-19 as a case study. We have conducted a sensitivity analysis to identify the key variables affecting the required vaccine supply. We have conducted a scenario analysis to assess the impact of changes in vaccine supply parameters on the number of severe cases in Japan. Production of different products at dual-use facilities has been suggested to tackle the variability in vaccine demand. The analysis provided insights into the feasibility and adequate timing for product-switch at dual-use facilities. The proposed method can be applied to other infectious diseases and can be expanded to support various aspects for decision-making for policy building.

When humanity faces a potentially contagious disease, most processes of society are affected, the workforce capable of performing tasks decreases, and healthcare systems become overwhelmed by sudden disease outbreaks. In 2020, the world fell victim to Covid-19. Its spread had devastating consequences in many countries, changing the lives of all individuals. The poor management of the pandemic on a global scale highlighted the lack of preparedness for this type of catastrophe, leading to efforts and research being conducted to facilitate the management of this disease. One of the most important endeavors undertaken to control the spread of the infectious virus was to attempt to predict its behavior and take measures to mitigate the damage caused. Pandemic control models, such as the SEIR model, were employed to create predictions, but the results proved to be imprecise due to the lack of infection data. Furthermore, a highly contagious virus that is transmitted by people behaves in a very erratic manner, making it more challenging to develop rigid prediction methods. It was determined that geographic and demographic characteristics greatly influenced the virus's behavior. Agent-Based Simulation was used to model processes and environments with unique characteristics while allowing for individual interaction. In this work, Agent-Based Simulation is employed to model the spread of a virus that affects individuals in a city in Cuba. [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]

This paper aims to develop a stochastic perturbation into SEIR (Susceptible-Exposed-Infected-Removed) epidemic model including a saturated estimated incidence. A set of stochastic differential equations is used to study its behavior, with the assumption that each population's exposure to environmental unpredictability is represented by noise terms. This kind of randomness is considerably more reasonable and realistic in the proposed model. The current study has been viewed as strengthening the body of literature because there is less research on the dynamics of this kind of model. We discussed the structure of all equilibriums' existence and the dynamical behavior of all the steady states. The fundamental replication number for the proposed method was used to discuss the stability of every equilibrium point; if R0 < 1, the infected free equilibrium is resilient, and if R0 < 1, the endemic equilibrium is resilient. The system's value is primarily described by its ambient stochasticity, which takes the form of Gaussian white noise. Additionally, the suggested model can offer helpful data for comprehending, forecasting, and controlling the spread of various epidemics globally. Numerical simulations are run for a hypothetical set of parameter values to back up our analytical conclusions. [ABSTRACT FROM AUTHOR]

The outbreak of a disease can lead to behavioral changes in the healthy to avert infection. We first establish a nonlinear SEIR epidemic model that incorporates the impact of individuals' behavioral response owe to information of the disease prevalence. Both the existence of equilibria and sharp sufficient conditions on stable equilibria are verified. Whereafter, the local and global sensitivity analyses are carried out to assess the relative effects of parameters on the basic reproduction number. Therewith the optimal control problem is considered to provide a theoretical basis for disease prevention and control, and the existence and uniqueness consequences for optimal control paths are demonstrated. Some numerical examples and discussions are given to support and visualize our analytical results, which can be derived that the combined use of three control measures is more effective than any single adopted control strategy to curb the spread of diseases. We also find that the information plays a crucial role in controlling infection. [ABSTRACT FROM AUTHOR]

During the recent pandemic caused by COVID‐19, media awareness played a crucial role in educating people about social distancing, wearing masks, quarantine, vaccination, and medication. Media awareness brought individual behavioral changes among the people, which in turn helped reduce the infection rate. Motivated by this, we have formulated a mathematical model introducing a media compartment to mitigate measles disease transmission. In this paper, the SEIR model is used to study measles disease in three cases: one with a delay in vaccination, the second with regular vaccination, and the third with the impact of media awareness on the spreading of measles disease. Further, the dynamical behavior of the models is studied in terms of positivity, boundedness, equilibrium, and basic reproduction number (BRN). The sensitivity analysis of the models is conducted, which verifies the importance of the BRN (R0$$ {R}_0 $$) to be less than one for disease eradication. The numerical study confirms the impact of media awareness on exposed and infected populations. [ABSTRACT FROM AUTHOR]

With the ongoing evolution of the novel coronavirus pathogen and continuous improvements in our social environment, the mortality rate of COVID-19 is on a decline. In response to this, we introduce an adaptive control strategy known as intentional control, which offers cost-efficiency and superior control effectiveness. The classical SEIR model faces limitations in accurately representing close contacts and sub-close contacts and fails to distinguish their varying levels of infectivity. To address this, our study modifies the classical model by incorporating close contact (E) and a sub-close contact (E2) while reworking the infectious mechanism. Once the model is formulated, we employ various statistical methods to identify crucial parameters, including R2, adjusted R2, and standard deviation. For disease control, we implement an intentional control program with four distinct grades. We develop and apply a scheme in MATLAB for our proposed model, generating diverse simulation results based on realistic parameter values for discussion. Additionally, we explore a range of strategy combinations to differentiate their effectiveness under various social conditions, aiming to identify an optimal approach. Comparing the intentional control strategy to random control, our findings consistently demonstrate the superiority of intentional control across all scenarios. Furthermore, the results indicate that our approach better aligns with the characteristics of the novel coronavirus, characterized by an "extremely low fatality rate and strong infectivity," while offering detailed insights into the transmission dynamics among different compartments. [ABSTRACT FROM AUTHOR]

A local COVID-19 outbreak with two community clusters occurred in a large industrial city, Shaoxing, China, in December 2021 after serial interventions were imposed. We aimed to understand the reason by analysing the characteristics of the outbreak and evaluating the effects of phase-adjusted interventions. Publicly available data from 7 December 2021 to 25 January 2022 were collected to analyse the epidemiological characteristics of this outbreak. The incubation period was estimated using Hamiltonian Monte Carlo method. A well-fitted extended susceptible-exposed-infectious-recovered model was used to simulate the impact of different interventions under various combination of scenarios. There were 387 SARS-CoV-2-infected cases identified, and 8.3% of them were initially diagnosed as asymptomatic cases. The estimated incubation period was 5.4 (95% CI 5.2–5.7) days for all patients. Strengthened measures of comprehensive quarantine based on tracing led to less infections and a shorter duration of epidemic. With a same period of incubation, comprehensive quarantine was more effective in containing the transmission than other interventions. Our findings reveal an important role of tracing and comprehensive quarantine in blocking community spread when a cluster occurred. Regions with tense resources can adopt home quarantine as a relatively affordable and low-impact intervention measure compared with centralized quarantine. [ABSTRACT FROM AUTHOR]

We consider the susceptible-exposed-infected-removed (SEIR) epidemic model and apply optimal control to it successfully. Here three control inputs are considered, so that the infection rate is decreased and exposed or infected individuals are removed. Our approach is to reduce the computation of the optimal control input to that of the stable manifold of an invariant manifold in a Hamiltonian system. Some numerical examples in which the computer software AUTO is used to numerically compute the stable manifold are given to demonstrate the usefulness of our approach for the optimal control in the SEIR model. Our study suggests how we can decrease the number of infected individuals quickly before a critical situation occurs while keeping social and economic burdens small. Our results for the SEIR model are very different from the previous one for the SIR model, which is similar but simpler than the present one. [ABSTRACT FROM AUTHOR]

This study introduces a novel fractional-order spatio-temporal SEIR model for epidemic modeling, providing an advanced approach to understanding disease dynamics. Our model, categorizing the population into Susceptible (S), Exposed (E), Infected (I), and Recovered (R), incorporates fractional calculus to accurately reflect the complex, non-linear nature of infectious diseases. Key findings include the confirmation of the existence and uniqueness of the model’s solutions, ensuring reliability for epidemiological predictions. Through rigorous stability analysis at both disease-free and endemic equilibrium points, we identified critical parameters influencing epidemic outcomes. Numerical simulations reveal that the fractional order significantly impacts disease progression, offering valuable insights for intervention strategies.

Outbreaks of COVID-19 in meat processing plants (MPPs) were recorded globally throughout the pandemic. There was speculation these outbreaks resulted in dissemination of COVID-19 throughout the surrounding county leading to high incidence rates. We aimed to investigate the dynamics of spread between MPPs and their surrounding counties. In this retrospective longitudinal study, data were collected on the number and size of outbreaks in 33 MPPs and county infections in Ireland between March 2020 and May 2021. These data were used to investigate the relationship between outbreaks in MPPs and county infection rates through statistical analysis, and the development of a novel SEIR model. We found an association between the number of MPPs present in a county and county incidence rates, however, incidence rates in the counties did not increase as a consequence of an outbreak in an MPP. The model results indicate that county incidence rates in the weeks prior to an MPP outbreak could reliably predict the size of that outbreak in a plant, r(49) = 0·62, p

While there has been much computational work on the effect of intervention measures, such as vaccination or quarantine, the influence of social distancing on the epidemics' outbursts is not well understood. We present a realistic, analytically solvable, framework for COVID-19 dynamics in the presence of social distancing measures. The model is a generalization of the compartmental SEIR model that accounts for the effects of these measures. We derive a closed-form mathematical expressions for the time dependence of epidemiological observables, in particular, the detected cases and fatalities. These analytical solutions indicate simple quantitative relations between the model variables and epidemiological observables, which give insights into cause-effect connections that underlie the outburst dynamics but are obscured in more standard (numerical) approaches. While the obtained results and conclusions are based on the study of the COVID-19 pandemic, the presented analysis has general applicability to infection outbursts. Our findings are particularly important in the emergence of new pandemics when effective pharmaceutical treatments are unavailable, and one must rely on well-timed and appropriately chosen social mitigation measures. [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]

The Covid-19 pandemic has required most countries to implement complex sequences of non-pharmaceutical interventions, with the aim of controlling the transmission of the virus in the population. To be able to take rapid decisions, a detailed understanding of the current situation is necessary. Estimates of time-varying, instantaneous reproduction numbers represent a way to quantify the viral transmission in real time. They are often defined through a mathematical compartmental model of the epidemic, like a stochastic SEIR model, whose parameters must be estimated from multiple time series of epidemiological data. Because of very high dimensional parameter spaces (partly due to the stochasticity in the spread models) and incomplete and delayed data, inference is very challenging. We propose a state-space formalization of the model and a sequential Monte Carlo approach which allow to estimate a daily-varying reproduction number for the Covid-19 epidemic in Norway with sufficient precision, on the basis of daily hospitalization and positive test incidences. The method was in regular use in Norway during the pandemics and appears to be a powerful instrument for epidemic monitoring and 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]

The rapid development of social media and information dissemination has profoundly affected the ideology and value orientation of college students and put forward new challenges and requirements for ideological education work in colleges and universities. This paper takes the characteristics of social media as an orientation, studies the problems of ideological education in colleges and universities, and carries out a SWOT analysis of ideological education under the influence of social media. Based on social media, we constructed a complex network, gave a measure of its network topological characteristics, and then combined it with the classical information dissemination model to establish a SEIR information dissemination model of Civic and Political Education in colleges under the influence of social media. Taking the “Tang Palace Night Banquet” in Province H and the Civic and Political Education Skills Competition in University H as research objects, we analyzed the characteristics of the social network of Civic and Political Education information and verified the explanatory ability of the SEIR model in the dissemination of Civic and Political Education information in colleges and universities. People’s Daily has the highest incidence value and middle centrality of 63 and 72 in social media networks, and its middle centrality is 28.57% higher than that of Henan Satellite TV. The SEIR model tends to stabilize on the 180th day of the evolution, when the refusers of the dissemination of information on civic and political education are 700, and the disseminators are 300. Social media can expand the content of Civic Education in colleges and universities, combined with diverse star network nodes, can enhance the ability of Civic Education in colleges and universities, and improve the level of students’ Civic Education.

Abstract Background With the global spread of COVID-19, detecting high-risk countries/regions timely and dynamically is essential; therefore, we sought to develop automatic, quantitative and scalable analysis methods to observe and estimate COVID-19 spread worldwide and further generate reliable and timely decision-making support for public health management using a comprehensive modeling method based on multiple mathematical models. Methods We collected global COVID-19 epidemic data reported from January 23 to September 30, 2020, to observe and estimate its possible spread trends. Countries were divided into three outbreak levels: high, middle, and low. Trends analysis was performed by calculating the growth rate, and then country grouping was implemented using group-based trajectory modeling on the three levels. Individual countries from each group were also chosen to further disclose the outbreak situations using two predicting models: the logistic growth model and the SEIR model. Results All 187 observed countries' trajectory subgroups were identified using two grouping strategies: with and without population consideration. By measuring epidemic trends and predicting the epidemic size and peak of individual countries, our study found that the logistic growth model generally estimated a smaller epidemic size than the SEIR model. According to SEIR modeling, confirmed cases in each country would take an average of 9–12 months to reach the outbreak peak from the day the first case occurred. Additionally, the average number of cases at the peak time will reach approximately 10–20% of the countries’ populations, and the countries with high trends and a high predicted size must pay special attention and implement public health interventions in a timely manner. Conclusions We demonstrated comprehensive observations and predictions of the COVID-19 outbreak in 187 countries using a comprehensive modeling method. The methods proposed in this study can measure COVID-19 development from multiple perspectives and are generalizable to other epidemic diseases. Furthermore, the methods also provide reliable and timely decision-making support for public health management.

Media coverage can greatly impact the spread of infectious diseases. Taking into consideration the impacts of media coverage, we propose an SEIR model with a media coverage mediated nonlinear infection force. For this novel disease model, we identify the basic reproduction number using the next generation matrix method and establish the global threshold results: If the basic reproduction number $ \mathcal{R}_{0} < 1 $, then the disease-free equilibrium $ P_{0} $ is stable, and the disease dies out. If $ \mathcal{R}_{0} > 1 $, then the endemic equilibrium $ P^{*} $ is stable, and the disease persists. Sensitivity analysis indicates that the basic reproduction number $ \mathcal{R}_{0} $ is most sensitive to the population recruitment rate $ \Lambda $ and the disease transmission rate $ \beta _{1} $.

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.

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.