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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)., (© 2024. The Author(s).)

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.

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.

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., (© 2023. The Author(s).)

This study aimed to predict the transmission trajectory of the 2019 Corona Virus Disease (COVID-19) and analyze the impact of preventive measures on the spread of the epidemic. Considering that tracking a long-term epidemic trajectory requires explanatory modeling with more complexities than short-term predictions, an improved Susceptible-Exposed-Infected-Removed (SEIR) transmission dynamic model is established. The model depends on defining various parameters that describe both the virus and the population under study. However, it is likely that several of these parameters will exhibit significant variations among different states. Therefore, regression algorithms and heuristic algorithms were developed to effectively adapt the population-dependent parameters and ensure accurate fitting of the SEIR model to data for any specific state. In this study, we consider the second outbreak of COVID-19 in Italy as a case study, which occurred in August 2020. We divide the epidemic data from February to September of the same year into two distinct stages for analysis. The numerical results demonstrate that the improved SEIR model effectively simulates and predicts the transmission trajectories of the Italian epidemic during both periods before and after the second outbreak. By analyzing the impact of anti-epidemic measures on the spread of the disease, our findings emphasize the significance of implementing anti-epidemic preventive measures in COVID-19 modeling., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Lu, Zheng, Jia and Tian.)

Non-pharmaceutical interventions (NPIs) play a central role in infectious disease outbreak response and control. Their usefulness cannot be overstated, especially during the early phases of a new epidemic when vaccines and effective treatments are not available yet. These interventions can be very effective in curtailing the spread of infectious diseases when adequately implemented and sufficiently adopted by the public. However, NPIs can be very disruptive, and the socioeconomic and cultural hardships that come with their implementation interfere with both the ability and willingness of affected populations to adopt such interventions. This can lead to reduced and unsteady adherence to NPIs, making disease control more challenging to achieve. Deciphering this complex interaction between disease dynamics, NPI stringency, and NPI adoption would play a critical role in informing disease control strategies. In this work, we formulate a general-purpose model that integrates government-imposed control measures and public adherence into a deterministic compartmental epidemic model and study its properties. By combining imitation dynamics and the health belief model to encode the unsteady nature of NPI adherence, we investigate how temporal variations in NPI adherence levels affect the dynamics and control of infectious diseases. Among the results, we note the occurrence of multiple epidemic waves as a result of temporal variations in NPI adherence and a trade-off between the stringency of control measures and adherence. Additionally, our results suggest that interventions that aim at increasing public adherence to NPIs are more beneficial than implementing more stringent measures. Our findings highlight the necessity of taking the socioeconomic and cultural realities of affected populations into account when devising public health interventions., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 N'konzi, Chukwu and Nyabadza.)

A modified version of the SEIR model with the effects of vaccination and inter-state movement is proposed to simulate the spread of COVID-19 in Malaysia. A mathematical analysis of the proposed model was performed to derive the basic reproduction number. To enhance the model's forecasting capabilities, the model parameters were estimated using the Nelder-Mead simplex method by fitting the model outputs to the observed data. Our results showed a good fit between the model outputs and available data, where the model was then able to perform short-term predictions. In line with the rapid vaccination program, our model predicted that the COVID-19 cases in the country would decrease by the end of August. Furthermore, our findings indicated that relaxing travel restrictions from a highly vaccinated region to a low vaccinated region would result in an epidemic outbreak., (© 2022. Prof. Dr. Jan van der Hoeven stichting voor theoretische biologie.)

Objectives: Waves of epidemics associated with Omicron variant of Coronavirus Disease 2019 (COVID-19) in major cities in China this year have been controlled. It is of great importance to study the transmission characteristics of these cases to support further interventions. Methods: We simulate the transmission trajectory and analyze the intervention influences of waves associated with Omicron variant in major cities in China using the Suspected-Exposed-Infectious-Removed (SEIR) model. In addition, we propose a model using a function between the maximum daily infections and the duration of the epidemic, calibrated with data from Chinese cities. Results: An infection period of 5 days and basic reproduction number R 0 between 2 and 8.72 are most appropriate for most cases in China. Control measures show a significant impact on reducing R 0 , and the earlier control measures are implemented, the shorter the epidemic will last. Our proposed model performs well in predicting the duration of the epidemic with an average error of 2.49 days. Conclusion: Our results show great potential in epidemic model simulation and predicting the end date of the Omicron epidemic effectively and efficiently., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Zheng and Wang.)

Human life is deeply influenced by infectious diseases. A vaccine, when available, is one of the most effective ways of controlling the spread of an epidemic. However, vaccine shortage and uncertain vaccine effectiveness in the early stage of vaccine production make vaccine allocation a critical issue. To tackle this issue, we propose a multi-objective framework to optimize the vaccine allocation strategy among different age groups during an epidemic under vaccine shortage in this study. Minimizing total disease onsets and total severe cases are the two objectives of this vaccine allocation optimization problem, and the multistage feature of vaccine allocation are considered in the framework. An improved Strength Pareto Evolutionary Algorithm (SPEA2) is used to solve the optimization problem. To evaluate the two objectives under different strategies, a deterministic age-stratified extended SEIR model is developed. In the proposed framework, different combinations of vaccine effectiveness and vaccine production capacity are investigated, and it is identified that for COVID-19 the optimal strategy is highly related to vaccine-related parameters. When the vaccine effectiveness is low, allocating most of vaccines to 0-19 age group or 65+ age group is a better choice under a low production capacity, while allocating most of vaccines to 20-49 age group or 50-64 age group is a better choice under a relatively high production capacity. When the vaccine effectiveness is high, a better strategy is to allocate vaccines to 65+ age group under a low production capacity, while to allocate vaccines to 20-49 age group under a relatively high production capacity., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Wu, Wang and Xu.)

We build a model that consider the falling antibody levels and vaccination to assess the impact of falling antibody levels and vaccination on the spread of the COVID-19 outbreak, and simulate the influence of vaccination rates and failure rates on the number of daily new cases in England. We get that the lower the vaccine failure rate, the fewer new cases. Over time, vaccines with low failure rates are more effective in reducing the number of cases than vaccines with high failure rates and the higher the vaccine efficiency and vaccination rate, the lower the epidemic peak. The peak arrival time is related to a boundary value. When the failure rate is less than this boundary value, the peak time will advance with the decrease of failure rate; when the failure rate is greater than this boundary value, the peak time is delayed with the decrease of failure rate. On the basis of improving the effectiveness of vaccines, increasing the vaccination rate has practical significance for controlling the spread of the epidemic.

Objective: Since December 2019, a new coronavirus viral was initially detected in Wuhan, China. Population migration increases the risk of epidemic transmission. Here, the objective of study is to estimate the output risk quantitatively and evaluate the effectiveness of travel restrictions of Wuhan city., Methods: We proposed a modified susceptible-exposed-infectious-recovered (SEIR) dynamics model to predict the number of coronavirus disease 2019 (COVID-19) symptomatic and asymptomatic infections in Wuhan. And, subsequently, we estimated the export risk of COVID-19 epidemic from Wuhan to other provinces in China. Finally, we estimated the effectiveness of travel restrictions of Wuhan city quantitatively by the export risk on the assumption that the measure was postponed., Results: The export risks of COVID-19 varied from Wuhan to other provinces of China. The peak of export risk was January 21-23, 2020. With the travel restrictions of Wuhan delayed by 3, 5, and 7 d, the export risk indexes will increase by 38.50%, 55.89%, and 65.63%, respectively., Conclusions: The results indicate that the travel restrictions of Wuhan reduced the export risk and delayed the overall epidemic progression of the COVID-19 epidemic in China. The travel restrictions of Wuhan city may provide a reference for the control of the COVID-19 epidemic all over the world.

We study a susceptible-exposed-infected-recovered (SEIR) model considered by Aguas et al. (In: Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics, 2021), Gomes et al. (In: J Theor Biol. 540:111063, 2022) where individuals are assumed to differ in their susceptibility or exposure to infection. Under this heterogeneity assumption, epidemic growth is effectively suppressed when the percentage of the population having acquired immunity surpasses a critical level - the herd immunity threshold - that is lower than in homogeneous populations. We derive explicit formulas to calculate herd immunity thresholds and stable configurations, especially when susceptibility or exposure are gamma distributed, and explore extensions of the model., (© 2022. The Author(s).)

Objective: To evaluate epidemiological characteristics of the COVID-19 outbreak that resurged in Yangzhou and to simulate the impact of different control measures at different regional scales., Methods: We collected personal information from 570 laboratory-confirmed cases in Yangzhou from 28 July to 26 August 2021, and built a modified susceptible-exposed-infected-removed (SEIR) model and an agent-based model., Results: The SEIR model showed that for passengers from medium-high risk areas, pre-travel nucleic acid testing within 3 days could limit the total number of infected people in Yangzhou to 50; among elderly persons, a 60% increase in vaccination rates could reduce the estimated infections by 253. The agent-based model showed that when the population density of the chess and card room dropped by 40%, the number of infected people would decrease by 54 within 7 days. A ventilation increase in the chess and card room from 25 to 50% could reduce the total number of infections by 33 within 7 days; increasing the ventilation from 25 to 75% could reduce the total number of infections by 63 within 7 days., Conclusions: The SEIR model and agent-based model were used to simulate the impact of different control measures at different regional scales successfully. It is possible to provide references for epidemic prevention and control work., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Shen, Li, Wei, Zhao, Ye, Ma, Xiao, Jia, Zhou, Cui, Gong and Cao.)

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.

In this work we use simple mathematical models to study the impact of vaccination against COVID-19 in Portugal. First, we fit a SEIR type model without vaccination to the Portuguese data on confirmed cases of COVID-19 by the date of symptom onset, from the beginning of the epidemic until the 23rd January of 2021, to estimate changes in the transmission intensity. Then, by including vaccination in the model we develop different scenarios for the fade-out of the non pharmacological intervention (NPIs) as vaccine coverage increases in the population according to Portuguese vaccination goals. We include a feedback function to mimic the implementation and relaxation of NPIs, according to some disease incidence thresholds defined by the Portuguese health authorities.

We present a classic SEIR model taking into account the daily movements of individuals in different places. The model also takes into account partial confinement of individuals. This model is coupled with a model of protection against the epidemic by the use of masks. We are studying the effects of combined confinement and protection measures on the dynamics of the epidemic. We consider a constant proportion of asymptomatic people. We assume that symptomatic infected people may change their urban travel behavior due to the disease which causes them to travel less to places where they used to move and to stay at home more often. We present a sensitivity study with respect to the parameters. We show that the combination of the use of masks with almost complete release of confinement makes it possible to avoid the occurrence of a secondary peak of the epidemic. The model predicts that a total release of confinement can be successful for an epidemic of [Formula: see text] if on average a proportion of [Formula: see text] of the population wears masks of [Formula: see text] efficacy. However, if [Formula: see text] of the population remains confined, the same goal can be achieved with a proportion of [Formula: see text] of the population wearing masks with efficacy of the order of [Formula: see text].

In this paper, deterministic and stochastic models are proposed to study the transmission dynamics of the Coronavirus Disease 2019 (COVID-19) in Wuhan, China. The deterministic model is formulated by a system of ordinary differential equations (ODEs) that is built upon the classical SEIR framework. The stochastic model is formulated by a continuous-time Markov chain (CTMC) that is derived based on the ODE model with constant parameters. The nonlinear CTMC model is approximated by a multitype branching process to obtain an analytical estimate for the probability of a disease outbreak. The local and global dynamics of the disease are analyzed by using the deterministic model with constant parameters, and the result indicates that the basic reproduction number $ \mathcal{R}_0 $ serves as a sharp disease threshold: the disease dies out if $ \mathcal{R}_0\le 1 $ and persists if $ \mathcal{R}_0 > 1 $. In contrast to the deterministic dynamics, the stochastic dynamics indicate that the disease may not persist when $ \mathcal{R}_0 > 1 $. Parameter estimation and validation are performed to fit our ODE model to the public reported data. Our result indicates that both the exposed and infected classes play an important role in shaping the epidemic dynamics of COVID-19 in Wuhan, China. In addition, numerical simulations indicate that a second wave of the ongoing pandemic is likely to occur if the prevention and control strategies are not implemented properly.

The outbreak of the coronavirus disease 2019 was first reported in Wuhan in December 2019 and gradually spread to other areas in China. After implementation of prevention and control measures, the estimation of the epidemic trend is needed. A phase- and region-adjusted SEIR model was applied for modeling and predicting the number of cases in Wuhan, Hubei Province and regions outside Hubei Province in China. The estimated number of infections could reach its peak in late February 2020 in Wuhan and Hubei Province, which is 55 303-84 520 and 83 944-129 312, respectively, while the epidemic peaks in regions outside Hubei Province in China could appear on February 13, 2020 with the estimated 13 035-19 108 cases. According to the estimation, the outbreak would abate in March and April all over China. Current estimation provided evidence for planned work resumption under stringent prevention and control in China to further support the fight against the epidemic. Nevertheless, there is still possibility of the second outbreak brought by the work resumption and population migration, especially from Hubei Province and high intensity cities outside Hubei Province. Strict prevention and control measures still need to be considered in the regions with high intensity of epidemic and densely-populated cities.

A delayed SEIR epidemic model with saturated incidence and saturated treatment function is considered in this paper. Sufficient conditions for the existence of local Hopf bifurcation are established by regarding the possible combination of the two delays as the bifurcation parameter. General formula for the direction, period and stability of the bifurcated periodic solutions are derived by using the normal form method and the centre manifold theory. Finally, some numerical simulations are given to illustrate the obtained results.

The 2014 Ebola outbreak in Sierra Leone is analyzed using a susceptible-exposed-infectious-removed (SEIR) epidemic compartmental model. The discrete time-stochastic model for the epidemic evolution is coupled to a set of ordinary differential equations describing the dynamics of the expected proportions of subjects in each epidemic state. The unknown parameters are estimated in a Bayesian framework by combining data on the number of new (laboratory confirmed) Ebola cases reported by the Ministry of Health and prior distributions for the transition rates elicited using information collected by the WHO during the follow-up of specific Ebola cases. The time-varying disease transmission rate is modeled in a flexible way using penalized B-splines. Our framework represents a valuable stochastic tool for the study of an epidemic dynamic even when only irregularly observed and possibly aggregated data are available. Simulations and the analysis of the 2014 Sierra Leone Ebola data highlight the merits of the proposed methodology. In particular, the flexible modeling of the disease transmission rate makes the estimation of the effective reproduction number robust to the misspecification of the initial epidemic states and to underreporting of the infectious cases., (© The Author 2016. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

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]

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 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]

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]

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]

In this paper, we investigate the qualitative behavior of a class of fractional SEIR epidemic models with a more general incidence rate function and time delay to incorporate latent infected individuals. We first prove positivity and boundedness of solutions of the system. The basic reproduction number R0$$ {\mathcal{R}}_0 $$ of the model is computed using the method of next generation matrix, and we prove that if R0<1$$ {\mathcal{R}}_0<1 $$, the healthy equilibrium is locally asymptotically stable, and when R0>1$$ {\mathcal{R}}_0>1 $$, the system admits a unique endemic equilibrium which is locally asymptotically stable. Moreover, using a suitable Lyapunov function and some results about the theory of stability of differential equations of delayed fractional‐order type, we give a complete study of global stability for both healthy and endemic steady states. The model is used to describe the COVID‐19 outbreak in Algeria at its beginning in February 2020. A numerical scheme, based on Adams–Bashforth–Moulton method, is used to run the numerical simulations and shows that the number of new infected individuals will peak around late July 2020. Further, numerical simulations show that around 90% of the population in Algeria will be infected. Compared with the WHO data, our results are much more close to real data. Our model with fractional derivative and delay can then better fit the data of Algeria at the beginning of infection and before the lock and isolation measures. The model we propose is a generalization of several SEIR other models with fractional derivative and delay in literature. [ABSTRACT FROM AUTHOR]

Background: From March to June 2022, an Omicron BA.2 epidemic occurred in Shanghai. We aimed to better understand the transmission dynamics and identify age-specific transmission characteristics for the epidemic. Methods: Data on COVID-19 cases were collected from the Shanghai Municipal Health Commission during the period from 20th February to 1st June. The effective reproductive number (Rt) and transmission distance between cases were calculated. An age-structured SEIR model with social contact patterns was developed to reconstruct the transmission dynamics and evaluate age-specific transmission characteristics. Least square method was used to calibrate the model. Basic reproduction number (R0) was estimated with next generation matrix. Results: R0 of Omicron variant was 7.9 (95% CI: 7.4 to 8.4). With strict interventions, Rt had dropped quickly from 3.6 (95% CI: 2.7 to 4.7) on 4th March to below 1 on 18th April. The mean transmission distance of the Omicron epidemic in Shanghai was 13.4 km (95% CI: 11.1 to 15.8 km), which was threefold longer compared with that of epidemic caused by the wild-type virus in Wuhan, China. The model estimated that there would have been a total 870,845 (95% CI: 815,400 to 926,289) cases for the epidemic from 20th February to 15th June, and 27.7% (95% CI: 24.4% to 30.9%) cases would have been unascertained. People aged 50–59 years had the highest transmission risk 0.216 (95% CI: 0.210 to 0.222), and the highest secondary attack rate (47.62%, 95% CI: 38.71% to 56.53%). Conclusions: The Omicron variant spread more quickly and widely than other variants and resulted in about one third cases unascertained for the recent outbreak in Shanghai. Prioritizing isolation and screening of people aged 40–59 might suppress the epidemic more effectively. Routine surveillance among people aged 40–59 years could also provide insight into the stage of the epidemic and the timely detection of new variants. Trial registration: We did not involve clinical trial. [ABSTRACT FROM AUTHOR]

We study the effect of population mobility on the transmission dynamics of infectious diseases by considering a susceptible-exposed-infectious-recovered (SEIR) epidemic model with graph Laplacian diffusion, that is, on a weighted network. First, we establish the existence and uniqueness of solutions to the SEIR model defined on a weighed graph. Then by constructing Liapunov functions, we show that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity and the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than unity. Finally, we apply our generalized weighed graph to Watts–Strogatz network and carry out numerical simulations, which demonstrate that degrees of nodes determine peak numbers of the infectious population as well as the time to reach these peaks. It also indicates that the network has an impact on the transient dynamical behaviour of the epidemic transmission. [ABSTRACT FROM AUTHOR]

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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]

In recent years, the new type of coronary pneumonia (COVID-19) has become a highly contagious disease worldwide, posing a serious threat to the public health. This paper is based on the SEIR model of the new coronavirus pneumonia, considering the impact of cold chain input and re-positive on the spread of the virus in the COVID-19. In the process of model design, the food cold chain and re-positive are used as parameters, and its stability is analyzed and simulated. The experimental results show that taking into account the cold chain input and re-positive can effectively simulate the spread of the epidemic. The research results have important research value and practical significance for the prevention and control of the COVID-19 and the prediction of important time nodes. [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]

It is urgent to identify the development of the Corona Virus Disease 2019 (COVID‐19) in countries around the world. Therefore, visualization is particularly important for monitoring the COVID‐19. In this paper, we visually analyze the real‐time data of COVID‐19, to monitor the trend of COVID‐19 in the form of charts. At present, the COVID‐19 is still spreading. However, in the existing works, the visualization of COVID‐19 data has not established a certain connection between the forecast of the epidemic data and the forecast of the epidemic. To better predict the development trend of the COVID‐19, we establish a logistic growth model to predict the development of the epidemic by using the same data source in the visualization. However, the logistic growth model only has a single feature. To predict the epidemic situation in an all‐round way, we also predict the development trend of the COVID‐19 based on the Susceptible Exposed Infected Removed epidemic model with multiple features. We fit the data predicted by the model to the real COVID‐19 epidemic data. The simulation results show that the predicted epidemic development trend is consistent with the actual epidemic development trend, and our model performs well in predicting the trend of COVID‐19. [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]

Introduction: In Hungary, where MMR vaccine coverage is 99%, in 2017, a minor measles epidemic started from imported cases due to two major factors – latent susceptible cohorts among the domestic population and the vicinity of measles-endemic countries. Suspended immunization activities due to the COVID-19 surge are an ominous precursor to a measles resurgence. This epidemiological demonstration is aimed at promoting a better public understanding of epidemiological data. Materials and Methods: Our previous MMR sero-epidemiological measurements (N of total measles cases = 3919, N of mumps cases = 2132, and N of rubella cases = 2132) were analyzed using open-source epidemiological data (ANTSZ) of a small-scale measles epidemic outbreak (2017, Hungary). A simplified SEIR model was applied in the analysis. Results: In case of measles, due to a cluster-specific inadequacy of IgG levels, the cumulative seropositivity ratios (measles = 89.97%) failed to reach the herd immunity threshold (HIT Measles = 92–95%). Despite the fact that 90% of overall vaccination coverage is just slightly below the HIT, unprotected individuals may pose an elevated epidemiological risk. According to the SEIR model, ≥74% of susceptible individuals are expected to get infected. Estimations based on the input data of a local epidemic may suggest an even lower effective coverage rate (80%) in certain clusters of the population. Conclusion: Serological survey-based, historical and model-computed results are in agreement. A practical demonstration of epidemiological events of the past and present may promote a higher awareness of infectious diseases. Because of the high R0 value of measles, continuous large-scale monitoring of humoral immunity levels is important.

Inspired by infectious disease dynamics and modern psychology, this paper aims at constructing a multi-dimensional function to get the model of information dissemination on social networks under epidemic-related panic base on the characteristics of individual differences and global characteristics, like emotional cumulative effect, herd effect, time-sensitive decline effect, cognitive level, intimacy, personal influence, etc. The results show that the psychological effect has a significant effect on the increase of the spread of panic news; When netizens are in an emotional atmosphere, their emotional self-regulation ability is limited; when the infection rate is relatively low, the characteristics of individual differences play a leading role in affecting the spreading process. When the infection rate is high enough, the herd effect and emotional cumulative effect play a major role in promoting information dissemination; In a society with a higher rate of emotional contact, it is easier to form a kind of collective wisdom, which can help the collective quickly identify rumors. Moreover, in this kind of society, the role of opinion leaders is limited, and timely refutation of rumors can significantly reduce the spread of panic news. [ABSTRACT FROM AUTHOR]

In order to propose a more realistic epidemic dynamics model and effective medical resource allocation strategy, this paper constructs an improved SEIR model combined with a dynamical medical resource allocation model and individual behavior sharing medical resources. Simultaneously, a genetic algorithm to solve the medical resource allocation model is proposed to obtain the optimum resource allocation strategy. In this SEIR model, there is an important critical value of the stored medical resources, when the number of stored medical resources is more than the critical value, the inhibition of epidemic can be continuously enhanced until it reaches a minimum threshold, and then stabilizes near a minimum value, but when the resource surplus is below the critical value, the inhibitory effect on epidemic will weaken. The results demonstrate that the number of patients in the proposed method decreased more than 40% compared with the conventional control experiment. Moreover, the algorithm can automatically make decisions according to individual behavior in sharing preferences and the epidemic development trend. [ABSTRACT FROM AUTHOR]

In this study, we developed a SEIR model, including social interactions and individual human mobility in everyday activities. For this purpose, daily mobility of people was considered by using the molecular dynamic method and the virus spreading was modeled employing the ordinary SEIR scheme. Utilizing this model, the variation of population size, density, and health strategy as well as the effect of busy places such as malls, were considered. The results show that our flexible model is able to consider the effects of different parameters such as distance between peoples, local population density and health strategy in the outbreak. [ABSTRACT FROM AUTHOR]

In this work, we present a particle-based SEIR epidemic simulator as a tool to assess the impact of different vaccination strategies on viral propagation and to model sterilizing and effective immunization outcomes. The simulator includes modules to support contact tracing of the interactions amongst individuals and epidemiological testing of the general population. The particles are distinguished by age to represent more accurately the infection and mortality rates. The tool can be calibrated by region of interest and for different vaccination strategies to enable locality-sensitive virus mitigation policy measures and resource allocation. Moreover, the vaccination policy can be simulated based on the prioritization of certain age groups or randomly vaccinating individuals across all age groups. The results based on the experience of the province of Lecco, Italy, indicate that the simulator can evaluate vaccination strategies in a way that incorporates local circumstances of viral propagation and demographic susceptibilities. Further, the simulator accounts for modeling the distinction between sterilizing immunization, where immunized people are no longer contagious, and effective immunization, where the individuals can transmit the virus even after getting immunized. The parametric simulation results showed that the sterilizing-age-based vaccination scenario results in the least number of deaths. Furthermore, it revealed that older people should be vaccinated first to decrease the overall mortality rate. Also, the results showed that as the vaccination rate increases, the mortality rate between the scenarios shrinks. [ABSTRACT FROM AUTHOR]

An epidemic disease caused by a new coronavirus has spread all over the world with a high rate of transmission. The main purpose of this article is to define an epidemic model for the Covid- 19 pandemic, to apply it to Turkey's data and to interpret it. Accordingly, a SEIR model was created to calculate the infected population and the number of deaths caused by this epidemic, and the stability of the model was examined. Since all the parameters affecting the stability cannot be calculated clearly, it cannot be expected to reach a realistic result. For this reason, a model was created with accessible parameters. Later, the diseased and non diseased equilibrium points of the model were discussed. The Hurwitz theorem is used to find the local stability of the model, while the Lyaponov function theory is used to investigate its global stability. Finally, some numerical results are given with the help of MATLAB program. [ABSTRACT FROM AUTHOR]

We introduce a diffusive SEIR model with nonlocal delayed transmission between the infected subpopulation and the susceptible subpopulation with a general nonlinear incidence. We show that our results on existence and nonexistence of traveling wave solutions are determined by the basic reproduction number R 0 = ∂ I F (S 0 , 0) / γ of the corresponding ordinary differential equations and the minimal wave speed c ∗ . The main difficulties lie in the fact that the semiflow generated here does not admit the order-preserving property. In the present paper, we overcome these difficulties to obtain the threshold dynamics. In view of the numerical simulations, we also obtain that the minimal wave speed is explicitly determined by the time delay and nonlocality in disease transmission and by the spatial movement pattern of the exposed and infected individuals. [ABSTRACT FROM AUTHOR]

Aim: to present a mathematical model of the development of COVID-19 in Moscow along with the analysis of some scenarios of epidemic control and possible epidemic consequences.Materials and Methods. The modeling of the epidemics was based on the extended SEIR model proposed lately in the group of Prof. R. Neher and realized as a freely available software program. The authors based the choice of the parameters of modeling on published data on the epidemiological properties of the novel coronavirus SARS-CoV-2 and open access data on the registered cases of COVID-19 in Moscow for 8-27 March 2020.Results. Five potential scenarios of the development of COVID-19 epidemics are studied. The scenarios are differed by the levels of the control measures: Null Scenario corresponded to the lack of protective measures, Scenario A – mild measures of the epidemic control (closing of schools and universities, recommendations for senior citizens to stay inside), Scenario B – medium level of control (closing of all public places, recommendation for the citizens to stay inside), Scenarios C and D – complete lockdown (from the beginning of May 2020 within Scenario C and from the beginning of April 2020 within Scenario D). It was shown that within the Null Scenario, the lethality from the novel coronavirus in Moscow will exceed 100 thousand people, and the number of critically ill patients on the peak of the epidemics will exceed the capacities of the system of healthcare. Scenarios A and B did not provide for a radical decrease in the fatality rate, and the number of critically ill patients at the peak of epidemics will still exceed the capacities of the system of healthcare. Besides, within Scenario B, the epidemics will last for more than a year. Scenarios C and D will allow for the control of epidemics and a significant decrease in the rate of letha lity (by 30 and 400 times, respectively). At the same time, these two scenarios prevent the population from developing herd immunity, which would result in the population susceptibility to repeated epidemics outbreaks. Conclusion. The scenarios intended for the slow development of herd immunity in the conditions of epidemic control would not bring sufficient results: the lethality would remain unacceptably high, the capacities of the system of healthcare would be overloaded, and the time of limiting measures would be unacceptably long. Such measures as complete lockdown would stop the present epidemics. The earlier they are introduced, the more efficient will be the results. To prevent further repeated outbreaks of the epidemics, it is necessary to establish a system of available, quick, and efficient testing in combination with point isolation of the infected patients and their contacts.

Background: Lumpy Skin Disease (LSD) is an infectious disease induced by the Capripoxvirus, causing epidemics in Turkey and several countries worldwide and inducing significant economic losses. Although this disease occurs in Turkish cattle every year, it is a notifiable disease. In this study, LSD in Turkey was modelled using the Susceptible, Exposed, Infectious, and Recovered (SEIR) epidemiological model, and production losses were estimated with predictions of the course of the disease. The animal population was categorized into four groups: Susceptible, Exposed, Infectious, and Recovered, and model parameters were obtained. The SEIR model was formulated with an outbreak calculator simulator applied for demonstration purposes. Results: Production losses caused by the LSD epidemic and the SEIR model's predictions on the disease's course were evaluated. Although 1282 cases were identified in Turkey during the study period, the prevalence of LSD was calculated as 4.51%, and the mortality rate was 1.09%. The relationship between the disease duration and incubation period was emphasized in the simulated SEIR model to understand the dynamics of LSD. Early detection of the disease during the incubation period significantly affected the peak time of the disease. According to the model, if the disease was detected during the incubation period, the sick animal's time could transmit the disease (Tinf) was calculated as 2.66 days. Production loss from LSD infection was estimated at US $ 886.34 for dairy cattle and the US $ 1,066.61 for beef cattle per animal. Conclusion: Detection of LSD infection during the incubation period changes the course of the disease and may reduce the resulting economic loss. [ABSTRACT FROM AUTHOR]

The World Health Organization (WHO) reported the covid-19 epidemic a global health emergency on January 30 and confirmed its transformation into a pandemic on March 11. China has been the hardest hit since the virus's outbreak, which may date back to late November. Saudi Arabia realized the danger of the Coronavirus in March 2020, took the initiative to take a set of pre-emptive decisions that preceded many countries of the world, and worked to harness all capabilities to confront the outbreak of the epidemic. Several researchers are currently using various mathematical and machine learning-based prediction models to estimate this pandemic's future trend. In this work, the SEIR model was applied to predict the epidemic situation in Saudi Arabia and evaluate the effectiveness of some epidemic control measures, and finally, providing some advice on preventive measures. [ABSTRACT FROM AUTHOR]

The recent worldwide epidemic of COVID-19 disease, for which there are no medications to cure it and the vaccination is still at an early stage, led to the adoption of public health measures by governments and populations in most of the affected countries to avoid the contagion and its spread. These measures are known as nonpharmaceutical interventions (NPIs), and their implementation clearly produces social unrest as well as greatly affects the economy. Frequently, NPIs are implemented with an intensity quantified in an ad hoc manner. Control theory offers a worthwhile tool for determining the optimal intensity of the NPIs in order to avoid the collapse of the healthcare system while keeping them as low as possible, yielding concrete guidance to policymakers. A simple controller, which generates a control law that is easy to calculate and to implement is proposed. This controller is robust to large parametric uncertainties in the model used and to some level of noncompliance with the NPIs. [ABSTRACT FROM AUTHOR]

This investigation is based on the application of Susceptible-Exposed-Infectious-Recovered (SEIR) model to simulate the number of diseases spread in a region, along with a historical approach of epidemic outbreak cases. Dengue fever pandemic outbreak is used to apply the proposed model for drug demand uncertainty in a pandemic. The aim of this research is to predict the number of drugs needed in a hospital for the treatment of dengue fever cases during the epidemic outbreak. The SEIR model is used to simulate the number of dengue fever patients in a hospital atGresik district, East Java in Indonesia. This analysis was carried out in a comparative way with the other forecasting methods. The result showed that the simulation’s result is different from other forecasting methods, depending on the context in which it is used, such as the disease type and the area of epidemic under study. In the future research, the proposed model is could applied in Malaria, COVID-19 pandemic, and another in order to ensuring the applicability of proposed model. This investigation is based on the application of Susceptible-Exposed-Infectious-Recovered (SEIR) model to simulate the number of diseases spread in a region, along with a historical approach of epidemic outbreak cases. Dengue fever pandemic outbreak is used to apply the proposed model for drug demand uncertainty in a pandemic. The aim of this research is to predict the number of drugs needed in a hospital for the treatment of dengue fever cases during the epidemic outbreak. The SEIR model is used to simulate the number of dengue fever patients in a hospital atGresik district, East Java in Indonesia. This analysis was carried out in a comparative way with the other forecasting methods. The result showed that the simulation’s result is different from other forecasting methods, depending on the context in which it is used, such as the disease type and the area of epidemic under study. In the future research, the proposed model is could applied in Malaria, COVID-19 pandemic, and another in order to ensuring the applicability of proposed model. [ABSTRACT FROM AUTHOR]

The COVID-19 outbreak is of great concern due to the high rates of infection and the large number of deaths worldwide. In this paper, we considered a Bayesian inference and failure mode and effects analysis of the modified susceptible-exposed-infectious-removed model for the transmission dynamics of COVID-19 with an exponentially distributed infectious period. We estimated the effective reproduction number based on laboratory-confirmed cases and death data using Bayesian inference and analyse the impact of the community spread of COVID-19 across the United Kingdom. We used the failure mode and effects analysis tool to evaluate the effectiveness of the action measures taken to manage the COVID-19 pandemic. We focused on COVID-19 infections and therefore the failure mode is taken as positive cases. The model is applied to COVID-19 data showing the effectiveness of interventions adopted to control the epidemic by reducing the reproduction number of COVID-19. Results have shown that the combination of Bayesian inference, compartmental modelling and failure mode and effects analysis is effective in modelling and studying the risks of COVID-19 transmissions, leading to the quantitative evaluation of the action measures and the identification of the lessons learned from the governmental measures and actions taken in response to COVID-19 in the United Kingdom. Analytical and numerical methods are used to highlight the practical implications of our findings. The proposed methodology will find applications in current and future COVID-19 like pandemics and wide quality engineering. [ABSTRACT FROM AUTHOR]

The COVID-19 outbreak is of great concern due to the high rates of infection and the large number of deaths worldwide. In this paper, we considered a Bayesian inference and failure mode and effects analysis of the modified susceptible-exposed-infectious-removed model for the transmission dynamics of COVID-19 with an exponentially distributed infectious period. We estimated the effective reproduction number based on laboratory-confirmed cases and death data using Bayesian inference and analyse the impact of the community spread of COVID-19 across the United Kingdom. We used the failure mode and effects analysis tool to evaluate the effectiveness of the action measures taken to manage the COVID-19 pandemic. We focused on COVID-19 infections and therefore the failure mode is taken as positive cases. The model is applied to COVID-19 data showing the effectiveness of interventions adopted to control the epidemic by reducing the reproduction number of COVID-19. Results have shown that the combination of Bayesian inference, compartmental modelling and failure mode and effects analysis is effective in modelling and studying the risks of COVID-19 transmissions, leading to the quantitative evaluation of the action measures and the identification of the lessons learned from the governmental measures and actions taken in response to COVID-19 in the United Kingdom. Analytical and numerical methods are used to highlight the practical implications of our findings. The proposed methodology will find applications in current and future COVID-19 like pandemics and wide quality engineering. [ABSTRACT FROM AUTHOR]