Integrating socio-psychological factors in the SEIR model optimized by a genetic algorithm for COVID-19 trend analysis.

The global spread of COVID-19 has profoundly affected health and economies, highlighting the need for precise epidemic trend predictions for effective interventions. In this study, we used infectious disease models to simulate and predict the trajectory of COVID-19. An SEIR (susceptible, exposed, infected, removed) model was established using Wuhan data to reflect the pandemic. We then trained a genetic algorithm-based SEIR (GA-SEIR) model using data from a specific U.S. region and focused on individual susceptibility and infection dynamics. By integrating socio-psychological factors, we achieved a significant enhancement to the GA-SEIR model, leading to the development of an optimized version. This refined GA-SEIR model significantly improved our ability to simulate the spread and control of the epidemic and to effectively track trends. Remarkably, it successfully predicted the resurgence of COVID-19 in mainland China in April 2023, demonstrating its robustness and reliability. The refined GA-SEIR model provides crucial insights for public health authorities, enabling them to design and implement proactive strategies for outbreak containment and mitigation. Its substantial contributions to epidemic modelling and public health planning are invaluable, particularly in managing and controlling respiratory infectious diseases such as COVID-19.

A novel collocation method with a coronavirus optimization algorithm for the optimal control of COVID-19: A case study of Wuhan, China.

In this study, we develop a numerical optimization approach to address the challenge of optimal control in the spread of COVID-19. We evaluate the impact of various control strategies aimed at reducing the number of exposed and infectious individuals. Our novel approach employs Legendre wavelets, their derivative operational matrix, and a collocation method to transform the COVID-19 transmission optimal control model into a nonlinear programming (NLP) problem. To solve this problem, we employ a coronavirus optimization algorithm (COVIDOA) to determine the optimal control, state variables, and objective value. We investigate three control plans for this highly contagious disease, focusing on individual protection, rapid detection and treatment, detection with delay in treatment, and environmental viral dispersion as time-based control functions. These strategies are applied within an SEIR-type control model specific to COVID-19 in China, designed to mitigate disease spread. Lastly, we analyze the effects of various parameters within the COVID-19 spread model. Our numerical results highlight the significant impact of strategies that minimize the number of exposed and infectious individuals, particularly those related to rapid detection, detection delay, and environmental viral dispersion, in controlling and preventing the transmission of the COVID-19 virus.

COVID-19 transmission between the community and meat processing plants in Ireland: A retrospective modelling study.

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 < 0·0001, RMSD = 5·6. In Ireland, outbreaks in MPPs were strongly correlated with high levels of infection in the surrounding county, rather than being a driver of infection in the county. The modified SEIR model described here can provide an explanation of the generative process required to cause outbreaks of the size and scale that occur in MPPs.

A novel indicator in epidemic monitoring through a case study of Ebola in West Africa (2014-2016).

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, ß(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).

Utilizing direct and indirect information to improve the COVID-19 vaccination booster scheduling.

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 study of the attenuation stage of a global infectious disease.

Introduction: Differences in control measures and response speeds between regions may be responsible for the differences in the number of infections of global infectious diseases. Therefore, this article aims to examine the decay stage of global infectious diseases. We demonstrate our method by considering the first wave of the COVID-19 epidemic in 2020. Methods: We introduce the concept of the attenuation rate into the varying coefficient SEIR model to measure the effect of different cities on epidemic control, and make inferences through the integrated adjusted Kalman filter algorithm. Results: We applied the varying coefficient SEIR model to 136 cities in China where the total number of confirmed cases exceeded 20 after the implementation of control measures and analyzed the relationship between the estimated attenuation rate and local factors. Subsequent analysis and inference results show that the attenuation rate is significantly related to the local annual GDP and the longitude and latitude of a city or a region. We also apply the varying coefficient SEIR model to other regions outside China. We find that the fitting curve of the average daily number of new confirmed cases simulated by the variable coefficient SEIR model is consistent with the real data. Discussion: The results show that the cities with better economic development are able to control the epidemic more effectively to a certain extent. On the other hand, geographical location also affected the effectiveness of regional epidemic control. In addition, through the results of attenuation rate analysis, we conclude that China and South Korea have achieved good results in controlling the epidemic in 2020.

Origins of the problematic E in SEIR epidemic models.

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.

On the date of the epidemic peak.

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.

Modeling the impact of distancing measures on infectious disease spread: a case study of COVID-19 in the Moroccan population.

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.

A nonstandard finite difference scheme for a time-fractional model of Zika virus transmission.

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.

Estimating SARS-CoV-2 transmission parameters between coinciding outbreaks in a university population and the surrounding community.

Prior studies suggest that population heterogeneity in SARS-CoV-2 (COVID-19) transmission plays an important role in epidemic dynamics. During the fall of 2020, many US universities and the surrounding communities experienced an increase in reported incidence of SARS-CoV-2 infections, with a high disease burden among students. We explore the transmission dynamics of an outbreak of SARS-CoV-2 among university students, how it impacted the non-student population via cross-transmission, and how it could influence pandemic planning and response. Using surveillance data of reported SARS-CoV-2 cases, we developed a two-population SEIR model to estimate transmission parameters and evaluate how these subpopulations interacted during the 2020 Fall semester. We estimated the transmission rate among the university students (ßU) and community residents (ßC), as well as the rate of cross-transmission between the two subpopulations (ßM) using particle Markov Chain Monte Carlo (pMCMC) simulation-based methods. We found that both populations were more likely to interact with others in their population and that cross-transmission was minimal. The cross-transmission estimate (ßM) was considerably smaller [0.04 × 10-5 (95% CI: 0.00 × 10-5, 0.15 × 10-5)] compared to the community estimate (ßC) at 2.09 × 10-5 (95% CI: 1.12 × 10-5, 2.90 × 10-5) and university estimate (ßU) at 27.92 × 10-5 (95% CI: 19.97 × 10-5, 39.15 × 10-5). The higher within population transmission rates among the university and the community (698 and 52 times higher, respectively) when compared to the cross-transmission rate, suggests that these two populations did not transmit between each other heavily, despite their geographic overlap. During the first wave of the pandemic, two distinct epidemics occurred among two subpopulations within a relatively small US county population where university students accounted for roughly 41% of the total population. Transmission parameter estimates varied substantially with minimal or no cross-transmission between the subpopulations. Assumptions that county-level and other small populations are well-mixed during a respiratory viral pandemic should be reconsidered. More granular models reflecting overlapping subpopulations may assist with better-targeted interventions for local public health and healthcare facilities.

Dynamically adjustable SVEIR(MH) model of multiwave epidemics: Estimating the effects of public health measures against COVID-19.

The COVID-19 pandemic was characterized by multiple subsequent, overlapping outbreaks, as well as extremely rapid changes in viral genomes. The information about local epidemics spread and the epidemic control measures was shared on a daily basis (number of cases and deaths) via centralized repositories. The vaccines were developed within the first year of the pandemic. New modes of monitoring and sharing of epidemic data were implemented using Internet resources. We modified the basic SEIR compartmental model to include public health measures, multiwave scenarios, and the variation of viral infectivity and transmissibility reflected by the basic reproduction number R0 of emerging viral variants. SVEIR(MH) model considers the capacity of the medical system, lockdowns, vaccination, and changes in viral reproduction rate on the epidemic spread. The developed model uses daily infection reports for assessing the epidemic dynamics, and daily changes of mobility data from mobile phone networks to assess the lockdown effectiveness. This model was deployed to six European regions Baden-Württemberg (Germany), Belgium, Czechia, Lombardy (Italy), Sweden, and Switzerland for the first 2 years of the pandemic. The correlation coefficients between observed and reported infection data showed good concordance for both years of the pandemic (ρ = 0.84-0.94 for the raw data and ρ = 0.91-0.98 for smoothed 7-day averages). The results show stability across the regions and the different epidemic waves. Optimal control of epidemic waves can be achieved by dynamically adjusting epidemic control measures in real-time. SVEIR(MH) model can simulate different scenarios and inform adjustments to the public health policies to achieve the target outcomes. Because this model is highly representative of actual epidemic situations, it can be used to assess both the public health and socioeconomic effects of the public health measures within the first 7 days of the outbreak.

Evaluation of phase-adjusted interventions for COVID-19 using an improved SEIR model.

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.

Impact of human mobility on the epidemic spread during holidays.

COVID-19 has posed formidable challenges as a significant global health crisis. Its complexity stems from factors like viral contagiousness, population density, social behaviors, governmental regulations, and environmental conditions, with interpersonal interactions and large-scale activities being particularly pivotal. To unravel these complexities, we used a modified SEIR epidemiological model to simulate various outbreak scenarios during the holiday season, incorporating both inter-regional and intra-regional human mobility effects into the parameterization scheme. In addition, evaluation metrics were used to evaluate the accuracy of the model simulation by comparing the congruence between simulated results and recorded confirmed cases. The findings suggested that intra-city mobility led to an average surge of 57.35% in confirmed cases of China, while inter-city mobility contributed to an average increase of 15.18%. In the simulation for Tianjin, China, a one-week delay in human mobility attenuated the peak number of cases by 34.47% and postponed the peak time by 6 days. The simulation for the United States revealed that human mobility played a more pronounced part in the outbreak, with a notable disparity in peak cases when mobility was considered. This study highlights that while inter-regional mobility acted as a trigger for the epidemic spread, the diffusion effect of intra-regional mobility was primarily responsible for the outbreak. We have a better understanding on how human mobility and infectious disease epidemics interact, and provide empirical evidence that could contribute to disease prevention and control measures.

Measuring the worldwide spread of COVID-19 using a comprehensive modeling method.

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.

Dynamics of an SEIR model with media coverage mediated nonlinear infectious force.

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} $.

Analysis and prediction of improved SEIR transmission dynamics model: taking the second outbreak of COVID-19 in Italy as an example.

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.

An algebraic formula, deep learning and a novel SEIR-type model for the COVID-19 pandemic.

The most extensively used mathematical models in epidemiology are the susceptible-exposed-infectious-recovered (SEIR) type models with constant coefficients. For the first wave of the COVID-19 epidemic, such models predict that at large times equilibrium is reached exponentially. However, epidemiological data from Europe suggest that this approach is algebraic. Indeed, accurate long-term predictions have been obtained via a forecasting model only if it uses an algebraic as opposed to the standard exponential formula. In this work, by allowing those parameters of the SEIR model that reflect behavioural aspects (e.g. spatial distancing) to vary nonlinearly with the extent of the epidemic, we construct a model which exhibits asymptoticly algebraic behaviour. Interestingly, the emerging power law is consistent with the typical dynamics observed in various social settings. In addition, using reliable epidemiological data, we solve in a numerically robust way the inverse problem of determining all model parameters characterizing our novel model. Finally, using deep learning, we demonstrate that the algebraic forecasting model used earlier is optimal.

Natural and socio-environmental factors contribute to the transmissibility of COVID-19: evidence from an improved SEIR model.

COVID-19 has ravaged Brazil, and its spread showed spatial heterogeneity. Changes in the environment have been implicated as potential factors involved in COVID-19 transmission. However, considerable research efforts have not elucidated the risk of environmental factors on COVID-19 transmission from the perspective of infectious disease dynamics. The aim of this study is to model the influence of the environment on COVID-19 transmission and to analyze how the socio-ecological factors affecting the probability of virus transmission in 10 states dramatically shifted during the early stages of the epidemic in Brazil. First, this study used a Pearson correlation to analyze the interconnection between COVID-19 morbidity and socio-ecological factors and identified factors with significant correlations as the dominant factors affecting COVID-19 transmission. Then, the time-lag effect of dominant factors on the morbidity of COVID-19 was investigated by constructing a distributed lag nonlinear model and standard two-stage meta-analytic model, and the results were considered in the improved SEIR model. Lastly, a machine learning method was introduced to explore the nonlinear relationship between the environmental propagation probability and socio-ecological factors. By analyzing the impact of environmental factors on virus transmission, it can be found that population mobility directly caused by human activities had a greater impact on virus transmission than temperature and humidity. The heterogeneity of meteorological factors can be accounted for by the diverse climate patterns in Brazil. The improved SEIR model was adopted to explore the interconnection of COVID-19 transmission and the environment, which revealed a new strategy to probe the causal links between them.

The lockdown and vaccination distribution in Thailand's COVID-19 epidemic: A model study.

Background: Several countries used varied degrees of social isolation measures in response to the COVID-19 outbreak. In 2021, the lockdown in Thailand began on July 20 and lasted for the following six weeks. The lockdown has extremely detrimental effects on the economy and society, even though it may reduce the number of COVID-19 instances. Our goals are to assess the impact of the lockdown policy, the commencement time of lockdown, and the vaccination rate on the number of COVID-19 cases in Thailand in 2021. Methods: We modeled the dynamics of COVID-19 in Thailand throughout 2021 using the SEIR model. The Google Mobility Index, vaccine distribution rate, and lockdown were added to the model. The Google Mobility Index represents the movement of individuals during a pandemic and shows how people react to lockdown. The model also examines the effect of vaccination rate on the incidence of COVID-19. Results: The modeling approach demonstrates that a 6-week lockdown decreases the incidence number of COVID-19 by approximately 15.49-18.17%, depending on the timing of the lockdown compared to a non-lockdown scenario. An increasing vaccination rate potentially reduce the incidence number of COVID-19 by 5.12-18.35% without launching a lockdown. Conclusion: Lockdowns can be an effective method to slow down the spread of COVID-19 when the vaccination program is not fully functional. When the vaccines are easily accessible on a large scale, the lockdown may terminated.