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We applied a generalized SEIR epidemiological model to the recent SARS-CoV-2 outbreak in the world, with a focus on Italy and its Lombardy, Piedmont, and Veneto regions. We focused on the application of a stochastic approach in fitting the model parameters using a Particle Swarm Optimization (PSO) solver, to improve the reliability of predictions in the medium term (30 days). We analyzed the official data and the predicted evolution of the epidemic in the Italian regions, and we compared the results with the data and predictions of Spain and South Korea. We linked the model equations to the changes in people’s mobility, with reference to Google’s COVID-19 Community Mobility Reports. We discussed the effectiveness of policies taken by different regions and countries and how they have an impact on past and future infection scenarios.

Measles, a highly contagious viral disease, spreads primarily through respiratory droplets and can result in severe complications, often proving fatal, especially in children. In this article, we propose an algorithm to solve a system of fractional nonlinear equations that model the measles disease. We employ a fractional approach by using the Caputo operator and validate the model's by applying the Schauder and Banach fixed-point theory. The fractional derivatives, which constitute an essential part of the model can be treated precisely by using the Broyden and Haar wavelet collocation methods (HWCM). Furthermore, we evaluate the system's stability by implementing the Ulam-Hyers approach. The model takes into account multiple factors that influence virus transmission, and the HWCM offers an effective and precise solution for understanding insights into transmission dynamics through the use of fractional derivatives. We present the graphical results, which offer a comprehensive and invaluable perspective on how various parameters and fractional orders influence the behaviours of these compartments within the model. The study emphasizes the importance of modern techniques in understanding measles outbreaks, suggesting the methodology's applicability to various mathematical models. Simulations conducted by using MATLAB R2022a software demonstrate practical implementation, with the potential for extension to higher degrees with minor modifications. The simulation's findings clearly show the efficiency of the proposed approach and its application to further extend the field of mathematical modelling for infectious illnesses.

With the development of digitalization and Internet technology, algorithm-driven international Chinese online language and culture dissemination mechanisms are becoming increasingly important and a key area of cultural exchange in globalization. This study explores the international Chinese online language and culture communication mechanism under algorithm-driven. By analyzing social network data and adopting quantitative methods such as the SEIR model, the study reveals the effects of network structure, user behavior and cultural content characteristics on communication. The study results show that in the algorithm-optimized network environment, the propagation speed of information is increased by about 50%, and the propagation efficiency of its central node is increased by nearly 70%. Simulations using the SEIR model show that the dissemination coverage of Chinese culture can be increased by more than 40% in a short period with the intervention of the algorithm. In addition, the survey data shows that about 60% of the respondents consider social media the main channel to learn about Chinese culture. The study also found that content with a high degree of interactivity is more likely to be disseminated, with an average interaction rate 30% higher than that of moderate content. Algorithm-driven Chinese cultural communication has higher speed and breadth, but it also needs to pay attention to the depth and diversity of cultural content.

In the past few years, there have been many studies addressing the simulation of COVID-19’s spatial transmission model of infectious disease in time. However, very few studies have focused on the effect of the epidemic environment variables in which an individual lives on the individual’s behavioral logic leading to changes in the overall epidemic transmission trend at larger scales. In this study, we applied Fuzzy Cognitive Maps (FCMs) to modeling individual behavioral logistics, combined with Agent-Based Modeling (ABM) to perform “Susceptible—Exposed—Infectious—Removed” (SEIR) simulation of the independent individual behavior affecting the overall trend change. Our objective was to simulate the spatiotemporal spread of diseases using the Bengaluru Urban District, India as a case study. The results show that the simulation results are highly consistent with the observed reality, in terms of trends, with a Root Mean Square Error (RMSE) value of 0.39. Notably, our approach reveals a subtle link between individual motivation and infection-recovery dynamics, highlighting how individual behavior can significantly impact broader patterns of transmission. These insights have potential implications for epidemiologic strategies and public health interventions, providing data-driven insights into behavioral impacts on epidemic spread. By integrating behavioral modeling with epidemic simulation, our study underscores the importance of considering individual and collective behavior in designing sustainable public health policies and interventions.

PurposeAfter the identification of a novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) at Wuhan, China, a pandemic was widely spread worldwide. In Italy, about 240,000 people were infected because of this virus including 34,721 deaths until the end of June 2020. To control this new pandemic, epidemiologists recommend the enforcement of serious mitigation measures like country lockdown, contact tracing or testing, social distancing and self-isolation.Design/methodology/approachThis paper presents the most popular epidemic model of susceptible (S), exposed (E), infected (I) and recovered (R) collectively called SEIR to understand the virus spreading among the Italian population.FindingsDeveloped SEIR model explains the infection growth across Italy and presents epidemic rates after and before country lockdown. The results demonstrated that follow-up of strict measures such that country lockdown along with high testing is making Italy practically a pandemic-free country.Originality/valueThese models largely help to estimate and understand how an infectious agent spreads in a particular country and how individual factors can affect the dynamics. Further studies like classical SEIR modeling can improve the quality of data and implementation of this modeling could represent a novelty of epidemic models.

In December 2019, the first confirmed case of pneumonia caused by a novel coronavirus was reported. Coronavirus disease 2019 (COVID-19) is currently spreading around the world. The relationships among the pandemic and its associated travel restrictions, social distancing measures, contact tracing, mask-wearing habits and medical consultation efficiency have not yet been extensively assessed. Based on the epidemic data reported by the Health Commission of Wenzhou, we analysed the developmental characteristics of the epidemic and modified the Susceptible-Exposed-Infectious-Removed (SEIR) model in three discrete ways. (1) According to the implemented preventive measures, the epidemic was divided into three stages: initial, outbreak and controlled. (2) We added many factors, such as health protections, travel restrictions and social distancing, close-contact tracing and the time from symptom onset to hospitalisation (TSOH), to the model. (3) Exposed and infected people were subdivided into isolated and free-moving populations. For the parameter estimation of the model, the average TSOH and daily cured cases, deaths and imported cases can be obtained through individual data from epidemiological investigations. The changes in daily contacts are simulated using the intracity travel intensity (ICTI) from the Baidu Migration Big Data platform. The optimal values of the remaining parameters are calculated by the grid search method. With this model, we calculated the sensitivity of the control measures with regard to the prevention of the spread of the epidemic by simulating the number of infected people in various hypothetical situations. Simultaneously, through a simulation of a second epidemic, the challenges from the rebound of the epidemic were analysed, and prevention and control recommendations were made. The results show that the modified SEIR model can effectively simulate the spread of COVID-19 in Wenzhou. The policy of the lockdown of Wuhan, the launch of the first-level Public Health Emergency Preparedness measures on 23 January 2020 and the implementation of resident travel control measures on 31 January 2020 were crucial to COVID-19 control.

During the COVID-19 pandemic, renewal equation estimates of time-varying effective reproduction numbers were useful to policymakers in evaluating the need for and impact of mitigation measures. Our objective here is to illustrate the utility of mechanistic expressions for the basic and effective (or intrinsic and realized) reproduction numbers, R 0 , R E , and related quantities derived from a Susceptible-Exposed-Infectious-Removed (SEIR) model including features of COVID-19 that might affect transmission of SARS-CoV-2, including asymptomatic, pre-symptomatic, and symptomatic infections, with which people may be hospitalized. Expressions from homogeneous host population models can be analyzed to determine the effort needed to reduce R E from R 0 to 1 and contributions of modeled mitigation measures. Our model is stratified by age, 0–4, 5–9, …, 75+ years, and location, the 50 states plus District of Columbia. Expressions from such heterogeneous host population models include subpopulation reproduction numbers, contributions from the above-mentioned infectious states, metapopulation numbers, subpopulation contributions, and equilibrium prevalence. While the population-immunity at which R E = 1 has captured the popular imagination, the metapopulation R E ≤ 1 could be attained in an infinite number of ways even if only one intervention (e.g., vaccination) were capable of reducing R E . However, gradients of expressions derived from heterogeneous host population models, ∇ R E , can be evaluated to identify optimal allocations of limited resources among subpopulations. We illustrate the utility of such analytical results by simulating two hypothetical vaccination strategies, one uniform and other indicated by ∇ R E , as well as the actual program estimated from one of the CDC’s nationwide seroprevalence surveys conducted from mid-summer 2020 through the end of 2021.

Background Mathematical modelling of infectious diseases is a powerful tool for the design of management policies and a fundamental part of the arsenal currently deployed to deal with the COVID-19 pandemic. Methods We present a compartmental model for the disease where symptomatic and asymptomatic individuals move separately. We introduced healthcare burden parameters allowing to infer possible containment and suppression strategies. In addition, the model was scaled up to describe different interconnected areas, giving the possibility to trigger regionalized measures. It was specially adjusted to Mendoza-Argentina’s parameters, but is easily adaptable for elsewhere. Results Overall, the simulations we carried out were notably more effective when mitigation measures were not relaxed in between the suppressive actions. Since asymptomatics or very mildly affected patients are the vast majority, we studied the impact of detecting and isolating them. The removal of asymptomatics from the infectious pool remarkably lowered the effective reproduction number, healthcare burden and overall fatality. Furthermore, different suppression triggers regarding ICU occupancy were attempted. The best scenario was found to be the combination of ICU occupancy triggers (on: 50%, off: 30%) with the detection and isolation of asymptomatic individuals. In the ideal assumption that 45% of the asymptomatics could be detected and isolated, there would be no need for complete lockdown, and Mendoza’s healthcare system would not collapse. Conclusions Our model and its analysis inform that the detection and isolation of all infected individuals, without leaving aside the asymptomatic group is the key to surpass this pandemic.

Epidemics of novel or re-emerging infectious diseases have quickly spread globally via air travel, as highlighted by pandemic H1N1 influenza in 2009 (pH1N1). Federal, state, and local public health responders must be able to plan for and respond to these events at aviation points of entry. The emergence of a novel influenza virus and its spread to the United States were simulated for February 2009 from 55 international metropolitan areas using three basic reproduction numbers (R0): 1.53, 1.70, and 1.90. Empirical data from the pH1N1 virus were used to validate our SEIR model. Time to entry to the U.S. during the early stages of a prototypical novel communicable disease was predicted based on the aviation network patterns and the epidemiology of the disease. For example, approximately 96% of origins (R0 of 1.53) propagated a disease into the U.S. in under 75 days, 90% of these origins propagated a disease in under 50 days. An R0 of 1.53 reproduced the pH1NI observations. The ability to anticipate the rate and location of disease introduction into the U.S. provides greater opportunity to plan responses based on the scenario as it is unfolding. This simulation tool can aid public health officials to assess risk and leverage resources efficiently.

The spread of coronavirus disease 2019 (COVID-19) in Italy prompted drastic measures for transmission containment. We examine the effects of these interventions, based on modeling of the unfolding epidemic. We test modeling options of the spatially explicit type, suggested by the wave of infections spreading from the initial foci to the rest of Italy. We estimate parameters of a metacommunity Susceptible–Exposed–Infected–Recovered (SEIR)-like transmission model that includes a network of 107 provinces connected by mobility at high resolution, and the critical contribution of presymptomatic and asymptomatic transmission. We estimate a generalized reproduction number (R₀ = 3.60 [3.49 to 3.84]), the spectral radius of a suitable next-generation matrix that measures the potential spread in the absence of containment interventions. The model includes the implementation of progressive restrictions after the first case confirmed in Italy (February 21, 2020) and runs until March 25, 2020. We account for uncertainty in epidemiological reporting, and time dependence of human mobility matrices and awareness-dependent exposure probabilities. We draw scenarios of different containment measures and their impact. Results suggest that the sequence of restrictions posed to mobility and human-to-human interactions have reduced transmission by 45% (42 to 49%). Averted hospitalizations are measured by running scenarios obtained by selectively relaxing the imposed restrictions and total about 200,000 individuals (as of March 25, 2020). Although a number of assumptions need to be reexamined, like age structure in social mixing patterns and in the distribution of mobility, hospitalization, and fatality, we conclude that verifiable evidence exists to support the planning of emergency measures.