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Abstract 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.

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

Background The Severe Acute Respiratory Syndrome Coronavirus 2 Omicron variant (SARS-CoV-2, Omicron) has been widely spread around the world. Since February 2022, Shenzhen was continuously affected by it as a major hub connecting domestic and international transportation, resulting in rapidly increasing number of infected cases. Objective To construct a modified susceptible-exposed-infected-recovered (SEIR) model for providing policy references and suggestions with applied value for epidemic prevention and control in Shenzhen, China, so as to alleviate the pressure of prevention and control. Methods This study developed a modified SEIR model targeting the epidemiological characteristics of the Omicron variant such as rapid transmission, high concealment, and general susceptibility of the population, introducing groups with policy characteristics as close contacts, secondary contacts, quarantined individuals and carriers, based on traditional SEIR model of infectious disease dynamics. The relevant parameters of the modified model were determined by fitting the Shenzhen epidemic data of February 18 to 28, 2022. Results The predicted data of the model were basically consistent with the actual data from March 01 to 04, 2022, providing a reliable basis for predicting the subsequent development of the epidemic. Subsequently, the Omicron variant outbreak in Shenzhen between 5 to 19 March 2022 was forecasted through this modified model to provide guidance for epidemic prevention and control measures in terms of the degree and time of manual intervention in epidemic prevention and control, and healthcare resource requirements such as patient beds and isolation rooms. Conclusion The modified SEIR model developed in this study has proved its practical value in forecasting epidemic development, formulating and adjusting epidemic control measures, and allocating health resources.

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

Identifiability of a mathematical model plays a crucial role in the parameterization of the model. In this study, we established the structural identifiability of a susceptible-exposed-infected-recovered (SEIR) model given different combinations of input data and investigated practical identifiability with respect to different observable data, data frequency, and noise distributions. The practical identifiability was explored by both Monte Carlo simulations and a correlation matrix approach. Our results showed that practical identifiability benefits from higher data frequency and data from the peak of an outbreak. The incidence data gave the best practical identifiability results compared to prevalence and cumulative data. In addition, we compared and distinguished the practical identifiability by Monte Carlo simulations and a correlation matrix approach, providing insights into when to use which method for other applications.

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

Abstract The coronavirus disease 2019 (COVID-19) remains serious around the world and causes huge deaths and economic losses. Understanding the transmission dynamics of diseases and providing effective control strategies play important roles in the prevention of epidemic diseases. In this paper, to investigate the effect of delays on the transmission of COVID-19, we propose a delayed SEIR model to describe COVID-19 virus transmission, where two delays indicating the incubation and recovery periods are introduced. For this system, we prove its solutions are nonnegative and ultimately bounded with the nonnegative initial conditions. Furthermore, we calculate the disease-free and endemic equilibrium points and analyze the asymptotical stability and the existence of Hopf bifurcations at these equilibrium points. Then, by taking the weighted sum of the opposite number of recovered individuals at the terminal time, the number of exposed and infected individuals during the time horizon, and the system cost of control measures as the cost function, we present a delay optimal control problem, where two controls represent the social contact and the pharmaceutical intervention. Necessary optimality conditions of this optimal control problem are exploited to characterize the optimal control strategies. Finally, numerical simulations are performed to verify the theoretical analysis of the stability and Hopf bifurcations at the equilibrium points and to illustrate the effectiveness of the obtained optimal strategies in controlling the COVID-19 epidemic.

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} $.

This paper introduces stochastic disturbances into a semi-parametric SEIR model with infectivity in an incubation period. The model combines the randomness of disease transmission and the nonlinearity of transmission rate, providing a flexible framework for more accurate description of the process of infectious disease transmission. On the basis of the discussion of the deterministic model, the stochastic semi-parametric SEIR model is studied. Firstly, we use Lyapunov analysis to prove the existence and uniqueness of global positive solutions for the model. Secondly, the conditions for disease extinction are established, and appropriate stochastic Lyapunov functions are constructed to discuss the asymptotic behavior of the model’s solution at the disease-free equilibrium point of the deterministic model. Finally, the specific transmission functions are enumerated, and the accuracy of the results are demonstrated through numerical simulations.

Mathematical formulations are crucial in understanding the dynamics of disease spread within a community. The objective of this research is to investigate the SEIR model of SARS-COVID-19 (C-19) with the inclusion of vaccinated effects for low immune individuals. A mathematical model is developed by incorporating vaccination individuals based on a proposed hypothesis. The fractal-fractional operator (FFO) is then used to convert this model into a fractional order. The newly developed SEVIR system is examined in both a qualitative and quantitative manner to determine its stable state. The boundedness and uniqueness of the model are examined to ensure reliable findings, which are essential properties of epidemic models. The global derivative is demonstrated to verify the positivity with linear growth and Lipschitz conditions for the rate of effects in each sub-compartment. The system is investigated for global stability using Lyapunov first derivative functions to assess the overall impact of vaccination. In fractal-fractional operators, fractal represents the dimensions of the spread of the disease, and fractional represents the fractional ordered derivative operator. We use combine operators to see real behavior of spread as well as control of COVID-19 with different dimensions and continuous monitoring. Simulations are conducted to observe the symptomatic and asymptomatic effects of the corona virus disease with vaccinated measures for low immune individuals, providing insights into the actual behavior of the disease control under vaccination effects. Such investigations are valuable for understanding the spread of the virus and developing effective control strategies based on justified outcomes.

In this paper, a generalized fractional-order SEIR model is proposed, denoted by SEIQRP model, which divided the population into susceptible, exposed, infectious, quarantined, recovered and insusceptible individuals and has a basic guiding significance for the prediction of the possible outbreak of infectious diseases like the coronavirus disease in 2019 (COVID-19) and other insect diseases in the future. Firstly, some qualitative properties of the model are analyzed. The basic reproduction number R0 is derived. When R01 , the endemic equilibrium point is also unique. Furthermore, some conditions are established to ensure the local asymptotic stability of disease-free and endemic equilibrium points. The trend of COVID-19 spread in the USA is predicted. Considering the influence of the individual behavior and government mitigation measurement, a modified SEIQRP model is proposed, defined as SEIQRPD model, which is divided the population into susceptible, exposed, infectious, quarantined, recovered, insusceptible and dead individuals. According to the real data of the USA, it is found that our improved model has a better prediction ability for the epidemic trend in the next two weeks. Hence, the epidemic trend of the USA in the next two weeks is investigated, and the peak of isolated cases is predicted. The modified SEIQRP model successfully capture the development process of COVID-19, which provides an important reference for understanding the trend of the outbreak.

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. [ABSTRACT FROM AUTHOR]

The availability of an effective vaccine is a major challenge in COVID-19 vaccination campaigns. In this article, we propose a comprehensive strategy incorporating distributed controls via vaccination and treatment while considering the limitations of available resources expressed as inequalities constrained. Our approach utilizes a spatiotemporal model that includes multiple strains of the virus and considers spatial heterogeneity, providing a more accurate representation of disease transmission. By using a generalized two-strain ODE model, we effectively capture the evolution of COVID-19, including various strains and variants. To validate our model, we establish the positivity and boundedness of the system’s solution. Through the exploration of vaccination and treatment controls. Our study aims to reduce the spread of the disease between strains and identify optimal values that minimize the number of infected individuals and associated costs. This work provides useful insights into effective strategies for controlling the COVID-19 epidemic, even with limited vaccination resources. Furthermore, we demonstrate the existence of controls and describe their characterizations in terms of state and adjoint functions. The penalty method is used to treat the inequalities constrained. More importantly, our numerical simulation shows that adequate vaccination resources and simultaneous treatment can effectively reduce and even eliminate the spread of COVID-19.

This study explores the intricacies of the COVID-19 pandemic by employing a four-compartment model with a fractal-fractional derivative based on Caputo concept. The analysis hinges on Schauder fixed point theorem, used to qualitatively examine the solutions and ascertain their existence and uniqueness within the model. The fundamental reproduction number is determined through the next-generation matrix approach. This study delves into the stability of equilibrium points and conducts a sensitivity analysis of model parameters. The equilibrium without infections is locally and globally stable when the basic reproduction number is less than 1. Also, this equilibrium becomes unstable when the basic reproduction number exceeds 1. Applying Lyapunov principles and the Routh–Hurwitz criteria, it is established that the endemic equilibrium point is globally stable for the basic reproduction number values greater than 1. The proposed model incorporates Ulam-Hyers stability through nonlinear functional analysis. Lagrange interpolation method estimates solutions for the fractal-fractional order COVID-19 model. Numerical simulations are performed using MATLAB software to exemplify the model behavior in the context of the Italian case study. Furthermore, fractal-fractional calculus techniques hold significant promise for comprehending and predicting the pandemic’s global dynamics in other countries.

The SEIR (susceptible-exposed-infected-recovered) model has become a valuable tool for studying infectious disease dynamics and predicting the spread of diseases, particularly concerning the COVID pandemic. However, existing models often oversimplify population characteristics and fail to account for differences in disease sensitivity and social contact rates that can vary significantly among individuals. To address these limitations, we have developed a new multi-feature SEIR model that considers the heterogeneity of health conditions (disease sensitivity) and social activity levels (contact rates) among populations affected by infectious diseases. Our model has been validated using the data of the confirmed COVID cases in Allegheny County (Pennsylvania, USA) and Hamilton County (Ohio, USA). The results demonstrate that our model outperforms traditional SEIR models regarding predictive accuracy. In addition, we have used our multi-feature SEIR model to propose and evaluate different vaccine prioritization strategies tailored to the characteristics of heterogeneous populations. We have formulated optimization problems to determine effective vaccine distribution strategies. We have designed extensive numerical simulations to compare vaccine distribution strategies in different scenarios. Overall, our multi-feature SEIR model enhances the existing models and provides a more accurate picture of disease dynamics. It can help to inform public health interventions during pandemics/epidemics.

Abstract The terms susceptibility, exposure, infectiousness, and recovered all have some inherent ambiguity because different population members have different susceptibility levels, exposure levels, infectiousness levels, and recovery patterns. This uncertainty becomes more pronounced when examining population subgroups characterized by distinct behaviors, cultural norms, and varying degrees of resilience across different age brackets, thereby introducing the possibility of fluctuations. There is a need for more accurate models that take into account the various levels of susceptibility, exposure, infectiousness, and recovery of the individuals. A fuzzy SEIR model of the dynamics of the measles disease is discussed in this article. The rates of disease transmission and recovery are treated as fuzzy sets. Three distinct numerical approaches, the forward Euler, fourth-order Runge-Kutta, and nonstandard finite difference (NSFD) are employed for the resolution of this fuzzy SEIR model. Next, the outcomes of the three methods are examined. The results of the simulation demonstrate that the NSFD method adeptly portrays convergent solutions across various time step sizes. Conversely, the conventional Euler and RK-4 methods only exhibit positivity and convergence solutions when handling smaller step sizes. Even when considering larger step sizes, the NSFD method maintains its consistency, showcasing its efficacy. This demonstrates the NSFD technique’s superior reliability when compared to the other two methods, while maintaining all essential aspects of a continuous dynamical system. Additionally, the results from numerical and simulation studies offer solid proof that the suggested NSFD technique is a reliable and effective tool for controlling these kinds of dynamical systems.The convergence and consistency analysis of the NSFD method are also studied.

Successive generalisations of the basic SEIR model have been proposed to accommodate the different needs of the organisations handling the SARS-CoV-2 epidemic and the assessment of the public health measures adopted and named under the common umbrella of Non-Pharmaceutical Interventions (NPIs). So far, these generalisations have not been able to assess the ability of these measures to avoid infection by the SARS-CoV-2 and thus their contribution to contain the spread of the disease. This work proposes a new generalisation of SEIR model and includes a heterogeneous and age-related generation of infections that depends both on a probability that a contact generates the transmission of the disease and a contact rate. The results show (1) thanks to the universal wearing of facial coverings, the probability that a contact provokes the transmission of the disease was reduced by at least 50% and (2) the impact of the other NPI is so significant that otherwise Portugal would have gone into a non-sustainable situation of having 80% of its population infected in the first 300 days of the pandemic. This situation would have led to a number of deaths almost twenty times higher than the number that was actually recorded by December 26th, 2020. Moreover, the results suggest that even if the requirement of universal wearing of facial coverings was adopted sooner jointly with closing workplaces and resorting to teleworking would have postponed the peak of the incidence, altought the epidemic path would have result in a number of infections hardly managed by the National Health System. Complementary, results confirm that (3) the health authorities adopted a conservative approach on the criteria to consider an infected individual not infective any longer; and (4) the most effective NPIs and stringency levels either impacting on self-protection against infection or reducing the contacts that would eventually result in infection are, in decreasing order of importance, the use of Facial coverings, Workplace closing and Stay at home requirements.