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.

The disutility of compartmental model forecasts during the COVID-19 pandemic.

During the COVID-19 pandemic, several forecasting models were released to predict the spread of the virus along variables vital for public health policymaking. Of these, the susceptible-infected-recovered (SIR) compartmental model was the most common. In this paper, we investigated the forecasting performance of The University of Texas COVID-19 Modeling Consortium SIR model. We considered the following daily outcomes: hospitalizations, ICU patients, and deaths. We evaluated the overall forecasting performance, highlighted some stark forecast biases, and considered forecast errors conditional on different pandemic regimes. We found that this model tends to overforecast over the longer horizons and when there is a surge in viral spread. We bolstered these findings by linking them to faults with the SIR framework itself.

To give or not to give? Pandemic vaccine donation policy.

OBJECTIVES: The purpose of this work is to characterize scenarios under which it may be in a donor country's own public health interests to donate vaccine doses to another country before its own population has been fully vaccinated. In these scenarios, vaccinating other countries can delay the evolution of new variants of the virus, decrease total deaths, and, in some cases, decrease deaths in the donor countries. STUDY DESIGN: We simulate the effects of different vaccine donation policies using an epidemiological model employing COVID-19 transmission parameters. METHODS: We use the epidemiological model of Holleran et al. that incorporates virus mutation to simulate epidemic progression and estimate numbers of deaths arising from several vaccine allocation policies (donor-first, non-donor-first, and vaccine sharing) across a number of scenarios. We analyze the results in light of herd immunity limits derived in Holleran et al. RESULTS: We identify realistic scenarios under which a donor country prefers to donate vaccines before distributing them locally in order to minimize local deaths during a pandemic. We demonstrate that a non-donor-first vaccination policy can delay, sometimes dramatically, the emergence of more-contagious variants. Even more surprising, donating all vaccines is sometimes better for the donor country than a sharing policy in which half of the vaccines are donated, and half are retained because of the impact donation can have on delaying the emergence of a more contagious virus. Non-donor-first vaccine allocation is optimal in scenarios in which the local health impact of the vaccine is limited or when delaying the emergence of a variant is especially valuable. CONCLUSION: In all cases, we find that vaccine distribution is not a zero-sum game between donor and non-donor countries, illustrating the general moral reasons to donate vaccines. In some cases, donor nations can also realize local health benefits from donating vaccines. The insights yielded by this framework can be used to guide equitable vaccine distribution in future pandemics.

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.

Bayesian inference for the onset time and epidemiological characteristics of emerging infectious diseases.

Background: Emerging infectious diseases pose a significant threat to global public health. Timely detection and response are crucial in mitigating the spread of such epidemics. Inferring the onset time and epidemiological characteristics is vital for accelerating early interventions, but accurately predicting these parameters in the early stages remains challenging. Methods: We introduce a Bayesian inference method to fit epidemic models to time series data based on state-space modeling, employing a stochastic Susceptible-Exposed-Infectious-Removed (SEIR) model for transmission dynamics analysis. Our approach uses the particle Markov chain Monte Carlo (PMCMC) method to estimate key epidemiological parameters, including the onset time, the transmission rate, and the recovery rate. The PMCMC algorithm integrates the advantageous aspects of both MCMC and particle filtering methodologies to yield a computationally feasible and effective means of approximating the likelihood function, especially when it is computationally intractable. Results: To validate the proposed method, we conduct case studies on COVID-19 outbreaks in Wuhan, Shanghai and Nanjing, China, respectively. Using early-stage case reports, the PMCMC algorithm accurately predicted the onset time, key epidemiological parameters, and the basic reproduction number. These findings are consistent with empirical studies and the literature. Conclusion: This study presents a robust Bayesian inference method for the timely investigation of emerging infectious diseases. By accurately estimating the onset time and essential epidemiological parameters, our approach is versatile and efficient, extending its utility beyond COVID-19.

Analysis of a COVID-19 model with media coverage and limited resources.

The novel coronavirus disease (COVID-19) pandemic has profoundly impacted the global economy and human health. The paper mainly proposed an improved susceptible-exposed-infected-recovered (SEIR) epidemic model with media coverage and limited medical resources to investigate the spread of COVID-19. We proved the positivity and boundedness of the solution. The existence and local asymptotically stability of equilibria were studied and a sufficient criterion was established for backward bifurcation. Further, we applied the proposed model to study the trend of COVID-19 in Shanghai, China, from March to April 2022. The results showed sensitivity analysis, bifurcation, and the effects of critical parameters in the COVID-19 model.

Development of the second version of Global Prediction System for Epidemiological Pandemic.

Coronavirus disease 2019 (COVID-19) is a severe global public health emergency that has caused a major crisis in the safety of human life, health, global economy, and social order. Moreover, COVID-19 poses significant challenges to healthcare systems worldwide. The prediction and early warning of infectious diseases on a global scale are the premise and basis for countries to jointly fight epidemics. However, because of the complexity of epidemics, predicting infectious diseases on a global scale faces significant challenges. In this study, we developed the second version of Global Prediction System for Epidemiological Pandemic (GPEP-2), which combines statistical methods with a modified epidemiological model. The GPEP-2 introduces various parameterization schemes for both impacts of natural factors (seasonal variations in weather and environmental impacts) and human social behaviors (government control and isolation, personnel gathered, indoor propagation, virus mutation, and vaccination). The GPEP-2 successfully predicted the COVID-19 pandemic in over 180 countries with an average accuracy rate of 82.7%. It also provided prediction and decision-making bases for several regional-scale COVID-19 pandemic outbreaks in China, with an average accuracy rate of 89.3%. Results showed that both anthropogenic and natural factors can affect virus spread and control measures in the early stages of an epidemic can effectively control the spread. The predicted results could serve as a reference for public health planning and policymaking.

Mathematical modeling for estimating influenza vaccine efficacy: A case study of the Valencian Community, Spain.

Vaccine efficacy and its quantification is a crucial concept for the proper design of public health vaccination policies. In this work we proposed a mathematical model to estimate the efficacy of the influenza vaccine in a real-word scenario. In particular, our model is a SEIR-type epidemiological model, which distinguishes vaccinated and unvaccinated populations. Mathematically, its dynamics is governed by a nonlinear system of ordinary differential equations, where the non-linearity arises from the effective contacts between susceptible and infected individuals. Two key aspects of this study is that we use a vaccine distribution over time that is based on real data specific to the elderly people in the Valencian Community and the calibration process takes into account that over one influenza season a specific proportion of the population becomes infected with influenza. To consider the effectiveness of the vaccine, the model incorporates a parameter, the vaccine attenuation factor, which is related with the vaccine efficacy against the influenza virus. With this framework, in order to calibrate the model parameters and to obtain an influenza vaccine efficacy estimation, we considered the 2016-2017 influenza season in the Valencian Community, Spain, using the influenza reported cases of vaccinated and unvaccinated. In order to ensure the model identifiability, we choose to deterministically calibrate the parameters for different scenarios and we find the one with the minimum error in order to determine the vaccine efficacy. The calibration results suggest that the influenza vaccine developed for 2016-2017 influenza season has an efficacy of approximately 76.7%, and that the risk of becoming infected is five times higher for an unvaccinated individual in comparison with a vaccinated one. This estimation partially agrees with some previous studies related to the influenza vaccine. This study presents a new integrated mathematical approach to study the influenza vaccine efficacy and gives further insight into this important public health topic.

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.

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.

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.

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.

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.

Model of strategy control for delayed panic spread in emergencies.

In emergencies similar to virus spreading in an epidemic model, panic can spread in groups, which brings serious bad effects to society. To explore the transmission mechanism and decision-making behavior of panic, a government strategy was proposed in this paper to control the spread of panic. First, based on the SEIR epidemiological model, considering the delay effect between susceptible and exposed individuals and taking the infection rate of panic as a time-varying variable, a SEIR delayed panic spread model was established and the basic regeneration number of the proposed model was calculated. Second, the control strategy was expressed as a state delayed feedback and solved using the exact linearization method of nonlinear control system; the control law for the system was determined, and its stability was proven. The aim was to eradicate panic from the group so that the recovered group tracks the whole group asymptotically. Finally, we simulated the proposed strategy of controlling the spread of panic to illustrate our theoretical results.

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.

On cognitive epidemic models: spatial segregation versus nonpharmaceutical interventions.

Fick's law and the Fokker-Planck law of diffusion are applied to manifest the cognitive dispersal of individuals in two reaction-diffusion SEIR epidemic models, where the disease transmission is illustrated by nonlocal infection mechanisms in heterogeneous environments. Building upon the well-posedness of solutions, threshold dynamics are discussed in terms of the basic reproduction numbers for the two cognitive epidemic models. The numerical investigation reveals that the Fokker-Planck law can better describe the diffusion of individuals by taking different dispersal strategies of exposed individuals in our cognitive epidemic models, and provides some insights on spatial segregation and nonpharmaceutical interventions: (i) spatial segregation occurs in the random diffusion model when the nonlocal infection radius is small, while it appears in the symmetric diffusion model when the radius is large; (ii) nonpharmaceutical interventions on restricting the dispersal of exposed and infected individuals do not contribute to reducing the infection proportion, but rather eliminate the disease in a region, which expands as the nonlocal infection radius increases. We additionally find that the final infection size in the random diffusion model is significantly smaller than that in the symmetric diffusion model and decreases as the nonlocal infection radius increases.

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.

Comparative reconstruction of SARS-CoV-2 transmission in three African countries using a mathematical model integrating immunity data.

Objectives: Africa has experienced fewer COVID-19 cases and deaths than other regions, with a contrasting epidemiological situation between countries, raising questions regarding the determinants of disease spread in Africa. Methods: We built a susceptible-exposed-infected-recovered model including COVID-19 mortality data where recovery class is structured by specific immunization and modeled by a partial differential equation considering the opposed effects of immunity decline and immunization. This model was applied to Tunisia, Senegal, and Madagascar. Results: Senegal and Tunisia experienced two epidemic phases. Initially, infections emerged in naive individuals and were limited by social distancing. Variants of concern (VOCs) were also introduced. The second phase was characterized by successive epidemic waves driven by new VOCs that escaped host immunity. Meanwhile, Madagascar demonstrated a different profile, characterized by longer intervals between epidemic waves, increasing the pool of susceptible individuals who had lost their protective immunity. The impact of vaccination on model parameters in Tunisia and Senegal was evaluated. Conclusions: Loss of immunity and vaccination-induced immunity have played crucial role in controlling the African pandemic. SARS-CoV-2 has become endemic now and will continue to circulate in African populations. However, previous infections provide significant protection against severe diseases, thus providing a basis for future vaccination strategies.