Time delay of the appearance of a new strain can affect vaccination behavior and disease dynamics: An evolutionary explanation.

The emergence of a novel strain during a pandemic, like the current COVID-19, is a major concern to the healthcare system. The most effective strategy to control this type of pandemic is vaccination. Many previous studies suggest that the existing vaccine may not be fully effective against the new strain. Additionally, the new strain's late arrival has a significant impact on the disease dynamics and vaccine coverage. Focusing on these issues, this study presents a two-strain epidemic model in which the new strain appears with a time delay. We considered two vaccination provisions, namely preinfection and postinfection vaccinations, which are governed by human behavioral dynamics. In such a framework, individuals have the option to commit vaccination before being infected with the first strain. Additionally, people who forgo vaccination and become infected with the first train have the chance to be vaccinated (after recovery) in an attempt to avoid infection from the second strain. However, a second strain can infect vaccinated and unvaccinated individuals. People may have additional opportunities to be vaccinated and to protect themselves from the second strain due to the time delay. Considering the cost of the vaccine, the severity of the new strain, and the vaccine's effectiveness, our results indicated that delaying the second strain decreases the peak size of the infected individuals. Finally, by estimating the social efficiency deficit, we discovered that the social dilemma for receiving immunization decreases with the delay in the arrival of the second strain.

Global stability analysis of a COVID-19 epidemic model with incubation delay

In this paper, we propose, analyze and simulate a time delay differential equation to investigate the transmission and spread of Coronavirus disease (COVID-19). The basic reproduction number of the model is determined and qualitatively used to investigate the global stability of the model's steady states. We use numerical simulations to support the analytical results in the study. From the simulation results, we note that whenever the basic reproduction number is greater than unity, the model solutions will be associated with periodic oscillations for a considerable time scale from the start before attaining stability. This suggests that the inclusion of the time delay factor destabilizes the endemic equilibrium point leading to periodic solutions that arise due to Hopf bifurcations for a certain time frame.

Capturing complexity over space and time via deep learning: An application to real-time delay prediction in railways

Predictive analytics is an increasingly popular tool for enhancing decision-making processes but is in many business settings based on rule-based models. These rule-based models reach their limits in complex settings. This study compares the performance of a rule-based system with a customised LSTM encoder-decoder deep learning model for predicting train delays. For this, we use a purposefully built real-world dataset on railway transportation, where trains' interdependence over the network makes delay prediction more difficult. Results show that the deep learning model, which incorporates rich spatiotemporal interdependency information in real-time, outperforms the rule-based system by 18%, with the difference increasing to above 23% with higher complexity. The study also dissects the performance difference across different settings: dense versus rural areas, peak versus off-peak hours, low versus high delay, and before versus during the COVID-19 pandemic. The deep learning model is implemented as a proof of concept for decision support within Belgium's railway infrastructure company Infrabel. © 2023 Elsevier B.V.

On the Aspects of Vitamin D and COVID-19 Infections and Modeling Time-Delay Body's Immune System with Time-Dependent Effects of Vitamin D and Probiotic

This chapter provides a summary of recent views on the aspects of vitamin D levels and the relationship between the prevalence rates of vitamin D deficiency and COVID-19 death toll of several countries in Europe and Asia. The chapter also discusses a new modified time-delay immune system model with time-dependent of the body's immune healthy cells, vitamin D, and probiotic. The model can be used to assess the timely progression of healthy immune cells with the effects of the levels of vitamin D and probiotics supplement. It also can help to predict when the infected cells and virus particles free state can ever be reached as time progresses with and without considering the vitamin D and probiotic supplements. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

A class of anomalous diffusion epidemic models based on CTRW and distributed delay

In recent years, the epidemic model with anomalous diffusion has gained popularity in the literature. However, when introducing anomalous diffusion into epidemic models, they frequently lack physical explanation, in contrast to the traditional reaction-diffusion epidemic models. The point of this paper is to guarantee that anomalous diffusion systems on infectious disease spreading remain physically reasonable. Specifically, based on the continuous-time random walk (CTRW), starting from two stochastic processes of the waiting time and the step length, time-fractional space-fractional diffusion, time-fractional reaction-diffusion and fractional-order diffusion can all be naturally introduced into the SIR (S: susceptible, I: infectious and R: recovered) epidemic models, respectively. The three models mentioned above can also be applied to create SIR epidemic models with generalized distributed time delays. Distributed time delay systems can also be reduced to existing models, such as the standard SIR model, the fractional infectivity model and others, within the proper bounds. Meanwhile, as an application of the above stochastic modeling method, the physical meaning of anomalous diffusion is also considered by taking the SEIR (E: exposed) epidemic model as an example. Similar methods can be used to build other types of epidemic models, including SIVRS (V: vaccine), SIQRS (Q: quarantined) and others. Finally, this paper describes the transmission of infectious disease in space using the real data of COVID-19. © 2023 World Scientific Publishing Company.

The analysis of a time delay fractional COVID-19 model via Caputo type fractional derivative.

Novel coronavirus (COVID-19), a global threat whose source is not correctly yet known, was firstly recognised in the city of Wuhan, China, in December 2019. Now, this disease has been spread out to many countries in all over the world. In this paper, we solved a time delay fractional COVID-19 SEIR epidemic model via Caputo fractional derivatives using a predictor-corrector method. We provided numerical simulations to show the nature of the diseases for different classes. We derived existence of unique global solutions to the given time delay fractional differential equations (DFDEs) under a mild Lipschitz condition using properties of a weighted norm, Mittag-Leffler functions and the Banach fixed point theorem. For the graphical simulations, we used real numerical data based on a case study of Wuhan, China, to show the nature of the projected model with respect to time variable. We performed various plots for different values of time delay and fractional order. We observed that the proposed scheme is highly emphatic and easy to implementation for the system of DFDEs.

On-scene time delays for epileptic seizures in emergencies during a social pandemic: A population-based study.

OBJECTIVES: The on-scene time of Emergency Medical Services (EMS), including time for hospital selection, is critical for people in an emergency. However, the outbreak of the novel coronavirus disease 2019 (COVID-19) led to longer delays in providing immediate care for individuals with non-COVID-19-related emergencies, such as epileptic seizures. This study aimed to examine factors associated with on-scene time delays for people with epilepsy (PWE) with seizures needing immediate amelioration. MATERIALS & METHODS: We conducted a population-based retrospective cohort study for PWE transported by EMS between 2016 and 2021. We used data from the Hiroshima City Fire Service Bureau database, divided into three study periods: "Pre period", the period before the COVID pandemic (2016-2019); "Early period", the early period of the COVID pandemic (2020); and "Middle period", the middle period of the COVID pandemic (2021). We performed linear regression modeling to identify factors associated with changes in EMS on-scene time for PWE during each period. In addition, we estimated the rate of total EMS call volume required to maintain the same on-scene time for PWE transported by EMS during the pandemic expansion. RESULTS: Among 2,205 PWE transported by EMS, significant differences in mean age and prevalence of impaired consciousness were found between pandemic periods. Total EMS call volume per month for all causes during the same month <5,000 (-0.55 min, 95% confidence interval [CI] -1.02 - -0.08, p = 0.022) and transport during the Early period (-1.88 min, 95%CI -2.75 - -1.00, p < 0.001) decreased on-scene time, whereas transport during the Middle period (1.58 min, 95%CI 0.70 - 2.46, p < 0.001) increased on-scene time for PWE transported by EMS. The rate of total EMS call volume was estimated as 0.81 (95%CI -0.04 - 1.07) during the expansion phase of the pandemic to maintain the same degree of on-scene time for PWE transported by EMS before the pandemic. CONCLUSIONS: On-scene time delays on PWE in critical care settings were observed during the Middle period. When the pandemic expanded, the EMS system required resource allocation to maintain EMS for time-sensitive illnesses such as epileptic seizures. Timely system changes are critical to meet dramatic social changes.

Dynamics of a Fractional-Order Delayed Model of COVID-19 with Vaccination Efficacy.

In this study, we provide a fractional-order mathematical model that considers the effect of vaccination on COVID-19 spread dynamics. The model accounts for the latent period of intervention strategies by incorporating a time delay τ. A basic reproduction number, R0, is determined for the model, and prerequisites for endemic equilibrium are discussed. The model's endemic equilibrium point also exhibits local asymptotic stability (under certain conditions), and a Hopf bifurcation condition is established. Different scenarios of vaccination efficacy are simulated. As a result of the vaccination efforts, the number of deaths and those affected have decreased. COVID-19 may not be effectively controlled by vaccination alone. To control infections, several non-pharmacological interventions are necessary. Based on numerical simulations and fitting to real observations, the theoretical results are proven to be effective.

A parallel approach to the fractional time delay model for predicting the spread of COVID-19

Due to the importance of forecast accuracy for diseases such as COVID-19, the existence of a mathematical model is particularly important. In this research, first, a model to describe the spread of the COVID-19 pandemic is examined. This model is based on a fractional ordinary differential equation. Then the predictor-corrector numerical method is presented to solve this model. Due to the computational challenge of numerically solving fractional models, a task-parallel approach with coarse granularity is presented to solve this model on shared memory systems. The initial data for testing the proposed approach is the data reported on December 31, 2019 by the Wuhan Municipal Commission of the outbreak of the COVID-19 pandemic in the city of Wuhan, China. The numerical results obtained from the proposed parallel approach show that the speedup of the parallel method compared to the sequential method reaches 2.76 in the prediction of 1000 days. © 2022 IEEE.

Delay dynamics of pandemic disease COVID-19 with compartmental mathematical modeling

In this paper, we propose a compartmental epidemic model which consists of four divisions named as non-quarantined susceptible population (Sn), quarantined susceptible population (Sq), infected population (I), and recovered or immune population (R) to analyze the dynamics of pandemic disease COVID19 introducing a time delay. We analytically calculate the basic reproduction number of the model to classify epidemic case and endemic case of the pandemic. In order to understand the dynamics of Novel Coronavirus under a time delay, we perform the stability analysis and a Hopfbifurcation analysis of the proposed model as well. Finally, numerical simulations are performed to illustrate the analytical findingsthat reflect a real scenario of the transmission of COVID-19. © CSP - Cambridge, UK;I&S - Florida, USA, 2023

Stability and Bifurcation Analysis of the Caputo Fractional-Order Asymptomatic COVID-19 Model with Multiple Time-Delays

Throughout the last few decades, fractional-order models have been used in many fields of science and engineering, applied mathematics, and biotechnology. Fractional-order differential equations are beneficial for incorporating memory and hereditary properties into systems. Our paper proposes an asymptomatic COVID-19 model with three delay terms τ1,τ2,τ3 and fractional-order α. Multiple constant time delays are included in the model to account for the latency of infection in a vector. We study the necessary and sufficient criteria for stability of steady states and Hopf bifurcations based on the three constant time-delays, τ1, τ2, and τ3. Hopf bifurcation occurs in the addressed model at the estimated bifurcation points τ10, τ20, τ30, and τ10*. The numerical simulations fit to real observations proving the effectiveness of the theoretical results. Fractional-order and time-delays successfully enhance the dynamics and strengthen the stability condition of the asymptomatic COVID-19 model. © 2023 World Scientific Publishing Company.

Stability analysis of a fractional-order SEIR epidemic model with general incidence rate and time delay

In this paper, we investigate the qualitative behavior of a class of fractional SEIR epidemic models with a more general incidence rate function and time delay to incorporate latent infected individuals. We first prove positivity and boundedness of solutions of the system. The basic reproduction number (Formula presented.) of the model is computed using the method of next generation matrix, and we prove that if (Formula presented.), the healthy equilibrium is locally asymptotically stable, and when (Formula presented.), the system admits a unique endemic equilibrium which is locally asymptotically stable. Moreover, using a suitable Lyapunov function and some results about the theory of stability of differential equations of delayed fractional-order type, we give a complete study of global stability for both healthy and endemic steady states. The model is used to describe the COVID-19 outbreak in Algeria at its beginning in February 2020. A numerical scheme, based on Adams–Bashforth–Moulton method, is used to run the numerical simulations and shows that the number of new infected individuals will peak around late July 2020. Further, numerical simulations show that around 90% of the population in Algeria will be infected. Compared with the WHO data, our results are much more close to real data. Our model with fractional derivative and delay can then better fit the data of Algeria at the beginning of infection and before the lock and isolation measures. The model we propose is a generalization of several SEIR other models with fractional derivative and delay in literature. © 2023 John Wiley & Sons, Ltd.

A Path to Establishing Delay and Disruption Claims for Contracts Entered into Prior to the Start of the COVID-19 Pandemic

Since early 2020, COVID-19 has had devastating and ongoing health and economic impacts worldwide. The construction industry has not been immune to these impacts. Although construction was generally deemed essential, in some jurisdictions only certain sectors of the construction industry were deemed essential and therefore allowed to continue with work. Any construction that took place was subject to additional precautions that may have resulted in delay and disruption claims. The methodology of the paper involves a review of primary and secondary legal resources in the United States that are used to derive applicable rules of law. Those rules of law are then applied to force majeure contract language from the American Institute of Architects to outline the criteria for successful delay and disruption claims. For construction contracts entered into prior to the onset of the pandemic, delay claims will likely result only in an extension of the contract time, whereas disruption claims may result in additional time and/or money depending on how the contract addresses unforeseen costs. In the absence of express contract terms addressing unforeseen costs in a situation such as COVID-19, principles of equity will dictate whether additional compensation is granted. © 2023 American Society of Civil Engineers.

Stability of a delayed SARS-CoV-2 reactivation model with logistic growth and adaptive immune response.

This paper develops and analyzes a SARS-CoV-2 dynamics model with logistic growth of healthy epithelial cells, CTL immune and humoral (antibody) immune responses. The model is incorporated with four mixed (distributed/discrete) time delays, delay in the formation of latent infected epithelial cells, delay in the formation of active infected epithelial cells, delay in the activation of latent infected epithelial cells, and maturation delay of new SARS-CoV-2 particles. We establish that the model's solutions are non-negative and ultimately bounded. We deduce that the model has five steady states and their existence and stability are perfectly determined by four threshold parameters. We study the global stability of the model's steady states using Lyapunov method. The analytical results are enhanced by numerical simulations. The impact of intracellular time delays on the dynamical behavior of the SARS-CoV-2 is addressed. We noted that increasing the time delay period can suppress the viral replication and control the infection. This could be helpful to create new drugs that extend the delay time period.

Global asymptotic stability of a delay differential equation model for SARS-CoV-2 virus infection mediated by ACE2 receptor protein.

The COVID-19 pandemic has brought a serious threat to human life safety worldwide. SARS-CoV-2 virus mainly binds to the target cell surface receptor ACE2 (Angiotensin-converting enzyme 2 ) through the S protein expressed on the surface of the virus, resulting in infection of target cells. During this infection process, the target cell ACE2 receptor plays a very important mediating role. In this paper, a delay differential equation model containing the mediated effect of target cell receptor is established according to the mechanism of SARS-CoV-2 virus invasion of target cells, and the global stability of the infection-free equilibrium and the infected equilibrium of the model is obtained by using the basic reproduction number  ℛ 0  and constructing the appropriate Lyapunov functional. The expression of the basic reproduction number  ℛ 0  intuitively gives the dependence on the expression ratio of the target cell surface ACE2 receptor, which is helpful for the understanding of the mechanism of SARS-CoV-2 virus infection.

Extinction and persistence of a stochastic delayed Covid-19 epidemic model.

We formulated a Coronavirus (COVID-19) delay epidemic model with random perturbations, consisting of three different classes, namely the susceptible population, the infectious population, and the quarantine population. We studied the proposed problem to derive at least one unique solution in the positive feasweible region of the non-local solution. Sufficient conditions for the extinction and persistence of the proposed model are established. Our results show that the influence of Brownian motion and noise on the transmission of the epidemic is very large. We use the first-order stochastic Milstein scheme, taking into account the required delay of infected individuals.

Stability analysis of time-delayed SAIR model for duration of vaccine in the context of temporary immunity for COVID-19 situation

As the COVID-19 continues threatening public health worldwide, when to vaccinate the booster shots becomes the hot topic. In this paper, based on the characteristics of COVID-19 and its vaccine, an SAIR model associated with temporary immunity is proposed to study the effect on epidemic situation. Second, we theoretically analyze the existence and stability of equilibrium and the system undergoes Hopf bifurcation when delay passes through some critical values. Third, we study the dynamic properties of Hopf bifurcation and derive the normal form of Hopf bifurcation to determine the stability and direction of bifurcating periodic solutions. After that, numerical simulations are carried out to demonstrate the application of the theoretical results. Particularly, in order to ensure the validity, statistical analysis of data is conducted to determine the values for model parameters. Next, we study the impact of the infection rates on booster vaccination time to simulate the mutants, and the results are consistent with the facts. Finally, we predict the mean time of completing a round of vaccination worldwide with the help fitting and put forward some suggestions by comparing with the critical time of booster vaccination.

A class of anomalous diffusion epidemic models based on CTRW and distributed delay

In recent years, the epidemic model with anomalous diffusion has gained popularity in the literature. However, when introducing anomalous diffusion into epidemic models, they frequently lack physical explanation, in contrast to the traditional reaction-diffusion epidemic models. The point of this paper is to guarantee that anomalous diffusion systems on infectious disease spreading remain physically reasonable. Specifically, based on the continuous-time random walk (CTRW), starting from two stochastic processes of the waiting time and the step length, time-fractional space-fractional diffusion, time-fractional reaction-diffusion and fractional-order diffusion can all be naturally introduced into the SIR (S: susceptible, I: infectious and R: recovered) epidemic models, respectively. The three models mentioned above can also be applied to create SIR epidemic models with generalized distributed time delays. Distributed time delay systems can also be reduced to existing models, such as the standard SIR model, the fractional infectivity model and others, within the proper bounds. Meanwhile, as an application of the above stochastic modeling method, the physical meaning of anomalous diffusion is also considered by taking the SEIR (E: exposed) epidemic model as an example. Similar methods can be used to build other types of epidemic models, including SIVRS (V: vaccine), SIQRS (Q: quarantined) and others. Finally, this paper describes the transmission of infectious disease in space using the real data of COVID-19.

Recurrent epidemic waves in a delayed epidemic model with quarantine.

In this paper, we are concerned with an epidemic model with quarantine and distributed time delay. We define the basic reproduction number R0 and show that if R0≤1, then the disease-free equilibrium is globally asymptotically stable, whereas if R0>1, then it is unstable and there exists a unique endemic equilibrium. We obtain sufficient conditions for a Hopf bifurcation that induces a nontrivial periodic solution which represents recurrent epidemic waves. By numerical simulations, we illustrate stability and instability parameter regions. Our results suggest that the quarantine and time delay play important roles in the occurrence of recurrent epidemic waves.

Artificial intelligence knacks-based computing for stochastic COVID-19 SIRC epidemic model with time delay

Time delays play an important part in modeling the fact that one cannot be communicable for a long time after becoming sick. Delay can be triggered by a variety of epidemiological situations. The most egregious causes of a delay are infection latency in the vector and infection latency in the infected host. The dynamics of susceptible, infected, recovered and cross-immune (SIRC) classed-based model having cross-immune and time-delay in the transmission for spread of COVID-19 abbreviated as (SIRC-CTC-19) are investigated in this study using an intelligent numerical computing paradigm based on the Levenberg–Marquardt Method backpropagated by neural networks (LM-BPNN). The model is mathematically governed by a system of ordinary differential equations that depicts the four nodes as susceptible, infected, recovered and cross-immune ones (SIRC) nodes with cross-immune class and time-delay in transmission components for COVID-19 dissemination (CTC-19). The reference solution of the SIRC model for the spread of COVID-19 is produced by using the explicit Runge–Kutta method for the many scenarios of this model arising from altering delay with regard to time. This reference solution permits the use of evolutionary computing to solve the SIRC-CTC-19 using train, validate and test techniques. The proposed LM-BPNN method’s accuracy has been proven by its results overlapping with explicit Runge–Kutta results Calculation of regression metrics, error analysis of histogram illustrations and learning curves on MSE effectively augment the LM-BPNN’s accuracy, convergence and reliability in solving the SIRC-CTC-19 model. [ FROM AUTHOR] Copyright of International Journal of Modern Physics B: Condensed Matter Physics;Statistical Physics;Applied Physics is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)