The Application of PageRank model in urban epidemic prevention and control

The ongoing COVID-19 epidemic has had a great impact on social activities and the economy. The usage technical analysis tools to provide a more accurate and efficient reference for epidemic control measures is of great significance. This paper analyzes the characteristics and deficiencies of the existing technical methods, such as regression model, simulation calculation, differential equation and so on. By analyzing past outbreak cases and comparing the epidemic prevention measures of different cities, we discuss the importance of early and timely prevention in controlling the epidemic, and the importance of analyzing and formulating plans in advance. We then make the key observation that the spread of the virus is related to the topology of the urban network. This paper further proposes an epidemic analysis model of the optimized PageRank model, and gives a ranking algorithm for virus transmission risk levels based on road nodes, forming a visual risk warning level map, and applies the algorithm to the epidemic analysis of Yuegezhuang area in Beijing. Finally, more in-depth research directions and suggestions for prevention and control measures are put forward. © 2023 SPIE.

Long-term prediction of the COVID-19 epidemics induced by Omicron-virus in China based on a novel non-autonomous delayed SIR model

Since the outbreak of COVID-19, the severe acute respiratory syndrome coronavirus 2 genome is still mutating. Omicron, a recently emerging virus with a shorter incubation period, faster transmission speed, and stronger immune escape ability, is soaring worldwide and becoming the mainstream virus in the COVID-19 pandemic. It is especially critical for the governments, healthcare systems, and economic sectors to have an accurate estimate of the trend of this disaster. By using different mathematical approaches, including the classical susceptible-infected-recovered (SIR) model and its extensions, many investigators have tried to predict the outbreaks of COVID-19. In this study, we employed a novel model which is based upon the well-known susceptible-infected-removed (SIR) model with the time-delay and time-varying coefficients in our previous works. We aim to predict the evolution of the epidemics effectively in nine cities and provinces of China, including A City, B City, C City, D City, E City, F City, G City, H City and I Province. The results show it is effective to model the spread of the large-scale and sporadic COVID-19 induced by Omicron virus by the novel non-autonomous delayed SIR compartment model. The significance of this study is that it can provide the management department of epidemic control with theoretical references and subsequent evaluation of the prevention, control measures, and effects.

Differential and Time-Discrete SEIRS Models with Vaccination: Local Stability, Validation and Sensitivity Analysis Using Bulgarian COVID-19 Data

Bulgaria has the lowest COVID-19 vaccination rate in the European Union and the second-highest COVID-19 mortality rate in the world. That is why we think it is important better to understand the reason for this situation and to analyse the development of the disease over time. In this paper, an extended time-dependent SEIRS model SEIRS-VB is used to investigate the long-term behaviour of the COVID-19 epidemic. This model includes vaccination and vital dynamics. To apply the SEIRS-VB model some numerical simulation tools have been developed and for this reason a family of time-discrete variants are introduced. Suitable inverse problems for the identification of parameters in discrete models are solved. A methodology is proposed for selecting a discrete model from the constructed family, which has the closest parameter values to these in the differential SEIRS-VB model. To validate the studied models, Bulgarian COVID-19 data are used. To obtain all these results for the discrete models a mathematical analysis is carried out to illustrate some biological properties of the differential model SEIRS-VB, such as the non-negativity, boundedness, existence, and uniqueness. Using the next-generation method, the basic reproduction number associated with the model in the autonomous case is defined. The local stability of the disease-free equilibrium point is studied. Finally, a sensitivity analysis of the basic reproduction number is performed.

A Computational Approach for the Characterization of Airborne Pathogen Transmission in Turbulent Molecular Communication Channels

Airborne pathogen transmission mechanisms play a key role in the spread of infectious diseases such as COVID-19. In this work, we propose a computational fluid dynamics (CFD) approach to model and statistically characterize airborne pathogen transmission via pathogen-laden particles in turbulent channels from a molecular communication viewpoint. To this end, turbulent flows induced by coughing and the turbulent dispersion of droplets and aerosols are modeled by using the Reynolds-averaged Navier-Stokes equations coupled with the realizable k-model and the discrete random walk model, respectively. Via simulations realized by a CFD simulator, statistical data for the number of received particles are obtained. These data are post-processed to obtain the statistical characterization of the turbulent effect in the reception and to derive the probability of infection. Our results reveal that the turbulence has an irregular effect on the probability of infection, which shows itself by the multi-modal distribution as a weighted sum of normal and Weibull distributions. Furthermore, it is shown that the turbulent MC channel is characterized via multi-modal, i.e., sum of weighted normal distributions, or stable distributions, depending on the air velocity. Crown

Modeling the influence of the information domain on countermeasure effectiveness in case of COVID-19

A common way to model an epidemic — restricted to contagion aspects only — is a modification of the Kermack-McKendrick SIR Epidemic model (SIR model) with differential equations. (Mis-)Information about epidemics may influence the behavior of the people and thus the course of epidemics as well. We have thus coupled an extended SIR model of the COVID-19 pandemic with a compartment model of the (mis-)information-based attitude of the population towards epidemic countermeasures. The resulting combined model is checked concerning basic plausibility properties like positivity and boundedness. It is calibrated using COVID-19 data from RKI and attitude data provided by the COVID-19 Snapshot Monitoring (COSMO) study. The values of parameters without corresponding observation data have been determined using an L2-fit under mild additional assumptions. The predictions of the calibrated model are essentially in accordance with observations. An uncertainty analysis of the model shows, that our results are in principle stable under measurement errors. We also assessed the scale, at which specific parameters can influence the evolution of epidemics. Another result of the paper is that in a multi-domain epidemic model, the notion of controlled reproduction number has to be redefined when being used as an indicator of the future evolution of epidemics.

A mathematical model and simulation scenarios for T and B cells immune response to severe acute respiratory syndrome-coronavirus-2

Severe acute respiratory syndrome coronavirus is a type 2 highly contagious, and transmissible among humans;the natural human immune response to severe acute respiratory syndrome-coronavirus-2 combines cell-mediated immunity (lymphocyte) and antibody production. In the present study, we analyzed the dynamic effects of adaptive immune system cell activation in the human host. The methodology consisted of modeling using a system of ordinary differential equations;for this model, the equilibrium free of viral infection was obtained, and its local stability was determined. Analysis of the model revealed that lymphocyte activation leads to total pathogen elimination by specific recognition of viral antigens;the model dynamics are driven by the interaction between respiratory epithelial cells, viral infection, and activation of helper T, cytotoxic T, and B lymphocytes. Numerical simulations showed that the model solutions match the dynamics involved in the role of lymphocytes in preventing new infections and stopping the viral spread;these results reinforce the understanding of the cellular immune mechanisms and processes of the organism against severe acute respiratory syndrome-coronavirus-2 infection, allowing the understanding of biophysical processes that occur in living systems, dealing with the exchange of information at the cellular level.

A fractional mathematical model with nonlinear partial differential equations for transmission dynamics of severe acute respiratory syndrome coronavirus 2 infection.

This study presents a fractional mathematical model based on nonlinear Partial Differential Equations (PDEs) of fractional variable-order derivatives for the host populations experiencing transmission and evolution of the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) pandemic. Five host population groups have been considered, the Susceptible, Exposed, Infected, Recovered, and Deceased (SEIRD). The new model, not introduced before in its current formulation, is governed by nonlinear PDEs with fractional variable-order derivatives. As a result, the proposed model is not compared with other models or real scenarios. The advantage of the proposed fractional partial derivatives of variable orders is that they can model the rate of change of subpopulation for the proposed model. As an efficient tool to obtain the solution of the proposed model, a modified analytical technique based on the homotopy and Adomian decomposition methods is introduced. Then again, the present study is general and is applicable to a host population in any country.

Development of parameter-free, two-fluid, viscous multiphase flow solver for cough-droplet simulations

Multiphase flows arise in various fields that involve complicated phenomena. Studies have shown that COVID-19 can occur via air microdroplets, and breathing jets with microdroplets turn into turbulent cloud or puffs in cases of coughing and sneezing (Bourouiba et al., 2014). Microdroplets are upturned by buoyancy in the turbulent cloud and transported without falling. Furthermore, they float in air for hours and can be transported over long distances (Mittal et al., 2020). This scenario also involves a mixed phase flow of air and droplets. To simulate these phenomena, a numerical model assuming mechanical and thermal non-equilibrium multiphase flow is required to predict the range of turbulent cloud transport. In this study, to better simulate the turbulent cloud trajectories, a viscosity term is added to a two-phase flow six-equation model (two-fluid modeling or effective-fluid modeling, EFM) developed by Liou et al. (2008). It is a development of a parameter-free, viscous multiphase flow code, based on a single-phase compressible finite-volume solver (Kitamura et al., 2013). This solver is validated in the Poiseuille flow and laminar-flat-plate problem with an isothermal wall through a comparison with the analytical solutions. A detailed simulation of coughing is performed. The location of the turbulent cloud upturned by buoyancy is compared with the data of past studies.

A multiconsistent computational methodology to resolve a diffusive epidemiological system with effects of migration, vaccination and quarantine.

BACKGROUND: We provide a compartmental model for the transmission of some contagious illnesses in a population. The model is based on partial differential equations, and takes into account seven sub-populations which are, concretely, susceptible, exposed, infected (asymptomatic or symptomatic), quarantined, recovered and vaccinated individuals along with migration. The goal is to propose and analyze an efficient computer method which resembles the dynamical properties of the epidemiological model. MATERIALS AND METHODS: A non-local approach is utilized for finding approximate solutions for the mathematical model. To that end, a non-standard finite-difference technique is introduced. The finite-difference scheme is a linearly implicit model which may be rewritten using a suitable matrix. Under suitable circumstances, the matrices representing the methodology are M-matrices. RESULTS: Analytically, the local asymptotic stability of the constant solutions is investigated and the next generation matrix technique is employed to calculate the reproduction number. Computationally, the dynamical consistency of the method and the numerical efficiency are investigated rigorously. The method is thoroughly examined for its convergence, stability, and consistency. CONCLUSIONS: The theoretical analysis of the method shows that it is able to maintain the positivity of its solutions and identify equilibria. The method's local asymptotic stability properties are similar to those of the continuous system. The analysis concludes that the numerical model is convergent, stable and consistent, with linear order of convergence in the temporal domain and quadratic order of convergence in the spatial variables. A computer implementation is used to confirm the mathematical properties, and it confirms the ability in our scheme to preserve positivity, and identify equilibrium solutions and their local asymptotic stability.

Estimating SARS-CoV-2 seroprevalence

Governments and public health authorities use seroprevalence studies to guide responses to the COVID-19 pandemic. Seroprevalence surveys estimate the proportion of individuals who have detectable SARS-CoV-2 antibodies. However, serologic assays are prone to misclassification error, and non-probability sampling may induce selection bias. In this paper, non-parametric and parametric seroprevalence estimators are considered that address both challenges by leveraging validation data and assuming equal probabilities of sample inclusion within covariate-defined strata. Both estimators are shown to be consistent and asymptotically normal, and consistent variance estimators are derived. Simulation studies are presented comparing the estimators over a range of scenarios. The methods are used to estimate severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) seroprevalence in New York City, Belgium, and North Carolina.

Identification of time delays in COVID-19 data

COVID-19 data released by public health authorities is subject to inherent time delays. Such delays have many causes, including delays in data reporting and the natural incubation period of the disease. We develop and introduce a numerical procedure to recover the distribution of these delays from data.We extend a previously-introduced compartmental model with a nonlinear, distributed-delay term with a general distribution, obtaining an integrodifferential equation. We show this model can be approximated by a weighted-sum of constant time-delay terms, yielding a linear problem for the distribution weights. Standard optimization can then be used to recover the weights, approximating the distribution of the time delays. We demonstrate the viability of the approach against data from Italy and Austria.We find that the delay-distributions for both Italy and Austria follow a Gaussian-like profile, with a mean of around 11 to 14 days. However, we note that the delay does not appear constant across all data types, with infection, recovery, and mortality data showing slightly different trends, suggesting the presence of independent delays in each of these processes. We also found that the recovered delay-distribution is not sensitive to the discretization resolution.These results establish the validity of the introduced procedure for the identification of time-delays in COVID-19 data. Our methods are not limited to COVID-19, and may be applied to other types of epidemiological data, or indeed any dynamical system with time-delay effects.

Transient zonal modeling of SARS-CoV-2 airborne infection risk for incomplete mixing air distribution methods

A widely used analytical model to quantitatively assess airborne infection risk is the Wells-Riley model based on the assumption of complete air mixing in a single zone. This study aimed to extend the Wells-Riley model so that the infection risk can be calculated in spaces where complete mixing is not present. This is done by evaluating the time-dependent distribution of infectious quanta in each zone and by solving the coupled system of differential equations based on the zonal quanta concentrations. In conclusion, this study shows that using the Wells-Riley model based on the assumption of completely mixing air may overestimate the long-range airborne infection risk compared to some high-efficiency ventilation systems such as displacement ventilation, but also underestimate the infection risk in a room heated with warm air supplied from the ceiling. © 2022 17th International Conference on Indoor Air Quality and Climate, INDOOR AIR 2022. All rights reserved.

Uncertain hypothesis test for uncertain differential equations

Uncertain hypothesis test is a statistical tool that uses uncertainty theory to determine whether some hypotheses are correct or not based on observed data. As an application of uncertain hypothesis test, this paper proposes a method to test whether an uncertain differential equation fits the observed data or not. In order to demonstrate the test method, some numerical examples are provided. Finally, both uncertain currency model and stochastic currency model are used to model US Dollar to Chinese Yuan (USD–CNY) exchange rates. As a result, it is shown that the uncertain currency model fits the exchange rates well, but the stochastic currency model does not.

New Control Chart Based On Neutrosophic Maxwell Distribution with Decision Making Applications

The neutrosophic approach is a potential area to provide a novel framework for dealing with uncertain data. This study aims to introduce the neutrosophic Maxwell distribution (M̃D) for dealing with imprecise data. The proposed notions are presented in such a manner that the proposed model may be used in a variety of circumstances involving indeterminate, ambiguous, and fuzzy data. The suggested distribution is particularly useful in statistical process control (SPC) for processing uncertain values in data collection. The existing formation of VSQ-chart is incapable of addressing uncertainty on the quality variables being investigated. The notion of neutrosophic VSQchart (Ṽ SQ) is developed based on suggested neutrosophic distribution. The parameters of the suggested Ṽ SQ-chart and other performance indicators, such as neutrosophic power curve (P̃C), neutrosophic characteristic curve (C̃C) and neutrosophic run length (R̃L) are established. The performance of the Ṽ SQ-chart under uncertain environment is also compared to the performance of the conventional model. The comparative findings depict that the proposed Ṽ SQ-chart outperforms in consideration of neutrosophic indicators. Finally, the implementation procedure for real data on the COVID-19 incubation period is explored to support the theoretical part of the proposed model © 2023,Neutrosophic Sets and Systems. All Rights Reserved.

The impact of security oversight on air cargo price and demand

This paper examines the effect of security oversight on air cargo price and demand. We exploit variations in security oversight instituted by the International Civil Aviation Organization (ICAO). We estimate a simultaneous equation model using proprietary operations data from a major airline in South Korea over the period 2009–2013. This study explores the shipping-charge behavior of a service provider through a modeling approach that considers air cargo security. Our findings show that security oversight increases air cargo demand, controlling for the effect of price. Improving security measures increases the air cargo price, but the magnitude of this increase is small. Our results should help policymakers gauge the benefit of improved security and help airlines design an effective model to determine future air cargo shipping charges under high uncertainty to mitigate short- and long-term financial risks.

Approach to the Impact of Digital Technologies on Sustainability Reporting through Structural Equation Modeling and Artificial Neural Networks

The motivation for study derives from the requirements imposed by the European Union Corporate Sustainability Reporting Directive, which increases the sustainability reporting scope and the need for companies to use emerging digital technologies. The research aim is to evaluate the digital transformation impact of the European Union companies on sustainability reporting expressed through three sustainable performance indicators (economic, social, and ecological) based on a conceptual model. The data were collected from Eurostat for 2011–2021. The study proposes a framework for sustainable performance analysis through linear regression models and structural equations. Additionally, a hierarchy of digitization indicators is created by modeling structural equations, depending on their impact on sustainability performance indicators, which is validated using neural networks. The results indicate that the company's digital transformation indicators positively influence economic and social performance and lead to an improved environmental protection (a decrease in pollution), proving the established hypotheses' validity. The proposed model can be the basis for companies to create their dashboards for analyzing and monitoring sustainable performance. This research can be the basis of other studies, having a significant role in establishing economic and environmental strategies to stimulate an increase of companies that carry out sustainability reporting.

Smart Embedded Framework of Real-Time Pollution Monitoring and Alert System

The sustainability and progress of humanity depend on a clean, pollution-free environment, which is essential for good health and hygiene. Huge indoor auditorium does not have proper ventilation for air flow so when the auditorium is crowded the carbon di-oxide is emitted and it stays there for many days this may be a chance to spreading of COVID-19 and other infectious diseases. Without proper ventilation virus may present in the indoor auditorium. In the proposed system, emissions are detected by air, noise, and dust sensors. If the signal limit is exceeded, a warning is given to the authorities via an Android application and WiFi, and data is stored in cloud networks. In this active system, CO2 sensor, noise sensor, dust sensor, Microcontroller and an exhaust fan are used. This ESP-32 based system is developed in Arduino Integrated Development Environment (Aurdino IDE) to monitor air, dust and noise pollution in an indoor auditorium to prevent unwanted health problems related to noise and dust. More importantly, using IoT Android Application is developed in Embedded C, which continuously records the variation in levels of 3 parameters mentioned above in cloud and display in Android screen. Also, it sends an alert message to the users if the level of parameters exceeds the minimum and maximum threshold values with more accuracy and sensitivity. Accuracy and sensitivity of this products are noted which is very high for various input values. © 2022 IEEE.

On a reaction–diffusion system modelling infectious diseases without lifetime immunity

In this paper, we study a mathematical model for an infectious disease caused by a virus such as Cholera without lifetime immunity. Due to the different mobility for susceptible, infected human and recovered human hosts, the diffusion coefficients are assumed to be different. The resulting system is governed by a strongly coupled reaction–diffusion system with different diffusion coefficients. Global existence and uniqueness are established under certain assumptions on known data. Moreover, global asymptotic behaviour of the solution is obtained when some parameters satisfy certain conditions. These results extend the existing results in the literature. The main tool used in this paper comes from the delicate theory of elliptic and parabolic equations. Moreover, the energy method and Sobolev embedding are used in deriving a priori estimates. The analysis developed in this paper can be employed to study other epidemic models in biological, ecological and health sciences.

THREE-DIMENSIONAL ANALYTICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION FOR AIR POLLUTION DISPERSION

We develop a new analytical solution of a three-dimensional atmospheric pollutant dispersion. The main idea is to subdivide vertically the planetary boundary layer into sub-layers, where the wind speed and eddy diffusivity assume average values for each sub-layer. Basically, the model is assessed and validated using data obtained from the Copenhagen diffusion and Prairie Grass experiments. Our findings show that there is a good agreement between the predicted and observed crosswind-integrated concentrations. Moreover, the calculated statistical indices are within the range of acceptable model performance.

The Analytic Solutions of the Fractional-Order Model for the Spatial Epidemiology of the COVID-19 Infection

This paper provides a mathematical fractional-order model that accounts for the mindset of patients in the transmission of COVID-19 disease, the continuous inflow of foreigners into the country, immunization of population subjects, and temporary loss of immunity by recovered individuals. The analytic solutions, which are given as series solutions, are derived using the fractional power series method (FPSM) and the residual power series method (RPSM). In comparison, the series solution for the number of susceptible members, using the FPSM, is proportional to the series solution, using the RPSM for the first two terms, with a proportional constant of ψΓnα+1, where ψ is the natural birth rate of the baby into the susceptible population, Γ is the gamma function, n is the nth term of the series, and α is the fractional order as the initial number of susceptible individuals approaches the population size of Ghana. However, the variation in the two series solutions of the number of members who are susceptible to the COVID-19 disease begins at the third term and continues through the remaining terms. This is brought on by the nonlinear function present in the equation for the susceptible subgroup. The similar finding is made in the series solution of the number of exposed individuals. The series solutions for the number of deviant people, the number of nondeviant people, the number of people quarantined, and the number of people recovered using the FPSM are unquestionably almost identical to the series solutions for same subgroups using the RPSM, with the exception that these series solutions have initial conditions of the subgroup of the population size. It is observed that, in this paper, the series solutions of the nonlinear system of fractional partial differential equations (PDEs) provided by the RPSM are more in line with the field data than the series solutions provided by the FPSM.