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1.
Comput Stat Data Anal ; : 107616, 2022 Sep 16.
Article in English | MEDLINE | ID: covidwho-2031230

ABSTRACT

Checking the models about the ongoing Coronavirus Disease 2019 (COVID-19) pandemic is an important issue. Some famous ordinary differential equation (ODE) models, such as the SIR and SEIR models have been used to describe and predict the epidemic trend. Still, in many cases, only part of the equations can be observed. A test is suggested to check possibly partially observed ODE models with a fixed design sampling scheme. The asymptotic properties of the test under the null, global and local alternative hypotheses are presented. Two new propositions about U-statistics with varying kernels based on independent but non-identical data are derived as essential tools. Some simulation studies are conducted to examine the performances of the test. Based on the available public data, it is found that the SEIR model, for modeling the data of COVID-19 infective cases in certain periods in Japan and Algeria, respectively, maybe not be appropriate by applying the proposed test.

2.
Symmetry ; 14(8):1594, 2022.
Article in English | ProQuest Central | ID: covidwho-2024222

ABSTRACT

In this paper, we will consider three deterministic models for the study of the interaction between the human immune system and a virus: the logistic model, the Gompertz model, and the generalized logistic model (or Richards model). A qualitative analysis of these three models based on dynamical systems theory will be performed by studying the local behavior of the equilibrium points and obtaining the local dynamics properties from the linear stability point of view. Additionally, we will compare these models in order to understand which is more appropriate to model the interaction between the human immune system and a virus. Some natural medical interpretations will be obtained, which are available for all three models and can be useful to the medical community.

3.
Mathematics ; 10(16):2881, 2022.
Article in English | ProQuest Central | ID: covidwho-2023879

ABSTRACT

A new approach to dividing the mathematical content into partial modules is presented. This allows to compose subjects with mathematical content from such partial modules and flexibly adapt these subjects to the needs of specific study programs at technical universities. The consistent and systematic implementation of this approach in a typical learning management system is described in detail. This approach means significant changes in the massive (or bulk) delivery of knowledge using available information technologies. The main benefits of the presented system consist in the increase the resulting level of knowledge of students along with their satisfaction with the results and the form of their study. The most important changes arising from our approach are the following. First, the study process became distributed in space and in time. Second, it can be piecewise continuous in time, and, since all students can study at their own pace, it runs in multiple individual time scales. The most important change, however, is the shift of the paradigm the educational process from transmissive “teach–learn” to active “study”.

4.
International Journal of Modeling, Simulation, and Scientific Computing ; 2022.
Article in English | Web of Science | ID: covidwho-2020372

ABSTRACT

This work has two principal goals. First, we investigate the asymptotic behavior of a two-group epidemiological model and determine the expression of its basic reproduction number using the dynamical systems approach based on the spectral radius of the relative matrix. Second, we simulate the obtained analytical results using a new deep learning method that associates the ordinary differential equations governing the model to neural networks. A general disease-free equilibrium is considered and sufficient conditions of stability and convergence are formulated. A detailed description of the neural network model used in the simulation is provided. Moreover, the proposed deep learning simulation algorithm is compared to the simulation provided by "odeint", a function from "SciPy" which is a Python library of mathematical routines.

5.
Journal of Applied Mathematics ; : 1-9, 2022.
Article in English | Academic Search Complete | ID: covidwho-2001952

ABSTRACT

The outbreak of the Coronavirus (COVID-19) pandemic around the world has caused many health and socioeconomic problems, and the identification of variants like Delta and Omicron with similar and often even more transmissible modes of transmission has motivated us to do this study. In this article, we have proposed and analyzed a mathematical model in order to study the effect of health precautions and treatment for a disease transmitted by contact in a constant population. We determined the four equilibria of the system of ordinary differential equations representing the model and characterized their existence using exact methods of algebraic geometry and computer algebra. The model is studied using the stability theory for systems of differential equations and the basic reproduction number R 0 . The stability of the equilibria is analyzed using the Lienard-Chipart criterion and Lyapunov functions. The asymptotic or global stability of endemic equilibria is established, and the disease-free equilibrium is globally asymptotically stable if R 0 < 1. Model simulation is done with Python software to study the effects of health precautions and treatment, and the results are analyzed. It is observed that if the rate of treatment and compliance with health precautions are high, the number of infections decreases in the classes of infectious and is canceled out over time. It is concluded that the high treatment rate accompanied by a suitable rate of compliance with health precautions allows for the control the disease. [ FROM AUTHOR] Copyright of Journal of Applied Mathematics is the property of Hindawi Limited 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.)

6.
Sustainability ; 14(15):9066, 2022.
Article in English | ProQuest Central | ID: covidwho-1994153

ABSTRACT

The growing economic inequality around the world is recognized as a global problem of mankind. At the same time, the key tool for reducing inequality and ensuring the achievement of sustainable development goals is the taxation system given its distributive function. That is why this paper puts forward and proves a scientific hypothesis according to which direct taxation has a significant impact on economic inequality, with its scale and sphere depending on the level of economic development and the specific architecture of the tax system adopted in a particular country. The study relies on data from 28 European Union countries, including the United Kingdom, whose tax systems are not identical but harmonized in accordance with European Union directives, the same as the legislation in other economic sectors. Accordingly, it can be concluded that similar institutional characteristics are present. We have used the method of two-stage cluster analysis, which is meant for identifying the natural splitting of the mass of data into groups, then carried out regression analysis and built some models. The contribution of the study is revealing a number of important regularities that are significant for characterizing the dependence of income inequality on direct taxation as well as formulation recommendations for improving the tax policies of European Union countries, with the potential of policy implications. The results obtained can play a significant role in the development and further harmonization of tax systems and resolving the global problem of increased inequality within and between countries.

7.
International Journal on Electrical Engineering and Informatics ; 14(2):344-357, 2022.
Article in English | ProQuest Central | ID: covidwho-1964796

ABSTRACT

The emergence of the COVID-19 virus in the world and Indonesia since March 2020 has made it difficult for all elements of society. At the same time, there is one alternative solution to provide an overview to the public and the government so that they can take further action in dealing with the pandemic, that is by modeling the spread of COVID-19. One of the known disease modeling is SIR model, which is a model that divides individuals into certain groups/compartments. The SIR model and one of its derivatives, namely SIR-D, was developed to analyze and simulate several scenarios of the spread of a pandemic. There are 3 simulation scenarios made, namely a scenario without vaccination, a scenario with vaccination, and a scenario with vaccination without being accompanied by strict health protocols. The simulations of the models show that the vaccination process has an impact on reducing the spread of COVID-19, although it is less significant due to the vaccination process that is not optimal and comprehensive. Meanwhile, if the vaccination process is not carried out according to health protocols, then the spread of the pandemic will increase rapidly and form a second wave in Indonesia. This indicates that the vaccination process cannot be underestimated, and the public must continue to keep following health protocol. In general, it can be concluded that the epidemiological model used can provide an overview of the COVID-19's spread simulation with accuracy level MAPE, 0.41198 for the SIR model and 0.01712 for the SIR-D model.

8.
Computation ; 10(7):120, 2022.
Article in English | ProQuest Central | ID: covidwho-1963769

ABSTRACT

In this paper, a model for the transmission of respiratory syncytial virus (RSV) in a constant human population in which there exist super spreading infected individuals (who infect many people during a single encounter) is considered. It has been observed in the epidemiological data for the diseases caused by this virus that there are cases where some individuals are super-spreaders of the virus. We formulate a simply SEIrIsR (susceptible–exposed–regular infected–super-spreading infected–recovered) mathematical model to describe the dynamics of the transmission of this disease. The proposed model is analyzed using the standard stability method by using Routh-Hurwitz criteria. We obtain the basic reproductive number (R0) using the next generation method. We establish that when R0<1, the disease-free state is locally asymptotically stable and the disease endemic state is unstable. The reverse is true when R0>1, the disease endemic state becomes the locally asymptotically stable state and the disease-free state becomes unstable. It is also established that the two equilibrium states are globally asymptotically stable. The numerical simulations show how the dynamics of the disease change as values of the parameters in the SEIrIsR are varied.

9.
Nonlinear Dynamics ; 2022.
Article in English | Scopus | ID: covidwho-1959060

ABSTRACT

We analyze a mathematical model of COVID-19 transmission control, which includes the interactions among different groups of the population: vaccinated, susceptible, exposed, infectious, super-spreaders, hospitalized and fatality, based on a system of ordinary differential equations, which describes compartment model of a disease and its treatment. The aim of the model is to predict the development disease under different types of treatment during some fixed time period. We develop a game theoretic approach and a dual dynamic programming method to formulate optimal conditions of the treatment for an administration of a vaccine. Next, we calculate numerically an optimal treatment. © 2022, The Author(s), under exclusive licence to Springer Nature B.V.

10.
IEEE Transactions on Services Computing ; : 1-12, 2022.
Article in English | Scopus | ID: covidwho-1948862

ABSTRACT

The purpose of this study is to present a novel perspective on decision support based on the conventional SEIR pandemic model paradigm considering the risks and opportunities as physical forces deviating the expected performance trajectory of a system. The impact of a pandemic is measured by the deviation of the social system’s performance trajectory within the geometrical framework of its Key Performance Indicators (KPIs). According to the overall premise of utilizing Ordinary Differential Equations to simulate epidemics, the deviations are connected to several alternative interventions. The model is essentially built on two sets of parameters: (i) social system parameters and (ii) pandemic parameters. The ultimate objective is to propose a multi-criteria performance framework to control pandemics that includes a combination of timely measures. On the one hand, the current study optimizes prospective strategies to manage the potential future pandemic, while on the other hand, it explores the COVID-19 epidemic in the state of Georgia (USA). IEEE

11.
Sustainability ; 14(13):8032, 2022.
Article in English | ProQuest Central | ID: covidwho-1934251

ABSTRACT

Because the strategy of stopping bus lines during an epidemic can negatively impact residents, this study proposes a bus passenger flow control model to optimize the safety of and access to bus transport. The information interaction environment can provide a means for the two-way regulation of buses and passengers. In this model, passengers first request their pick-up and drop-off location, and then the bus feeds back information on whether it accepts the request. Through this method, passenger flow control can be realized through complete information interaction. The study aimed to establish a multi-objective function that minimizes the weighted total cost of the safety cost, the passenger travel cost, and the bus travel cost during an epidemic. The constraints were the full load and riding rates of urban buses in peak periods under the condition of epidemic prevention and control. The results showed that, in the morning peak period, the passenger flow control scheme reduced the passenger infection probability by 17.89%, compared with no passenger flow control scheme. The weighted total cost of the epidemic safety cost, the passenger travel cost, and the bus operation cost was reduced by 8.04%. The optimization effect of the passenger flow control scheme of this model is good, and not only reduces the probability of passengers being infected, but also meets the requirements of epidemic prevention and the travel needs of residents.

12.
Mathematical Problems in Engineering ; 2022, 2022.
Article in English | ProQuest Central | ID: covidwho-1932845

ABSTRACT

In the present investigation, new explicit approaches by the Milstein method and increment function of the Jacobian derivative of the drift coefficient are designed. Several numerical tests such as Cox–Ingersoll–Ross process, stochastic Brusselator, and Davis-Skodje system are presented to illustrate the accuracy and the efficiency of our schemes. Furthermore, we show that the strong convergence rate of our procedures is approximately one.

13.
35th Conference on Neural Information Processing Systems, NeurIPS 2021 ; 14:11364-11383, 2021.
Article in English | Scopus | ID: covidwho-1898139

ABSTRACT

Modeling a system's temporal behaviour in reaction to external stimuli is a fundamental problem in many areas. Pure Machine Learning (ML) approaches often fail in the small sample regime and cannot provide actionable insights beyond predictions. A promising modification has been to incorporate expert domain knowledge into ML models. The application we consider is predicting the patient health status and disease progression over time, where a wealth of domain knowledge is available from pharmacology. Pharmacological models describe the dynamics of carefully-chosen medically meaningful variables in terms of systems of Ordinary Differential Equations (ODEs). However, these models only describe a limited collection of variables, and these variables are often not observable in clinical environments. To close this gap, we propose the latent hybridisation model (LHM) that integrates a system of expert-designed ODEs with machine-learned Neural ODEs to fully describe the dynamics of the system and to link the expert and latent variables to observable quantities. We evaluated LHM on synthetic data as well as real-world intensive care data of COVID-19 patients. LHM consistently outperforms previous works, especially when few training samples are available such as at the beginning of the pandemic. © 2021 Neural information processing systems foundation. All rights reserved.

14.
Networks and Heterogeneous Media ; 17(3):333-357, 2022.
Article in English | Scopus | ID: covidwho-1875875

ABSTRACT

In this paper, we investigate the well-posedness and dynamics of a class of hybrid models, obtained by coupling a system of ordinary differential equations and an agent-based model. These hybrid models intend to integrate the microscopic dynamics of individual behaviors into the macroscopic evolution of various population dynamics models, and can be applied to a great number of complex problems arising in economics, sociology, geography and epidemiology. Here, in particular, we apply our general framework to the current COVID-19 pandemic. We establish, at a theoretical level, sufficient conditions which lead to particular solutions exhibiting irregular oscillations and interpret those particular solutions as pandemic waves. We perform numerical simulations of a set of relevant scenarios which show how the microscopic processes impact the macroscopic dynamics. © 2022, American Institute of Mathematical Sciences. All rights reserved.

15.
SIAM Journal on Control and Optimization ; 60(2):S221-S245, 2022.
Article in English | Scopus | ID: covidwho-1874687

ABSTRACT

In this paper, a distributed optimal control epidemiological model is presented. The model describes the dynamics of an epidemic with social distancing as a control policy. The model belongs to the class of continuous-time models, usually involving ordinary/partial differential equations, but has a novel feature. The core model-a single integral equation-does not explicitly use transition rates between compartments. Instead, it is based on statistical information on the disease status of infected individuals, depending on the time since infection. The approach is especially relevant for the coronavirus disease 2019 (COVID-19) in which infected individuals are infectious before onset of symptoms during a relatively long incubation period. Based on the analysis of the proposed optimal control problem, including necessary optimality conditions, this paper outlines some efficient numerical approaches. Numerical solutions show some interesting features of the optimal policy for social distancing, depending on the weights attributed to the number of isolated individuals with symptoms and to economic losses due to the enforcement of the control policy. The general nature of the model allows for inclusion of additional epidemic features with minor adaptations in the basic equations. Therefore, the modeling approach may contribute to the analysis of combined intervention strategies and to the guidance of public health decisions. © 2022 Society for Industrial and Applied Mathematics

16.
PLoS Computational Biology ; 18(4), 2022.
Article in English | ProQuest Central | ID: covidwho-1842856

ABSTRACT

We evaluate the efficiency of various heuristic strategies for allocating vaccines against COVID-19 and compare them to strategies found using optimal control theory. Our approach is based on a mathematical model which tracks the spread of disease among different age groups and across different geographical regions, and we introduce a method to combine age-specific contact data to geographical movement data. As a case study, we model the epidemic in the population of mainland Finland utilizing mobility data from a major telecom operator. Our approach allows to determine which geographical regions and age groups should be targeted first in order to minimize the number of deaths. In the scenarios that we test, we find that distributing vaccines demographically and in an age-descending order is not optimal for minimizing deaths and the burden of disease. Instead, more lives could be saved by using strategies which emphasize high-incidence regions and distribute vaccines in parallel to multiple age groups. The level of emphasis that high-incidence regions should be given depends on the overall transmission rate in the population. This observation highlights the importance of updating the vaccination strategy when the effective reproduction number changes due to the general contact patterns changing and new virus variants entering.

17.
Mathematics ; 10(9):1583, 2022.
Article in English | ProQuest Central | ID: covidwho-1842594

ABSTRACT

As the novel coronavirus pandemic has spread globally since 2019, most countries in the world are conducting vaccination campaigns. First, based on the traditional SIR infectious disease model, we introduce a positive feedback mechanism associated with the vaccination rate, and consider the time delay from antibody production to antibody disappearance after vaccination. We establish an UVaV model for COVID-19 vaccination with a positive feedback mechanism and time-delay. Next, we verify the existence of the equilibrium of the formulated model and analyze its stability. Then, we analyze the existence of the Hopf bifurcation, and use the multiple time scales method to derive the normal form of the Hopf bifurcation, further determining the direction of the Hopf bifurcation and the stability of the periodic solution of the bifurcation. Finally, we collect the parameter data of some countries and regions to determine the reasonable ranges of multiple parameters to ensure the authenticity of simulation results. Numerical simulations are carried out to verify the correctness of the theoretical results. We also give the critical time for controllable widespread antibody failure to provide a reference for strengthening vaccination time. Taking two groups of parameters as examples, the time of COVID-19 vaccine booster injection should be best controlled before 38.5 weeks and 35.3 weeks, respectively. In addition, study the impact of different expiration times on epidemic prevention and control effectiveness. We further explore the impact of changes in vaccination strategies on trends in epidemic prevention and control effectiveness. It could be concluded that, under the same epidemic vaccination strategy, the existence level of antibody is roughly the same, which is consistent with the reality.

18.
Hemato ; 2(3):441, 2021.
Article in English | ProQuest Central | ID: covidwho-1834787

ABSTRACT

In this paper, we explore the application of Chimeric Antigen Receptor (CAR) T cell therapy for the treatment of Acute Lymphocytic Leukaemia (ALL) by means of in silico experimentation, mathematical modelling through first-order Ordinary Differential Equations and nonlinear systems theory. By combining the latter with systems biology on cancer evolution we were able to establish a sufficient condition on the therapy dose to ensure complete response. The latter is illustrated across multiple numerical simulations when comparing three mathematically formulated administration protocols with one of a phase 1 dose-escalation trial on CAR-T cells for the treatment of ALL on children and young adults. Therefore, both our analytical and in silico results are consistent with real-life scenarios. Finally, our research indicates that tumour cells growth rate and the killing efficacy of the therapy are key factors in the designing of personalised strategies for cancer treatment.

19.
Complexity ; 2022, 2022.
Article in English | ProQuest Central | ID: covidwho-1832704

ABSTRACT

In this work, we study a stochastic SIS epidemic model with Lévy jumps and nonlinear incidence rates. Firstly, we present our proposed model and its parameters. We establish sufficient conditions for the extinction and persistence of the disease in the population using some stochastic analysis background. We illustrate our theoretical results by numerical simulations. We conclude that the white noise and Lévy jump influence the transmission of the epidemic.

20.
Discrete Dynamics in Nature and Society ; 2022, 2022.
Article in English | ProQuest Central | ID: covidwho-1807672

ABSTRACT

This work explores Routh–Hurwitz stability and complex dynamics in models for awareness programs to mitigate the spread of epidemics. Here, the investigated models are the integer-order model for awareness programs and their corresponding fractional form. A non-negative solution is shown to exist inside the globally attracting set (GAS) of the fractional model. It is also shown that the diseasefree steady state is locally asymptotically stable (LAS) given that R0 is less than one, where R0 is the basic reproduction number. However, as R0>1, an endemic steady state is created whose stability analysis is studied according to the extended fractional Routh–Hurwitz scheme, as the order lies in the interval (0,2]. Furthermore, the proposed awareness program models are numerically simulated based on the predictor-corrector algorithm and some clinical data of the COVID-19 pandemic in KSA. Besides, the model’s basic reproduction number in KSA is calculated using the selected data R0=1.977828168. In conclusion, the findings indicate the effectiveness of fractional-order calculus to simulate, predict, and control the spread of epidemiological diseases.

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