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Appl Math Comput 2022 Oct 8;431:127312. Epub 2022 Jun 8.

Mari State University, 424020 Lenin sqr. 1, Yoshkar-Ola, Russia.

We investigate a class of iteratively regularized methods for finding a quasi-solution of a noisy nonlinear irregular operator equation in Hilbert space. The iteration uses an a priori stopping rule involving the error level in input data. In assumptions that the Frechet derivative of the problem operator at the desired quasi-solution has a closed range, and that the quasi-solution fulfills the standard source condition, we establish for the obtained approximation an accuracy estimate linear with respect to the error level. Read More

Appl Math Comput 2022 May 15;421:126911. Epub 2022 Jan 15.

Business School, University of Shanghai for Science and Technology, 334 Jungong Road, Shanghai, 200093, China.

Dimension governs dynamical processes on networks. The social and technological networks which we encounter in everyday life span a wide range of dimensions, but studies of spreading on finite-dimensional networks are usually restricted to one or two dimensions. To facilitate investigation of the impact of dimension on spreading processes, we define a flexible higher-dimensional small world network model and characterize the dependence of its structural properties on dimension. Read More

Appl Math Comput 2021 Nov 12;408:126364. Epub 2021 May 12.

Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.

The world is going through a critical period due to a new respiratory disease called coronavirus disease 2019 (COVID-19). This disease is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Mathematical modeling is one of the most important tools that can speed up finding a drug or vaccine for COVID-19. Read More

Appl Math Comput 2021 Sep 8;405:126273. Epub 2021 Apr 8.

Departamento de Control Automático, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional. Av Instituto Politécnico Nacional 2508, San Pedro Zacatenco, Gustavo A. Madero, Mexico City 07360, Mexico.

Due to the current COVID-19 pandemic, much effort has been put on studying the spread of infectious diseases to propose more adequate health politics. The most effective surveillance system consists of doing massive tests. Nonetheless, many countries cannot afford this class of health campaigns due to limited resources. Read More

Appl Math Comput 2021 Sep 1;404:126251. Epub 2021 Apr 1.

Agricultural and Ecological Research Unit, Indian Statistical Institute, Kolkata 700108, West Bengal, India.

An outbreak of respiratory disease caused by a novel coronavirus is ongoing from December 2019. As of December 14, 2020, it has caused an epidemic outbreak with more than 73 million confirmed infections and above 1.5 million reported deaths worldwide. Read More

Appl Math Comput 2021 Aug 19;403:126172. Epub 2021 Mar 19.

School of Information and Control Engineering, Xi'an University of Architecture and Technology, Xi'an 710311, China.

Nowadays, vaccination is the most effective way to control the epidemic spreading. In this paper, an epidemic SEIRV (susceptible-exposed-infected-removed -vaccinated) model and an evolutionary game model are established to analyze the difference between mandatory vaccination method and voluntary vaccination method on heterogeneous networks. Firstly, we divide the population into four categories, including susceptible individuals, exposed individuals, infected individuals and removed individuals. Read More

Appl Math Comput 2021 Sep 19;404:126207. Epub 2021 Mar 19.

Department of Mathematics, Ramsaday College, Amta, Howrah 711401, India.

The ongoing pandemic situation due to COVID-19 originated from the Wuhan city, China affects the world in an unprecedented scale. Unavailability of totally effective vaccination and proper treatment regimen forces to employ a non-pharmaceutical way of disease mitigation. The world is in desperate demand of useful control intervention to combat the deadly virus. Read More

Appl Math Comput 2021 Mar 18;393. Epub 2020 Nov 18.

Department of Mathematics, Montclair State University, Montclair, NJ 07043.

Aggregation of proteins towards amyloid formation is a significant event in many neurodegenerative diseases. Low-molecular weight oligomers are considered to be the primary toxic agents in many of these maladies. Therefore, there is an increasing interest in understanding their formation and behavior. Read More

Appl Math Comput 2021 Jun 17;398:125983. Epub 2021 Jan 17.

School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China.

Social distancing can be divided into two categories: spontaneous social distancing adopted by the individuals themselves, and public social distancing promoted by the government. Both types of social distancing have been proved to suppress the spread of infectious disease effectively. While previous studies examined the impact of each social distancing separately, the simultaneous impacts of them are less studied. Read More

Appl Math Comput 2021 Mar 5;392:125715. Epub 2020 Oct 5.

Dipartimento di Studi Aziendali e Quantitativi, Università di Napoli "Parthenope", Via Generale Parisi, 13, Napoli I-80133, Italy.

This paper investigates the problem of defining an optimal long-term investment strategy, where the investor can exit the investment before maturity without severe loss. Our setting is a multi-period one, where the aim is to make a plan for allocating all of wealth among the assets within a time horizon of periods. In addition, the investor can rebalance the portfolio at the beginning of each period. Read More

Appl Math Comput 2021 Feb 10;390:125648. Epub 2020 Sep 10.

School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P.R.China.

This work applies a novel geometric criterion for global stability of nonlinear autonomous differential equations generalized by Lu and Lu (2017) to establish global threshold dynamics for several SVEIS epidemic models with temporary immunity, incorporating saturated incidence and nonmonotone incidence with psychological effect, and an SVEIS model with saturated incidence and partial temporary immunity. Incidentally, global stability for the SVEIS models with saturated incidence in Cai and Li (2009), Sahu and Dhar (2012) is completely solved. Furthermore, employing the DEDiscover simulation tool, the parameters in Sahu and Dhar'model are estimated with the 2009-2010 pandemic H1N1 case data in Hong Kong China, and it is validated that the vaccination programme indeed avoided subsequent potential outbreak waves of the pandemic. Read More

Appl Math Comput 2021 Jan 25;388:125536. Epub 2020 Jul 25.

Institute of Quantitative & Technical Economics, Chinese Academy of Social Sciences, Beijing 100732, China.

The interaction between epidemic spreading and information diffusion is an interdisciplinary research problem. During an epidemic, people tend to take self-protective measures to reduce the infection risk. However, with the diffusion of rumor, people may be difficult to make an appropriate choice. Read More

Appl Math Comput 2020 Nov 20;385:125428. Epub 2020 Jun 20.

Cybersecurity Research Institute, Sichuan University, Chengdu 610065, China.

Recent studies have demonstrated that the allocation of individual resources has a significant influence on the dynamics of epidemic spreading. In the real scenario, individuals have a different level of awareness for self-protection when facing the outbreak of an epidemic. To investigate the effects of the heterogeneous self-awareness distribution on the epidemic dynamics, we propose a resource-epidemic coevolution model in this paper. Read More

Appl Math Comput 2020 May 8;372. Epub 2020 Jan 8.

Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, USA.

This work focuses on the definition and study of the -dimensional -vector, an algorithm devised to perform orthogonal range searching in static databases with multiple dimensions. The methodology first finds the order in which to search the dimensions, and then, performs the search using a modified projection method. In order to determine the dimension order, the algorithm uses the -vector, a range searching technique for one dimension that identifies the number of elements contained in the searching range. Read More

Appl Math Comput 2019 Nov 19;361:87-97. Epub 2019 Jun 19.

Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, People's Republic of China.

Traditional infectious diseases models on metapopulation networks focus on direct transportations (e.g., direct flights), ignoring the effect of indirect transportations. Read More

Appl Math Comput 2019 Oct 14;359:512-524. Epub 2019 May 14.

School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China.

Numerous efforts have been devoted to investigating the network activities and dynamics of isolated networks. Nevertheless, in practice, most complex networks might be interconnected with each other (due to the existence of common components) and exhibit layered properties while the connections on different layers represent various relationships. These types of networks are characterized as multiplex networks. Read More

Appl Math Comput 2018 Sep 10;332:437-448. Epub 2018 Apr 10.

Complex Systems Research Center, Shanxi University, Taiyuan 030006, PR China.

The interaction between disease and disease information on complex networks has facilitated an interdisciplinary research area. When a disease begins to spread in the population, the corresponding information would also be transmitted among individuals, which in turn influence the spreading pattern of the disease. In this paper, firstly, we analyze the propagation of two representative diseases ( and ) in the real-world population and their corresponding information on Internet, suggesting the high correlation of the two-type dynamical processes. Read More

Appl Math Comput 2017 May 26;300:70-78. Epub 2016 Dec 26.

Biomedical Imaging Center, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, U.S.A.

The radiative transfer equation (RTE) arises in a wide variety of applications, in particular, in biomedical imaging applications associated with the propagation of light through the biological tissue. However, highly forward-peaked scattering feature in a biological medium makes it very challenging to numerically solve the RTE problem accurately. One idea to overcome the difficulty associated with the highly forward-peaked scattering is through the use of a delta-Eddington phase function. Read More

Appl Math Comput 2016 Jun 22;283:339-354. Epub 2016 Mar 22.

College of Science, Air Force Engineering University, Xi'an 710051, PR China.

In reality, the outbreak of emerging infectious diseases including SARS, A/H1N1 and Ebola are accompanied by the common cold and flu. The selective treatment measure for mitigating and controlling the emerging infectious diseases should be implemented due to limited medical resources. However, how to determine the threshold infected cases and when to implement the selective treatment tactics are crucial for disease control. Read More

Appl Math Comput 2015 Oct;268:717-727

PTC Inc., 41 West Otterman Street, Greensburg, PA 15601, USA.

The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversions using a fixed Talbot algorithm as well as on the ones using the Trefethen-Weideman-Schmelzer and maximum entropy methods are presented via a simulation study. Read More

Appl Math Comput 2016 Jan;272(Pt 1):148-158

Department CISE, University of Florida, USA.

Geometrically continuous ( ) constructions naturally yield families of finite elements for isogeometric analysis (IGA) that are also for non-tensor-product layout. This paper describes and analyzes one such concrete geometrically generalized IGA element (short: gIGA element) that generalizes bi-quadratic splines to quad meshes with irregularities. The new gIGA element is based on a recently-developed surface construction that recommends itself by its a B-spline-like control net, low (least) polynomial degree, good shape properties and reproduction of quadratics at irregular (extraordinary) points. Read More

Appl Math Comput 2015 Apr;256:37-51

Institute of Nonlinear Science and Engineering Computing, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, PR China.

Let [Formula: see text] be the open unit disk, [Formula: see text] an analytic self-map of [Formula: see text] and [Formula: see text] an analytic function on [Formula: see text]. Let be the differentiation operator and [Formula: see text] the weighted composition operator. The boundedness and compactness of the product-type operator [Formula: see text] from the weighted Bergman-Orlicz space to the Bers type space, weighted Bloch space and weighted Zygmund space on [Formula: see text] are characterized. Read More

Appl Math Comput 2013 Nov;224:205-215

Department of Mathematical Science, Montclair State University, Montclair, NJ 07043, United States.

Protein misfolding and concomitant aggregation towards amyloid formation is the underlying biochemical commonality among a wide range of human pathologies. Amyloid formation involves the conversion of proteins from their native monomeric states (intrinsically disordered or globular) to well-organized, fibrillar aggregates in a nucleation-dependent manner. Understanding the mechanism of aggregation is important not only to gain better insight into amyloid pathology but also to simulate and predict molecular pathways. Read More

Appl Math Comput 2014 Mar;231:357-376

Department of Mathematics, University of Southern California Los Angeles, CA 90089.

We develop a blind deconvolution scheme for input-output systems described by distributed parameter systems with boundary input and output. An abstract functional analytic theory based on results for the linear quadratic control of infinite dimensional systems with unbounded input and output operators is presented. The blind deconvolution problem is then reformulated as a series of constrained linear and nonlinear optimization problems involving infinite dimensional dynamical systems. Read More

Appl Math Comput 2014 Mar 23;230:473-483. Epub 2014 Jan 23.

Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada.

A general compartmental model of disease transmission is studied. The generality comes from the fact that new infections may enter any of the infectious classes and that there is an ordering of the infectious classes so that individuals can be permitted (or not) to pass from one class to the next. The model includes staged progression, differential infectivity, and combinations of the two as special cases. Read More

Appl Math Comput 2014 Feb 17;229:480-498. Epub 2014 Jan 17.

Mathematics Discipline, Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia.

This paper deals with the numerical study of population model based on the epidemics of Severe Acute Respiratory Syndrome (). (susceptible, exposed, infected, diagnosed, recovered) model of epidemic is considered with net in flow of individuals into a region. Transmission of disease is analyzed by solving the system of differential equations using numerical methods with different initial population distributions. Read More

Appl Math Comput 2014 Jan 12;226:83-100. Epub 2013 Nov 12.

Department of Applied Mathematics, University of Calcutta, Kolkata, West Bengal, India.

Choice of interaction function is one of the most important parts for modelling a food chain. Many models have been proposed as a diseased-prey predator model with Holling type-I or type-II or type-III interactions, but there is no model with general Holling type interactions. In this paper, we study a diseased prey-predator model with general Holling type interactions. Read More

Appl Math Comput 2013 Sep 2;221:786-801. Epub 2013 Aug 2.

College of Computer Science, Chongqing University, Chongqing 400044, China.

In this paper, by considering pathogen evolution and human interventions behaviors with vaccines or drugs, we build up a novel SEIRW model with the vaccination to the newborn children. The stability of the SEIRW model with time-varying perturbation to predict the evolution tendency of the disease is analyzed. Furthermore, we introduce a time-varying delay into the susceptible and infective stages in the model and give some global exponential stability criteria for the time-varying delay system. Read More

Appl Math Comput 2013 Apr;219(16):8730-8737

Biostatistics and Epidemiology Branch, Health Effects Laboratory Division, National Institute for Occupational Safety and Health, Morgantown, WV 26505, USA.

The problem of recovering a cumulative distribution function of a positive random variable via the scaled Laplace transform inversion is studied. The uniform upper bound of proposed approximation is derived. The approximation of a compound Poisson distribution as well as the estimation of a distribution function of the summands given the sample from a compound Poisson distribution are investigated. Read More

Appl Math Comput 2012 Sep;219(1):45-53

Institut für Computersprachen, Vienna University of Technology, Austria.

Axiomatization of Physics (and science in general) has many drawbacks that are correctly criticized by opposing philosophical views of science. This paper shows that, by giving formal proofs a more prominent role in the formalization, many of the drawbacks can be solved and many of the opposing views are naturally conciliated. Moreover, this approach allows, by means of proof theory, to open new conceptual bridges between the disciplines of Physics and Computer Science. Read More