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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Get The News Out Loudly And Quickly: Modeling The Influence Of The Media On Limiting Infectious Disease, Anna Mummert, Howard Weiss
Get The News Out Loudly And Quickly: Modeling The Influence Of The Media On Limiting Infectious Disease, Anna Mummert, Howard Weiss
Mathematics Faculty Research
During outbreaks of infectious diseases with high morbidity and mortality, individuals closely follow media reports of the outbreak. Many will attempt to minimize contacts with other individuals in order to protect themselves from infection and possibly death. This process is called social distancing. Social distancing strategies include restricting socializing and travel, and using barrier protections. We use modeling to show that for short-term outbreaks, social distancing can have a large influence on reducing outbreak morbidity and mortality. In particular, public health agencies working together with the media can significantly reduce the severity of an outbreak by providing timely accounts of …
Local Lagged Adapted Generalized Method Of Moments Dynamic Process, Gangaram S. Ladde, Olusegun M. Otunuga, Nathan G. Ladde
Local Lagged Adapted Generalized Method Of Moments Dynamic Process, Gangaram S. Ladde, Olusegun M. Otunuga, Nathan G. Ladde
Mathematics Faculty Research
Aspects of a local lagged adapted generalized method of moments (LLGMM) dynamic process are described herein. In one embodiment, the LLGMM process includes obtaining a discrete time data set as past state information of a continuous time dynamic process over a time interval, developing a stochastic model of the continuous time dynamic process, generating a discrete time interconnected dynamic model of local sample mean and variance statistic processes (DTIDMLSMVSP) based on the stochastic model, and calculating a plurality of admissible parameter estimates for the stochastic model using the DTIDMLSMVSP. Further, in some embodiments, the process further includes, for at least …
The Special Atom Space And Haar Wavelets In Higher Dimensions, Eddy Kwessi, G. De Souza, N. Djitte, M. Ndiaye
The Special Atom Space And Haar Wavelets In Higher Dimensions, Eddy Kwessi, G. De Souza, N. Djitte, M. Ndiaye
Mathematics Faculty Research
In this note, we will revisit the special atom space introduced in the early 1980s by Geraldo De Souza and Richard O'Neil. In their introductory work and in later additions, the space was mostly studied on the real line. Interesting properties and connections to spaces such as Orlicz, Lipschitz, Lebesgue, and Lorentz spaces made these spaces ripe for exploration in higher dimensions. In this article, we extend this definition to the plane and space and show that almost all the interesting properties such as their Banach structure, Hölder's-type inequalities, and duality are preserved. In particular, dual spaces of special atom …
Discrete Evolutionary Population Models: A New Approach, K. Mokni, Saber Elaydi, M. Ch-Chaoui, A. Eladdadi
Discrete Evolutionary Population Models: A New Approach, K. Mokni, Saber Elaydi, M. Ch-Chaoui, A. Eladdadi
Mathematics Faculty Research
In this paper, we apply a new approach to a special class of discrete time evolution models and establish a solid mathematical foundation to analyse them. We propose new single and multi-species evolutionary competition models using the evolutionary game theory that require a more advanced mathematical theory to handle effectively. A key feature of this new approach is to consider the discrete models as non-autonomous difference equations. Using the powerful tools and results developed in our recent work [E. D'Aniello and S. Elaydi, The structure of ω-limit sets of asymptotically non-autonomous discrete dynamical systems, Discr. Contin. Dyn. Series B. …
The Chebyshev Difference Equation, Tom Cuchta
The Chebyshev Difference Equation, Tom Cuchta
Mathematics Faculty Research
We define and investigate a new class of difference equations related to the classical Chebyshev differential equations of the first and second kind. The resulting “discrete Chebyshev polynomials” of the first and second kind have qualitatively similar properties to their continuous counterparts, including a representation by hypergeometric series, recurrence relations, and derivative relations.
Quantitative Analysis Of A Stochastic Seitr Epidemic Model With Multiple Stages Of Infection And Treatment, Olusegun M. Otunuga, Mobolaji O. Ogunsolu
Quantitative Analysis Of A Stochastic Seitr Epidemic Model With Multiple Stages Of Infection And Treatment, Olusegun M. Otunuga, Mobolaji O. Ogunsolu
Mathematics Faculty Research
We present a mathematical analysis of the transmission of certain diseases using a stochastic susceptible-exposed-infectious-treated-recovered (SEITR) model with multiple stages of infection and treatment and explore the effects of treatments and external fluctuations in the transmission, treatment and recovery rates. We assume external fluctuations are caused by variability in the number of contacts between infected and susceptible individuals. It is shown that the expected number of secondary infections produced (in the absence of noise) reduces as treatment is introduced into the population. By defining RT,n and ℛT,n as the basic deterministic and stochastic reproduction …
Dynamic Gompertz Model, Tom Cuchta, Sabrina Streipert
Dynamic Gompertz Model, Tom Cuchta, Sabrina Streipert
Mathematics Faculty Research
After a brief introduction that includes some fundamentals of time scales, we lay the foundation for dynamic Gompertz models. We derive their unique solutions, present examples in the discrete, quantum, and mixed time scale settings, and we compare its behavior to the solution in the continuous time setting. A discussion of the results and open problems are addressed in the conclusion.