Asymptotic Carrier Research Articles

Insight into the treatment strategy on pneumonia transmission with asymptotic carrier stage using fractional order modeling approach

Pneumonia remains a significant global health concern, claiming millions of lives annually. This study introduces a novel approach by developing and analyzing a Caputo fractional order pneumonia infection model that incorporates pneumonia asymptomatic carriers. Through a qualitative lens, we establish the existence and uniqueness of model solutions by applying the well-known Picard–Lindelöf criteria. Employing a next-generation approach, we compute the model's basic reproduction number, determine equilibrium points, and probe their stabilities. The main objective of this study is to investigate the transmission dynamics of pneumonia infection with a focus on asymptomatic carriers using fractional order modeling. Our findings reveal innovative outcomes as we showcase numerical simulations, providing a practical verification of the qualitative results. Notably, we explore the fractional order model solutions in-depth, examining the influence of specific model parameters and fractional orders on the dynamics of pneumonia disease transmission. The significant contributions of this study lie in advancing the theoretical foundation of infectious disease modeling, particularly in the context of pneumonia. Through rigorous analysis and numerical simulations, we provide valuable insights into the behavior of the proposed fractional order model. These findings hold practical implications for understanding and managing pneumonia transmission in real-world scenarios. Our study serves as a vital resource for researchers, policymakers, and healthcare practitioners involved in combating and preventing the spread of pneumonia, ultimately contributing to global efforts in public health.

Mathematical Modelling, Analysis of Novel Corona Disease, and Its Effect on the Human Being

The present study is about the outbreak of novel Corona disease (COVID-19). The study proposes the mathematical modelling of COVID-19 disease as quadratic growth. Correlation coefficient associated with the characteristic of the modelling trend has been obtained by least square method using matlab function. Analysis of variance show the model proposed is significant. The study gave the information about the transmission of the disease and the prevention observed by the medical practitioner. The graphical representation has shown the outcome of the spread of the disease in India. This disease can be of respiratory type, pneumonia type, or asymptotic carrier type. The simulation result obtained is in accordance to the quadratic model fitted and can be used for the prediction of the growth. Results obtained on the basis of R2 were of approximately 97% in agreement. The only possibilities to avoid the spread of the disease is to monitor self-isolation, maintain cleanliness, improve immunity, and be protected.

A fuzzy fractional model of coronavirus (COVID-19) and its study with Legendre spectral method

The virus which belongs to the family of the coronavirus was seen first in Wuhan city of China. As it spreads so quickly and fastly, now all over countries in the world are suffering from this. The world health organization has considered and declared it a pandemic. In this presented research, we have picked up the existing mathematical model of corona virus which has six ordinary differential equations involving fractional derivative with non-singular kernel and Mittag-Leffler law. Another new thing is that we study this model in a fuzzy environment. We will discuss why we need a fuzzy environment for this model. First of all, we find out the approximate value of ABC fractional derivative of simple polynomial function (t-a)n. By using this approximation we will derive and developed the Legendre operational matrix of fractional differentiation for the Mittag-Leffler kernel fractional derivative on a larger interval [0,b],b⩾1,b∈N. For the numerical investigation of the fuzzy mathematical model, we use the collocation method with the addition of this newly developed operational matrix. For the feasibility and validity of our method we pick up a particular case of our model and plot the graph between the exact and numerical solutions. We see that our results have good accuracy and our method is valid for the fuzzy system of fractional ODEs. We depict the dynamics of infected, susceptible, exposed, and asymptotically infected people for the different integer and fractional orders in a fuzzy environment. We show the effect of fractional order on the suspected, exposed, infected, and asymptotic carrier by plotting graphs.

A novel mathematical approach of COVID-19 with non-singular fractional derivative.

We analyze a proposition which considers new mathematical model of COVID-19 based on fractional ordinary differential equation. A non-singular fractional derivative with Mittag-Leffler kernel has been used and the numerical approximation formula of fractional derivative of function is obtained. A new operational matrix of fractional differentiation on domain [0, a], a ≥ 1, a ∈ N by using the extended Legendre polynomial on larger domain has been developed. It is shown that the new mathematical model of COVID-19 can be solved using Legendre collocation method. Also, the accuracy and validity of our developed operational matrix have been tested. Finally, we provide numerical evidence and theoretical arguments that our new model can estimate the output of the exposed, infected and asymptotic carrier with higher fidelity than the previous models, thereby motivating the use of the presented model as a standard tool for examining the effect of contact rate and transmissibility multiple on number of infected cases are depicted with graphs.

Dynamical features of pine wilt disease model with asymptotic carrier

The mathematical version for the transmission dynamics of pine wilt disease is explored, and its important mathematical features is analysed. Explicit formula for the reproduction number is calculated. Analytically, it is proved that the disease can be eradicated if the basic reproduction number becomes below unity. If this number exceeds unity, then a constant level of infectious and non-infectious classes is obtained. To explore the most influential factors for spread of the disease, we perform sensitivity analysis of the parameters. More interestingly, effective control programs have been designed on the basis of these sensitive parameters. Graphically, it has been shown that significant reduction has been occurred in the infected classes of pine trees by applying these controls.

Posterior concentration for a misspecified Bayesian regression model with functional covariates

We address a Bayesian regression model with a functional covariate and a scalar response. The model is misspecified in two ways: the posterior distribution is calculated by using normal errors and, mostly, by restraining the functional regression coefficient to a possibly small subset of L2([0,1]). A first general concentration result shows that the posterior distribution concentrates within Kullback–Leibler type neighborhoods of a set called the asymptotic carrier. This result is valid whether the asymptotic carrier is empty or not and includes the misspecified and the well specified cases. We focus on the particular misspecified case in which the functional regression parameter is restrained to a union of finite dimensional linear spaces. This restriction is motivated by the practical situation in which the functional regression parameter is expressed by a finite combination of B-splines with free knots. We provide sufficient conditions for the posterior concentration with respect to the norm of the parameter space along with a precise description of the asymptotic carrier.

A dynamical model of asymptomatic carrier zika virus with optimal control strategies

A dynamical model of asymptomatic carrier zika virus model with optimal control strategies is presented. The basic model zika without control and basic mathematical results are obtained. The stability results for the zika model without controls are obtained when the basic reproduction number is less than unity at the disease free case. We show that the zika model without controls is locally and globally asymptotically stable when the basic reproduction number is less than 1. Further, we show the model stability at the endemic equilibrium and present that the model at the endemic equilibrium is locally and globally asymptotically stable when R0>1. Further, for the case when R0=1, we analyze the model and presents its backward bifurcation, and it may have the phenomena of backward bifurcation if the conditions provided is satisfied. After that we chose the appropriate controls for the zika virus eliminations and formulated the zika control model. These controls are the preventions through bednets, the treatment of the infected individuals due to zika virus infection, and the insecticides spraying on mosquitoes. With these controls, the model and the optimal controls characterizations are obtained. Furthermore, we provided the existence of optimal control problem. The model with controls and the model without controls are solved numerically by using backward Runge–Kutta method and obtain the graphical results. The graphical results are obtained by setting appropriate set of controls and the associated results are shown. We show that each strategy has its own importance for the elimination of zika virus infection, but we suggest based on the numerical results that the uses of bednets as a prevention from the zika mosquitoes, the treatment of individuals infected through zika mosquitoes and the insecticides spraying on mosquitoes could be more useful for the elimination of zika virus infection from the community. With this new idea of asymptotic carrier class the results provided in the present paper would be more useful for public health department and other health agencies to reduce the burden of zika virus infection from the community.

A fast binary feedback-based distributed adaptive carrier synchronisation for transmission among clusters of disconnected IoT nodes in smart spaces

We propose a transmission scheme among groups of disconnected IoT devices in a smart space. In particular, we propose the use of a local random search implementation to speed up the synchronisation of carriers for distributed adaptive transmit beamforming. We achieve a sharp bound on the asymptotic carrier synchronisation time which is significantly lower than for previously proposed carrier synchronisation processes. Also, we consider the impact of environmental conditions in smart spaces on this synchronisation process in simulations and a case study.

Quantum Machine Using Cold Atoms

For a machine to be useful in practice, it preferably has to meet two requirements: namely, (i) to be able to perform work under a load and (ii) its operational regime should ideally not depend on the time at which the machine is switched-on. We devise a minimal setup, consisting of two atoms only, for an ac-driven quantum motor which fulfills both these conditions. Explicitly, the motor consists of two different interacting atoms placed into a ring-shaped periodic optical potential -- an optical "bracelet" --, resulting from the interference of two counter-propagating Laguerre-Gauss laser beams. This bracelet is additionally threaded by a pulsating magnetic flux. While the first atom plays a role of a quantum "carrier", the second serves as a quantum "starter", which sets off the "carrier" into a steady rotational motion. For fixed zero-momentum initial conditions the asymptotic carrier velocity saturates to a unique, nonzero value which becomes increasingly independent on the starting time with increasing "bracelet"-size. We identify the quantum mechanisms of rectification and demonstrate that our quantum motor is able to perform useful work.

Ac-Driven Atomic Quantum Motor

We propose an ac-driven quantum motor consisting of two different, interacting ultracold atoms placed into a ring-shaped optical lattice and submerged in a pulsating magnetic field. While the first atom carries a current, the second one serves as a quantum starter. For fixed zero-momentum initial conditions the asymptotic carrier velocity converges to a unique nonzero value. We also demonstrate that this quantum motor performs work against a constant load.

Characterization of the radiation-induced defects in Si detectors by carrier transport and decay transients

Temperature variations of the microwave probed photoconductivity (MW-PCD) transients have been shown to be a non-invasive tool for separation of recombination and trapping centers associated with radiation induced defects in Si detectors. Peaks in the asymptotic carrier decay lifetime temperature changes, attributed to carrier capture/recombination effects, are analyzed. The correlative investigations of the MW-PCD transients and kinetics of the carrier transit within detector are simultaneously performed in the proton irradiated Si pad detectors to clarify field redistribution effects. Carrier decay and transit regimes varying applied electric field are analyzed. The recombination and trapping lifetime variations with irradiation fluence are discussed.

Investigation of recombination parameters in silicon structures by infrared and microwave transient absorption techniques

Contactless techniques of infrared and microwave absorption by free carriers for the monitoring of silicon structures are described. Theoretical principles of photoconductivity decay analysis and methodology for the determination of recombination parameters are given for both homogeneous and non-homogeneous excess carrier generation. Different approximations (the methods of decay amplitude - asymptotic lifetime analysis, the simulation of the whole decay curve, the variation of effective lifetime with wafer thickness and the asymptotic lifetime measurement for stepwise varying parameters in layered structure) corresponding to real experimental conditions for various structures and treatments of materials, which are important for microelectronics, are discussed. The determined recombination parameters in the range of bulk lifetime , velocity of surface recombination and diffusion coefficient are illustrated for Si wafers obtained by various doping and preparation processes. The necessity to consider carrier trapping effects and nonlinear recombination processes is demonstrated by the analysis of experimental results obtained at different excitation levels for carrier concentrations in the range . The possibility of extracting the parameters of the traps (with activation energy values , and ) from the temperature-dependent asymptotic carrier lifetime measurements is illustrated for neutron transmutation doped wafers.

Sequential appearance of Epstein-Barr virus nuclear and lymphocyte-detected membrane antigens in B cell transformation.

One of the central questions of Epstein-Barr (EB) virus biology concerns the nature of the asymptotic carrier state1,2 whereby the virus, which in vitro transforms B cells into permanent lymphoblastoid cell lines with such efficiency3,4, is harboured for life in the B lymphoid tissues of all previously-infected (seropositive) individuals5. It seems highly probable that this persistent infection is primarily controlled by memory T cells (cytotoxic precursors) specifically primed to the EB virus-induced lymphocyte-detected membrane antigen LYDMA6–9. Thus the degree to which the infection can progress without interruption in individual B cells of the immune host will depend upon the timing of LYDMA expression relative to that of other viral gene functions. We now demonstrate that during EB virus-induced B cell transformation in vitro LYDMA is expressed on the cell surface soon after the appearance of the virus-associated nuclear antigen EBNA10 and coincident with, but not dependent upon, the initiation of cellular DNA synthesis. This suggests that in the lymphoid tissues of the infected host, immunological control over virus-B cell interactions can be exercised early in the cycle at the very onset of virus-induced cell proliferation.

Limiting Behavior of Posterior Distributions when the Model is Incorrect

The large sample behavior of posterior distributions is examined without the assumption that the model is correct. Under certain conditions it is shown that asymptotically, the posterior distribution for a parameter $\theta$ is confined to a set (called the asymptotic carrier) which may, in general, contain more than one point. The asymptotic carrier depends on the model, the carrier of the prior distribution and the actual distribution of the observations. An example shows that, in general, there need be no convergence (in any sense) of the posterior distribution to a limiting distribution over the asymptotic carrier. This is in contrast to the (known) asymptotic behavior when the model is correct; see e.g. [7], p. 304: the asymptotic carrier then contains only one point, the "true value" of $\theta$ and the posterior distribution converges in distribution to the distribution degenerate at the "true value."