On fractional order models for Hepatitis C

A systematic review of the prediction of consumer preference using EEG measures and machine-learning in neuromarketing research

Introduction

The present paper discusses the findings of a systematic review of EEG measures in neuromarketing, identifying which EEG measures are the most robust predictor of customer preference in neuromarketing. The review investigated which TF effect (e.g., theta-band power), and ERP component (e.g., N400) was most consistently reflective of self-reported preference. Machine-learning prediction also investigated, along with the use of EEG when combined with physiological measures such as eye-tracking.

Methods

Search terms ‘neuromarketing’ and ‘consumer neuroscience’ identified papers that used EEG measures. Publications were excluded if they were primarily written in a language other than English or were not published as journal articles (e.g., book chapters). 174 papers were included in the present review.

Results

Frontal alpha asymmetry (FAA) was the most reliable TF signal of preference and was able to differentiate positive from negative consumer responses. Similarly, the late positive potential (LPP) was the most reliable ERP component, reflecting conscious emotional evaluation of products and advertising. However, there was limited consistency across papers, with each measure showing mixed results when related to preference and purchase behaviour.

Conclusions and implications

FAA and the LPP were the most consistent markers of emotional responses to marketing stimuli, consumer preference and purchase intention. Predictive accuracy of FAA and the LPP was greatly improved through the use of machine-learning prediction, especially when combined with eye-tracking or facial expression analyses.

Hepatitis C virus fractional-order model: mathematical analysis

Mathematical analysis of epidemics is crucial for the prediction of diseases over time and helps to guide decision makers in terms of public health policy. It is in this context that the purpose of this paper is to study a fractional-order differential mathematical model of HCV infection dynamics, incorporating two fundamental modes of transmission of the infection; virus-to-cell and cell-to-cell along with a cure rate of infected cells. The model includes four compartments, namely, the susceptible hepatocytes, the infected ones, the viral load and the humoral immune response, which is activated in the host to attack the virus. Each compartment involves a long memory effect that is modeled by a Caputo fractional derivative. Our paper starts with the investigation of some basic analytical results. First, we introduce some preliminaries about the needed fractional calculus tools. Next, we establish the well-posedness of our mathematical model in terms of proving the existence, positivity and boundedness of solutions. We present the different problem steady states depending on some reproduction numbers. After that, the paper moves to the stage of proving the global stability of the three steady states. To evaluate the theoretical study of the global stability, we apply a numerical method based on the fundamental theorem of fractional calculus as well as a three-step Lagrange polynomial interpolation method. The numerical simulations show that the free-endemic equilibrium is stable if the basic reproduction number is less than unity. In addition, the numerical tests demonstrate the stability of the other endemic equilibria under some optimal conditions. It is observed that the numerical simulations and the founding theoretical results are coherents.

Modeling the Adaptive Immune Response in an HBV Infection Model with Virus to Cell Transmission in Both Liver with CTL Immune Response and the Extrahepatic Tissue

The objective of this paper is to investigate a mathematical model describing the infection of hepatitis B virus (HBV) in intrahepatic and extrahepatic tissues. Additionally, the model includes the effect of the cytotoxic T cell (CTL) immunity, which is described by a linear activation rate by infected cells. The positivity and boundedness of solutions for non-negative initial data are proven, which is consistent with the biological studies. The local stability of the equilibrium is established. In addition to this, the global stability of the disease-free equilibrium and the endemic equilibrium is fulfilled by using appropriate Lyapanov functions. Finally, numerical simulations are performed to support our theoretical findings. It has been revealed that the fractional-order derivatives have no influence on the stability but only on the speed of convergence toward the equilibria.

Effect of DAA therapy in hepatitis C treatment - an impulsive control approach

In this article, we have presented a mathematical model to study the dynamics of hepatitis C virus (HCV) disease considering three populations namely the uninfected liver cells, infected liver cells, and HCV with the aim to control the disease. The model possesses two equilibria namely the disease-free steady state and the endemically infected state. There exists a threshold condition (basic reproduction number) that determines the stability of the disease-free equilibrium and the number of the endemic states. We have further introduced impulsive periodic therapy using DAA into the system and studied the efficacy of the DAA therapy for hepatitis C infected patients in terms of a threshold condition. Finally, impulse periodic dosing with varied rate and time interval is adopted for cost effective disease control for finding the proper dose and dosing interval for the control of HCV disease.

Spatio-temporal numerical modeling of reaction-diffusion measles epidemic system

In this work, we investigate the numerical solution of the susceptible exposed infected and recovered measles epidemic model. We also evaluate the numerical stability and the bifurcation value of the transmission parameter from susceptibility to a disease of the proposed epidemic model. The proposed method is a chaos free finite difference scheme, which also preserves the positivity of the solution of the given epidemic model.

On the solution of fractional order SIS epidemic model

We consider the fractional order epidemic model based on assumption that people will recover after disease and may be infected again on a time interval of non fatal disease. Our mathematical formulation is based on the fractional Caputo derivative. The existence and uniqueness of the solution is discussed. Furthermore, numerical solution is studied by variational iteration method and Euler method. Consequently, some numerical results are presented within.

Deterministic stability and random behavior of a Hepatitis C model

The deterministic stability of a model of Hepatitis C which includes a term defining the effect of immune system is studied on both local and global scales. Random effect is added to the model to investigate the random behavior of the model. The numerical characteristics such as the expectation, variance and confidence interval are calculated for random effects with two different distributions from the results of numerical simulations. In addition, the compliance of the random behavior of the model and the deterministic stability results is examined.

A fractional-order model of HIV infection: Numerical solution and comparisons with data of patients

In this paper, a fractional-order model which describes the human immunodeficiency type-1 virus (HIV-1) infection is presented. Numerical solutions are obtained using a generalized Euler method (GEM) to handle the fractional derivatives. The fractional derivatives are described in the Caputo sense. We show that the model established in this paper possesses non-negative solutions. Comparisons between the results of the fractional-order model, the results of the integer model and the measured real data obtained from 10 patients during primary HIV-1 infection are presented. These comparisons show that the results of the fractional-order model give predictions to the plasma virus load of the patients better than those of the integer model.

SOME APPLICATIONS OF FRACTIONAL ORDER CALCULUS TO DESIGN DIGITAL FILTERS FOR BIOMEDICAL SIGNAL PROCESSING

The goal of this paper is to describe some applications of fractional order calculus to biomedical signal processing with emphasis on the ability of this mathematical tool to remove noise, enhance useful information, and generate fractal signals. Three types of digital filters are considered, namely, lowpass differentiation filter, smoothing filter, and 1/fβ-noise generation filter. The filter impulse responses are functions of the fractional order and the sampling period only, and thus can be computed easily. Application examples are presented for illustrations.