Joydip Dhar

Dynamics of an SEQIHRS epidemic model with media coverage, quarantine and isolation in a community with pre-existing immunity

Abstract An autonomous deterministic non-linear epidemic model SEQIHRS is proposed for the transmission dynamics of an infectious disease with quarantine and isolation control strategies in a community with pre-existing immunity. The model exhibits two equilibria, namely, the disease-free and a unique endemic equilibrium. The existence and local stability of the disease free and endemic equilibria are explored in terms of the effective reproduction number R C . It is observed that media coverage does not affect the effective reproduction number, but it helps to mitigate disease burden by lowering the number of infectious individuals at the endemic steady state and also lowering the infection peak. A new approach is proposed to estimate the coefficient of media coverage. Using the results of central manifold theory, it is established that as R C passes through unity, transcritical bifurcation occurs in the system and the unique endemic equilibrium is asymptotically stable. It is observed that the population level impact of quarantine and isolation depend on the level of transmission by the isolated individuals. Moreover, the higher level of pre-existing immunity in the population decreases the infection peak and causes its early arrival. Theoretical findings are supported by numerical simulation. Sensitivity analysis is performed for R C and state variables at endemic steady state with respect to model parameters.

Network Selection in Heterogeneous Wireless Environment: A Ranking Algorithm

Vertical handoff decision algorithms facilitate the terminal to be connected to the network which suffice the requirements of the application. It ushers the terminal to be connected to the most optimum network amongst those in the purview of the mobile terminal. The selection criterion involves multiple attributes. Although many ranking algorithms have been proposed, there is a need to lay a stress on the user requirements and the terminal power consumption. In this paper we propose a ranking algorithm keeping in view the user preferences and the application priorities. Having a close proximity with TOPSIS algorithm, the idea proposed overcomes the ranking abnormalities and scores high on efficiency.

Role of Delay on Planktonic Ecosystem in the Presence of a Toxic Producing Phytoplankton

A mathematical model is proposed to study the role of distributed delay on plankton ecosystem in the presence of a toxic producing phytoplankton. The model includes three state variables, namely, nutrient concentration, phytoplankton biomass, and zooplankton biomass. The release of toxic substance by phytoplankton species reduces the growth of zooplankton and this plays an important role in plankton dynamics. In this paper, we introduce a delay (time-lag) in the digestion of nutrient by phytoplankton. The stability analysis of all the feasible equilibria are studied and the existence of Hopf-bifurcation for the interior equilibrium of the system is explored. From the above analysis, we observe that the supply rate of nutrient and delay parameter play important role in changing the dynamical behaviour of the underlying system. Further, we have derived the explicit algorithm which determines the direction and the stability of Hopf-bifurcation solution. Finally, numerical simulation is carried out to support the theoretical result.

Modeling optimal release policy under fuzzy paradigm in imperfect debugging environment

Context: In this study, a software optimal release time with cost-reliability criteria has been discussed in an imperfect debugging environment. Objective: The motive of this study is to model uncertainty involved in estimated parameters of the software reliability growth model (SRGM). Method: Initially the reliability parameters of SRGM are estimated using least square estimation (LSE). Considering the uncertainty involved in the estimated parameters due to human behavior being subjective in nature and the dynamism of the testing environment, the concept of fuzzy set theory is applicable in developing SRGM. Finally, using arithmetic operations on fuzzy numbers, the reliability and total software cost are calculated. Results: Various reliability measures have been computed at different levels of uncertainties, and a comparison has been made with the existing results reported in the literature. Conclusion: It is evident from the results that a better prediction of reliability measures, namely, software reliability and total software cost can be made under the fuzzy paradigm.

Sequential combination of statistics, econometrics and Adaptive Neural-Fuzzy Interface for stock market prediction

Since last decade advanced data simulations help to identify hidden trends in a time series. Our purpose is to identify uncertainties during recession period using statistical analysis, econometrical analysis and Adaptive Neural-Fuzzy networks. In this paper, initially through computational analysis we are testing financial data using correlation tests, likelihood tests, heteroscedastic characteristics analysis and hypothesis tests. These statistical and econometrical tests give us exact nature of data set and relation between data points. All tests and analysis are studied on NASDAQ Stock Market over last 2-years. Then after, optimized subtractive data clustering method is used to cluster the data and create fuzzy membership functions by using Sugeno-type Fuzzy Interface System (FIS). Finally, we are using optimized hybrid learning algorithm in customized Adaptive Neural Fuzzy Interface System (ANFIS) to train the network. Hence, we got an efficient Adaptive Neural-Fuzzy network to check and test the data sets and use it for forecasting the stock market index. During this, the hybrid learning algorithm combines Least-Square method and the Back-propagation gradient descent methods for training the Fuzzy Interface System (FIS) with the help of optimized membership functions and parameters. This paper presents a state-of-art for Adaptive Neural-Fuzzy Network (ANFN) application to forecast stock market index and involved market uncertainties by combining the econometrical test to optimize the ANFIS and FIS function.

Minimal variability OWA operator combining ANFIS and fuzzy c-means for forecasting BSE index

Stock data sets usually consist of many varied components or multiple periods of stock prices, resulting in a tedious stock market prediction using such high dimensional data. To reduce data dimensions, it is crucial to fuse high dimensional data into a useful forecasting factor without losing information contained in the original variables. Decision makers may desire low variability associated with a chosen weighting vector, further complicating proper weight assignment for past stock prices. In this paper a new time series algorithm is proposed to overcome above mentioned shortcomings, which employs a minimal variation order weighted average (OWA) operator to aggregate values of high dimensional data into a single attribute. Based on the proposed model a hybrid network based fuzzy inference system combined with fuzzy c-means clustering is used to forecast Bombay Stock Exchange Index (BSE30).

Role of instant nutrient replenishment on plankton dynamics with diffusion in a closed system: A pattern formation

Abstract A mathematical model is proposed to study the role of instantaneous nutrient recycling on the plankton ecosystem. In this model, we include three state variables namely, nutrient biomass, phytoplankton and zooplankton population with Holling type II response function for the population density transformation from phytoplankton to zooplankton. It is obtained that the local stability of different equilibrium depends on the nutrient supply rate to the phytoplankton for the temporal system and also existence of the oscillatory behavior of the temporal system is established by using Bendixson–Dulac criteria. In the spatiotemporal model, we also determine the diffusion-driven instability condition, with the numerical support for the effect of diffusivity coefficients on chaotic behavior of the system. Furthermore, we obtained the instability condition for linear and no-linear system from the higher order stability analysis. Finally, we analyze the time evaluation pattern formation of the spatial system. This shows that it is useful to use the reaction–diffusion system to reveal the spatial dynamics in the real world.

Intelligent Biometric System using PCA and R-LDA

The paper presents a novel biometric authentication approach using Principal Component Analysis (PCA), Regularized-Linear Discriminant Analysis (R-LDA) and supervised neural networks. Low dimensional feature vectors of human face images are required to drive neural networks effectively. After histogram equalization process each image is presented to PCA or R-LDA for normalization and dimension reduction. The preprocessing steps of PCA or R-LDA produce Low dimensional feature vectors appropriate for training. Neural network has a great deal of nerve cell and can accomplish parallel distributing operation. Back Propagation (BP), Radial Basis Function(RBF) & Learning Vector Quantization (LVQ) are used as classifiers. The analysis of obtained results shown that R-LDA preprocessed feature vectors driven by supervised neural networks are having better recognition performance than PCA. While among supervised neural networks RBF gave most matched output during testing.

Software reliability growth modeling with dynamic faults and release time optimization using GA and MAUT

Abstract Software testing is an essential part of software life cycle as during this period, an effort is made to improve software reliability and quality. In this phase, perfect debugging is not possible because of time lag in fault removal process or new faults may get introduced in fault removal and fault detection process. In this paper, we have studied software reliability growth model (SRGM) incorporating generalized modified Weibull (GMW) testing effort function in imperfect debugging environment with constant and time varying fault detection rates, respectively. The parameters involved in the models are estimated using maximum likelihood estimation (MLE) and non-linear least square estimation (NLLSE) methods. The performance of the proposed models is validated using mean square error (MSE), accuracy of estimation (AE), χ 2 test, etc. Moreover, optimal release policy is discussed by keeping fault detection rate as a constant using both genetic algorithm (GA) and multi-attribute utility theory (MAUT). A comparison has been made with existing models reported in literature. From the empirical results, it is observed that our proposed models performed better. Further, the reliability measures are more factual in the case of time varying fault detection rate in comparison to constant fault detection rate model.

Discrete-time dynamics of a system with crowding effect and predator partially dependent on prey

In the present study, the stability and bifurcation analysis of discrete-time predator-prey system with predator partially dependent on prey and crowding effect of predator is examined. Global stability of the system at the fixed points has been discussed. The specific conditions for existence of flip bifurcation and Hopf bifurcation in the interior of R + 2 have been derived by using a center manifold theorem and bifurcation theory. Numerical simulations have been carried out to show the complex dynamical behavior of the system and to justify our analytic results. In case of flip bifurcation, numerical simulations presented cascade of period-doubling bifurcation in the orbits of period 2, 4, 8, chaotic orbits and stable window of period 9 orbit; whereas in case of Hopf bifurcation, smooth invariant circle bifurcates from the fixed point. The complexity of dynamical behavior is confirmed by computation of Lyapunov exponents.