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Analysis of a Model with Multiple Infectious Stages and Arbitrarily Distributed Stage Durations

Y. Yang, D. Xu, Z. Feng (2008)

Mathematical Modelling of Natural Phenomena

Infectious diseases may have multiple infectious stages with very different epidemiological attributes, including infectivity and disease progression. These stages are often assumed to have exponentially distributed durations in epidemiological models. However, models that use the exponential distribution assumption (EDA) may generate biased and even misleading results in some cases. This discrepancy is particularly damaging if the models are employed to assist policy-makers in disease control...

Analysis of The Impact of Diabetes on The Dynamical Transmission of Tuberculosis

D.P. Moualeu, S. Bowong, J.J. Tewa, Y. Emvudu (2012)

Mathematical Modelling of Natural Phenomena

Tuberculosis (TB) remains a major global health problem. A possible risk factor for TB is diabetes (DM), which is predicted to increase dramatically over the next two decades, particularly in low and middle income countries, where TB is widespread. This study aimed to assess the strength of the association between TB and DM. We present a deterministic model for TB in a community in order to determine the impact of DM in the spread of the disease....

Application of coupled neural oscillators for image texture segmentation and modeling of biological rhythms

Paweł Strumiłło, Michał Strzelecki (2006)

International Journal of Applied Mathematics and Computer Science

The role of relaxation oscillator models in application fields such as modeling dynamic systems and image analysis is discussed. A short review of the Van der Pol, Wilson-Cowan and Terman-Wang relaxation oscillators is given. The key property of such nonlinear oscillators, i.e., the oscillator phase shift (called the Phase Response Curve) as a result of external pulse stimuli is indicated as a fundamental mechanism to achieve and sustain synchrony in networks of coupled oscillators. It is noted...

Asymptotic behaviour of a discrete dynamical system generated by a simple evolutionary process

Iwona Karcz-Dulęba (2004)

International Journal of Applied Mathematics and Computer Science

A simple model of phenotypic evolution is introduced and analysed in a space of population states. The expected values of the population states generate a discrete dynamical system. The asymptotic behaviour of the system is studied with the use of classical tools of dynamical systems. The number, location and stability of fixed points of the system depend on parameters of a fitness function and the parameters of the evolutionary process itself. The influence of evolutionary process parameters on...

Backpropagation generalized delta rule for the selective attention Sigma-if artificial neural network

Maciej Huk (2012)

International Journal of Applied Mathematics and Computer Science

In this paper the Sigma-if artificial neural network model is considered, which is a generalization of an MLP network with sigmoidal neurons. It was found to be a potentially universal tool for automatic creation of distributed classification and selective attention systems. To overcome the high nonlinearity of the aggregation function of Sigma-if neurons, the training process of the Sigma-if network combines an error backpropagation algorithm with the self-consistency paradigm widely used in physics....

Bayesian methods in hydrology: a review.

David Ríos Insua, Raquel Montes Díez, Jesús Palomo Martínez (2002)

RACSAM

Hydrology and water resources management are inherently affected by uncertainty in many of their involved processes, including inflows, rainfall, water demand, evaporation, etc. Statistics plays, therefore, an essential role in their study. We review here some recent advances within Bayesian statistics and decision analysis which will have a profound impact in these fields.

Bilinear system as a modelling framework for analysis of microalgal growth

Štěpán Papáček, Sergej Čelikovský, Dalibor Štys, Javier Ruiz (2007)

Kybernetika

A mathematical model of the microalgal growth under various light regimes is required for the optimization of design parameters and operating conditions in a photobioreactor. As its modelling framework, bilinear system with single input is chosen in this paper. The earlier theoretical results on bilinear systems are adapted and applied to the special class of the so-called intermittent controls which are characterized by rapid switching of light and dark cycles. Based on such approach, the following...

Comparison of six models of antiangiogenic therapy

Andrzej Świerniak (2009)

Applicationes Mathematicae

Six models of antiangiogenic therapy are compared and analyzed from control-theoretic point of view. All of them consist of a model of tumor growth bounded by the capacity of a vascular network developed by the tumor in the process of angiogenesis and different models of dynamics of this network, and are based on the idea proposed by Hahnfeldt et al. Moreover, we analyse optimal control problems resulting from their use in treatment protocol design.

Competitive Exclusion in a Discrete Stage-Structured Two Species Model

A. S. Ackleh, P. Zhang (2009)

Mathematical Modelling of Natural Phenomena

We develop a stage-structured model that describes the dynamics of two competing species each of which have sexual and clonal reproduction. This is typical of many plants including irises. We first analyze the dynamical behavior of a single species model. We show that when the inherent net reproductive number is smaller than one then the population will go to extinction and if it is larger than one then an interior equilibrium exists and it is globally asymptotically stable. Then we analyze...

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