ANGELA CLARO TORRES - Academia.edu (original) (raw)

Papers by ANGELA CLARO TORRES

Vaccine, 2006

In this paper, we have considered a dynamical model of infectious disease that spread by asymptom... more In this paper, we have considered a dynamical model of infectious disease that spread by asymptomatic carriers and symptomatically infectious individuals with varying total population size, saturation incidence rate and discrete time delay to become infectious. It is assumed that there is a time lag (s) to account for the fact that an individual infected with bacteria or virus is not infectious until after some time after exposure. The probability that an individual remains in the latency period (exposed class) at least t time units before becoming infectious is given by a step function with value 1 for 0 6 t 6 s and value zero for t > s. The probability that an individual in the latency period has survived is given by e Àls , where l denotes the natural mortality rate in all epidemiological classes. Pulse vaccination is an effective and important strategy for the elimination of infectious diseases and so we have analyzed this model with pulse vaccination. We have defined two positive numbers R 1 and R 2. It is proved that there exists an infection-free periodic solution which is globally attractive if R 1 < 1 and the disease is permanent if R 2 > 1. The important mathematical findings for the dynamical behaviour of the infectious disease model are also numerically verified using MATLAB. Finally epidemiological implications of our analytical findings are addressed critically.

We study existence and approximation of solutions of some second order nonlinear periodic boundar... more We study existence and approximation of solutions of some second order nonlinear periodic boundary value problem of the type x00(t) = f(t; x; x0); t 2 (0; T ); x(0) = x(T ); x0(0) = x0(T ); in the presence of lower and upper solutions. We develop the upper and lower solutions method and the quasilinearization technique for the existence and approximation of solutions. We apply our theoretical results to a medical problem.

Nonlinear Analysis: Real World Applications, 2010

ABSTRACT Hepatitis B virus (HBV) infection is an important health problem worldwide. In this pape... more ABSTRACT Hepatitis B virus (HBV) infection is an important health problem worldwide. In this paper, we introduce an improved HBV model with standard incidence function and cytokine-mediated ‘cure’ based on empirical evidences. By carrying out a global analysis of the modified model and studying the stability of the equilibria, we show that infection-free equilibrium is globally asymptotically stable if the basic reproduction number of virus is less than one and, conversely, the infection equilibrium is globally asymptotically stable if the basic reproduction number of virus is greater than one. The study and information derived from this model and other related models may have an important impact on preventing mortality due to hepatitis B virus in the future.

Nonlinear Analysis: Real World Applications, 2012

An SIR epidemic model with state dependent pulse vaccination is proposed in this paper. Using the... more An SIR epidemic model with state dependent pulse vaccination is proposed in this paper. Using the Poincaré map, the differential inequality and the method of qualitative analysis, we prove the existence and the stability of positive order-1 or order-2 periodic solution for this model. Moreover, we show that there is no periodic solution with order larger than or equal to three. Numerical simulations are carried out to illustrate the feasibility of our main results and the suitability of state dependent pulse vaccination is also discussed.

Nonlinear Analysis: Theory, Methods & Applications, 2000

ABSTRACT The authors apply abstract results on equations of the type Lu=Nu which are based on the... more ABSTRACT The authors apply abstract results on equations of the type Lu=Nu which are based on the method of lower and upper solutions to a boundary value problem for a nonautonomous nonlinear second-order ordinary differential equation modelling intracraneal aneurysm.

Neurological Research, 2003

The basic hypothesis of this study is that the intracranial aneurysm may enlarge and rupture due ... more The basic hypothesis of this study is that the intracranial aneurysm may enlarge and rupture due to dynamic instabilities of the blood ow and pressure inside the aneurysm. The speci c question we attempted to answer is: which parameter(s) of aneurysmal geometry can serve as a reliable predictor(s) for aneurysmal rupture? We consider an idealized cylindrical aneurysm of the human common carotid artery and develop a mathematical model of blood ow through a normal artery and aneurysm connected in series. The mathematical model is nonlinear. It comprises nonlinear rheological properties of the normal artery and aneurysmal materials, and the inertial and resistance properties of the blood ow. The model equations were solved numerically and analyzed by methods of nonlinear dynamics. The critical aneurysmal diameter (CAD) is de ned as a boundary point between the stable and unstable states of the model equations. The results con rm that a limit point of ow stability can occur only for a certain difference between aneurysmal and artery radii which are pre-disposed from a difference in their material properties. It was shown that CAD is dependent on both aneurysmal length and age of patient. Finally, the results suggest that the ratio between aneurysmal and normal artery diameters is a more reliable predictor of the aneurysmal rupture than the diameter alone. We conclude that an aneurysm diameter twice that of the normal artery could be dangerous.

DNA Sequence, 2003

Given two DNA sequences, one is usually interested in measuring their similarity. For this purpos... more Given two DNA sequences, one is usually interested in measuring their similarity. For this purpose we have to consider different alignments of both the sequences. The number of alignments grows rapidly with the length of the sequences. In this short communication, we give an exact formula for the number of possible alignments using the theory of difference equations.

Journal of Theoretical Biology, 2010

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service... more This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Journal of Theoretical Biology, 2009

Journal of the Neurological Sciences, 2000

The formation and rupture of aneurysms is a significant medical problem, but is not clearly under... more The formation and rupture of aneurysms is a significant medical problem, but is not clearly understood. Most intracranial aneurysm are located in the circle of Willis. We consider a nonlinear mathematical model that simulates the blood flow inside the aneurysm, one of the relevant factors in the evolution of an aneurysm. Different techniques from nonlinear analysis are used in order to obtain, from the model, several consequences that would help to understand some medical aspects of aneurysms of the circle of Willis.

Journal of Biomedicine and Biotechnology, 2007

Pulse vaccination, the repeated application of vaccine over a defined age range, is gaining promi... more Pulse vaccination, the repeated application of vaccine over a defined age range, is gaining prominence as an effective strategy for the elimination of infectious diseases. An SIR epidemic model with pulse vaccination and distributed time delay is proposed in this paper. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution of the impulsive epidemic system and prove that the infection-free periodic solution is globally attractive if the vaccination rate is larger enough. Moreover, we show that the disease is uniformly persistent if the vaccination rate is less than some critical value. The permanence of the model is investigated analytically. Our results indicate that a large pulse vaccination rate is sufficient for the eradication of the disease.

Journal of Biomedicine and Biotechnology, 2006

The purpose of this paper is to present a general view of the current applications of fuzzy logic... more The purpose of this paper is to present a general view of the current applications of fuzzy logic in medicine and bioinformatics. We particularly review the medical literature using fuzzy logic. We then recall the geometrical interpretation of fuzzy sets as points in a fuzzy hypercube and present two concrete illustrations in medicine (drug addictions) and in bioinformatics (comparison of genomes).

Boundary Value Problems, 2009

A viral infection model with a nonlinear infection rate is constructed based on empirical evidenc... more A viral infection model with a nonlinear infection rate is constructed based on empirical evidences. Qualitative analysis shows that there is a degenerate singular infection equilibrium. Furthermore, bifurcation of cusp-type with codimension two i.e., Bogdanov-Takens bifurcation is confirmed under appropriate conditions. As a result, the rich dynamical behaviors indicate that the model can display an Allee effect and fluctuation effect, which are important for making strategies for controlling the invasion of virus.

BMC Bioinformatics, 2014

Background: In this study we consider DNA sequences as mathematical strings. Total and reduced al... more Background: In this study we consider DNA sequences as mathematical strings. Total and reduced alignments between two DNA sequences have been considered in the literature to measure their similarity. Results for explicit representations of some alignments have been already obtained. Results: We present exact, explicit and computable formulas for the number of different possible alignments between two DNA sequences and a new formula for a class of reduced alignments. Conclusions: A unified approach for a wide class of alignments between two DNA sequences has been provided. The formula is computable and, if complemented by software development, will provide a deeper insight into the theory of sequence alignment and give rise to new comparison methods.

Bioinformatics, 2003

Motivation: Any triplet codon may be regarded as a 12-dimensional fuzzy code. Sufficient informat... more Motivation: Any triplet codon may be regarded as a 12-dimensional fuzzy code. Sufficient information about a particular sequence may not be available in certain situations. The investigator will be confronted with imprecise sequences, yet want to make comparisons of sequences. Fuzzy polynucleotides can be compared by using geometrical interpretation of fuzzy sets as points in a hypercube. Results: We introduce the space of fuzzy polynucleotides and a means of measuring dissimilitudes between them. We establish mathematical principles to measure dissimilarities between fuzzy polynucleotides and present several examples in this metric space. We calculate the frequencies of the nucleotides at the three base sites of a codon in the coding sequences of Escherichia coli K-12 and Mycobacterium tuberculosis H37Rv, and consider them as points in that fuzzy space. We compute the distance between the genomes of E.coli and M.tuberculosis. Availability: Available on request from the authors. Con...

Artificial Intelligence in Medicine, 2007

As Dr. Sadegh-Zadeh indicates in his work [1], sequence analysis and sequence comparison are cruc... more As Dr. Sadegh-Zadeh indicates in his work [1], sequence analysis and sequence comparison are crucial in the exploration and comparison of genetic material. In a seminal paper [2], he fuzzified the concept of sequence and present different examples. Following his idea, we study the fuzzy polynucleotide space (FPS) in Ref. [3]. In our opinion, both approaches are of course related, but different. In the approach of Sadegh-Zadeh, one takes into account every letter in its corresponding order to compare two sequences. Hence, one has to use huge vectors in order to represent a real genome like that of M. tuberculosis. In our approach, one needs only a vector with 12 components. Doing this corresponds to a projection from a high dimensional vector space to a 12-dimensional space thus some information is lost. It is like in the three-dimensional space. There are many vectors having the same projection along the same axis (for example x-axis). If one uses just this projection of course the vectors will appear to be the same although the most precise expression should be that we have vectors having the same projection. In this sense, our algorithm is a way to reduce the necessary information that one needs to keep in order to represent a large real genome. It is evident that information is lost in this procedure. The idea of using point sets representing a genome and distances between them has been used by many authors from different schools. In Ref. [3], we studied the genome of M. tuberculosis (4.4E06 bp) by projecting the sequence into the 12-dimensional FPS. Using the ideas of Sadegh-Zadeh, one would need to use a 1.76E09dimensional space. With the technology of [3], it is possible to obtain some useful information (for example to know the C + T content).

Artificial Intelligence in Medicine, 2003

Using Kosko&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;a... more Using Kosko&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s hypercube, we identify a fuzzy set with a point in a unit hypercube. A non-fuzzy or crisp subset of a set is a vertex of the hypercube. We introduce some new ideas: the definition of the fuzzy segment joining two given fuzzy subsets of a set, the set of midpoints between those two fuzzy subsets, and the set of equidistant points from given points. We present some basic properties and relations between these concepts and provide a complete description of fuzzy segments and midpoints. In the majority of cases, there is no unique midpoint; one has an infinite set of possibilities to choose from. This situation is totally different from classical Euclidean geometry where, for two given points, there is a unique midpoint. We use the obtained results to study two sets of medical data and present two applications in medicine: the fuzzy degree of two concurrent food and drug addictions, and a fuzzy representation of concomitant causal mechanisms of stroke.