Biomedical subjects

Juan J Nieto

Publications and source records attributed to Juan J Nieto.

7 recordsLinked to original sources

PubMed2006

Analysis of a delayed epidemic model with pulse vaccination and saturation incidence.

Pulse vaccination is an important strategy for the elimination of infectious diseases. An SEIRS epidemic model with time delays and pulse vaccination is formulated 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 than theta*. Moreover, we show that the disease is uniformly persistent if the vaccination rate is less than theta*. The permanence of the model is investigated analytically. Our results indicate that a long latent period of the disease is sufficient condition for the extinction of the disease.

Disease Outbreaks↗

PubMed2006

Fuzzy polynucleotide spaces and metrics.

The study of genetic sequences is of great importance in biology and medicine. Mathematics is playing an important role in the study of genetic sequences and, generally, in bioinformatics. In this paper, we extend the work concerning the Fuzzy Polynucleotide Space (FPS) introduced in Torres, A., Nieto, J.J., 2003. The fuzzy polynucleotide Space: Basic properties. Bioinformatics 19(5); 587-592 and Nieto, J.J., Torres, A., Vazquez-Trasande, M.M. 2003. A metric space to study differences between polynucleotides. Appl. Math. Lett. 27:1289-1294: by studying distances between nucleotides and some complete genomes using several metrics. We also present new results concerning the notions of similarity, difference and equality between polynucleotides. The results are encouraging since they demonstrate how the notions of distance and similarity between polynucleotides in the FPS can be employed in the analysis of genetic material.

Algorithms↗

PubMed2006

Fuzzy logic in medicine and bioinformatics.

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).

Journal Article↗

PubMed2003

The fuzzy polynucleotide space: basic properties.

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.

Algorithms↗

PubMed2003

Midpoints for fuzzy sets and their application in medicine.

Using Kosko'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.

Adolescent↗

PubMed2003

An exact formula for the number of alignments between two DNA sequences.

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.

Algorithms↗

PubMed2003

Biomathematical modeling and analysis of blood flow in an intracranial aneurysm.

The basic hypothesis of this study is that the intracranial aneurysm may enlarge and rupture due to dynamic instabilities of the blood flow and pressure inside the aneurysm. The specific 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 flow 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 flow. The model equations were solved numerically and analyzed by methods of nonlinear dynamics. The critical aneurysmal diameter (CAD) is defined as a boundary point between the stable and unstable states of the model equations. The results confirm that a limit point of flow 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.

Cerebrovascular Circulation↗