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Works (25)
Updated: April 4th, 2024 18:02
2020 journal article
Mechanistic model of hormonal contraception
PLOS COMPUTATIONAL BIOLOGY, 16(6).
MeSH headings : Adult; Contraceptive Agents / therapeutic use; Estrogens / therapeutic use; Female; Follicle Stimulating Hormone / physiology; Hormonal Contraception; Humans; Hypothalamus / drug effects; Luteinizing Hormone / physiology; Menstrual Cycle / drug effects; Models, Biological; Ovary / drug effects; Pituitary Gland / drug effects; Progestins / therapeutic use
TL;DR:
This new model predicts mean daily blood concentrations of key hormones during a contraceptive state achieved by administering progestins, synthetic estrogens, or a combined treatment, and shows that contraception can be achieved with synthetic estrogen, with progestin, and by combining the two hormones.
(via Semantic Scholar)
open access via journals.plos.org (publisher PDF)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science; OpenAlex)
5. Gender Equality
(Web of Science)
Source: Web Of Science
Added: August 24, 2020
2017 journal article
A model of ovulatory regulation examining the effects of insulin-mediated testosterone production on ovulatory function
JOURNAL OF THEORETICAL BIOLOGY, 416, 149–160.
author keywords: Polycystic ovary syndrome; Steroidogenesis
MeSH headings : Adult; Androgens / physiology; Female; Humans; Hyperinsulinism; Insulin / physiology; Insulin Resistance; Menstrual Cycle; Models, Theoretical; Ovulation; Polycystic Ovary Syndrome; Testosterone / biosynthesis; Testosterone / physiology
TL;DR:
A mathematical model of the menstrual cycle is presented that incorporates regulation by the pituitary-ovarian axis and mechanisms of ovarian testosterone production and suggests that variations in the response of ovarian follicles to essential signals can alter the degree to which hyperinsulinemia disrupts the ovulatory cycle.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(OpenAlex)
5. Gender Equality
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2015 journal article
A delay differential equation model of follicle waves in women
JOURNAL OF BIOLOGICAL DYNAMICS, 10(1), 200–221.
author keywords: Estradiol; parameter; pituitary gland; superfecundation; bifurcation
MeSH headings : Female; Gonadal Steroid Hormones / blood; Humans; Models, Theoretical; Ovarian Follicle / physiology; Ovulation; Pituitary Hormones / blood
TL;DR:
A mathematical model for hormonal regulation of the menstrual cycle which predicts the occurrence of follicle waves in normally cycling women and modifications of the model equations result in simulations which predict the possibility of two ovulations at different times during the same menstrual cycle and, hence, the occurrences of dizygotic twins via a phenomenon referred to as superfecundation.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2014 journal article
Bifurcation analysis of a menstrual cycle model reveals multiple mechanisms linking testosterone and classical PCOS
JOURNAL OF THEORETICAL BIOLOGY, 361, 31–40.
author keywords: Hysteresis; Parameters; Estradiol; Follicle; Pituitary
MeSH headings : Female; Humans; Luteinizing Hormone / metabolism; Menstrual Cycle; Models, Biological; Pituitary Gland / metabolism; Pituitary Gland / physiopathology; Polycystic Ovary Syndrome / metabolism; Polycystic Ovary Syndrome / physiopathology
TL;DR:
The model suggests that for some women androgenic activity at the levels of both the pituitary and the ovaries may contribute to the etiology of PCOS.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018
2014 journal article
Modeling endocrine regulation of the menstrual cycle using delay differential equations
MATHEMATICAL BIOSCIENCES, 257, 11–22.
author keywords: Bifurcation; Estradiol; Follicle; Parameter; Pituitary gland
MeSH headings : Estradiol / physiology; Female; Humans; Menstrual Cycle / physiology; Models, Biological; Pituitary Gland / physiology
TL;DR:
An effective mathematical procedure for modeling hormonal regulation of the menstrual cycle of adult women and correctly predicts blood levels of ovarian and pituitary hormones found in the biological literature for normally cycling women is reviewed.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018
2013 journal article
A lifelong model for the female reproductive cycle with an antimullerian hormone treatment to delay menopause
JOURNAL OF THEORETICAL BIOLOGY, 326, 21–35.
author keywords: Menstrual cycle; Primordial follicle; Parameter identification
MeSH headings : Adult; Anti-Mullerian Hormone / administration & dosage; Computer Simulation; Female; Humans; Longevity / physiology; Menopause / drug effects; Menstrual Cycle / drug effects; Menstrual Cycle / physiology; Middle Aged; Models, Biological; Primary Ovarian Insufficiency / prevention & control; Reproduction / physiology; Time Factors; Young Adult
TL;DR:
A system of 16 non-linear, delay differential equations with 66 parameters is developed to model hormonal regulation of the menstrual cycle of a woman from age 20 to 51 and shows that the transfer of non-growing primordial follicles to the active state can be slowed enough to provide more follicles for development later in life and to cause a delay in the onset of menopause.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
5. Gender Equality
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2013 journal article
Modeling Endocrine Control of the Pituitary-Ovarian Axis: Androgenic Influence and Chaotic Dynamics
BULLETIN OF MATHEMATICAL BIOLOGY, 76(1), 136–156.
author keywords: Modeling; Androgens
MeSH headings : Androgens / physiology; Computer Simulation; Feedback, Physiological; Female; Follicle Stimulating Hormone / physiology; Humans; Hypothalamo-Hypophyseal System / physiology; Luteinizing Hormone / physiology; Mathematical Concepts; Menstrual Cycle / physiology; Models, Biological; Nonlinear Dynamics; Ovarian Follicle / physiology; Ovary / physiology; Polycystic Ovary Syndrome / etiology; Polycystic Ovary Syndrome / physiopathology; Systems Biology
TL;DR:
It is shown that varying a follicular growth parameter produces preantral stockpiling and a period-doubling cascade resulting in apparent chaotic menstrual cycle behavior and a new model may allow investigators to study possible interventions returning acyclic patients to regular cycles and guide developments of individualized treatments for PCOS patients.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(OpenAlex)
5. Gender Equality
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2011 journal article
Dynamics and bifurcation of a model for hormonal control of the menstrual cycle with inhibin delay
MATHEMATICAL BIOSCIENCES, 234(2), 95–107.
author keywords: Estradiol; Follicle; Hill function; Degenerate Hopf bifurcation
MeSH headings : Computer Simulation; Estradiol / physiology; Female; Follicle Stimulating Hormone / antagonists & inhibitors; Follicle Stimulating Hormone / physiology; Humans; Inhibins / physiology; Menstrual Cycle / physiology; Models, Biological; Ovarian Follicle / physiology; Ovulation / physiology
TL;DR:
A system of 13 ordinary differential equations with 42 parameters is presented to model hormonal regulation of the menstrual cycle and requires a 36 h time delay for the effect of inhibin on the synthesis of follicle stimulating hormone.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2010 journal article
Bifurcation analysis of a model for hormonal regulation of the menstrual cycle
MATHEMATICAL BIOSCIENCES, 225(2), 108–114.
author keywords: Estradiol; Follicle; Parameter; Transcritical bifurcation
TL;DR:
To attain a normal ovulatory menstrual cycle in this model, a balance must be maintained between healthy development of the follicles and flexibility in estradiol levels needed to produce the surge in luteinizing hormone.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2009 journal article
A model for hormonal control of the menstrual cycle: Structural consistency but sensitivity with regard to data
JOURNAL OF THEORETICAL BIOLOGY, 260(4), 572–580.
author keywords: Estradiol; Follicle; Parameter; Bifurcation
MeSH headings : Estradiol / blood; Estradiol / physiology; Female; Gonadotropins, Pituitary / blood; Gonadotropins, Pituitary / physiology; Humans; Luteinizing Hormone / biosynthesis; Luteinizing Hormone / physiology; Menstrual Cycle / physiology; Models, Biological; Ovarian Follicle / physiology; Ovulation / physiology; Polycystic Ovary Syndrome / physiopathology
TL;DR:
A 13-dimensional system of delayed differential equations which predicts serum concentrations of five hormones important for regulation of the menstrual cycle and it is observed that models with greater early follicular growth rates may have a greater risk of cycling abnormally.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science; OpenAlex)
Source: Web Of Science
Added: August 6, 2018
2009 journal article
Dynamical behaviour of a discrete selection-migration model with arbitrary dominance
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 15(4), 371–385.
author keywords: natural selection; immigration; transgene; dominance; attractor
TL;DR:
The existence and uniqueness of a polymorphic genetic equilibrium is proved under a general assumption about dominance in fitnesses and conditions are found which guarantee the existence of and determine the location of the global attractor for this model.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
10. Reduced Inequalities
(OpenAlex)
Source: Web Of Science
Added: August 6, 2018
2007 article
Global attractors for a discrete selection model with periodic immigration
Selgrade, J. F., & Roberds, J. H. (2007, April). JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, Vol. 13, pp. 275–287.
author keywords: natural selection; periodic immigration; complete dominance; no dominance; global attractor
TL;DR:
A one-island selection-migration model is used to study the periodic immigration of a population of fixed allele frequency into a natural population and the existence and location of global attractors are established.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
10. Reduced Inequalities
(OpenAlex)
Source: Web Of Science
Added: August 6, 2018
2005 journal article
On a system of rational difference equations
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 11(7), 565–580.
author keywords: difference equation; global asymptotic stability; invariant set; monotone map; stable manifold
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2005 journal article
Results on asymptotic behaviour for discrete, two-patch metapopulations with density-dependent selection
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 11(4-5), 459–476.
author keywords: metapopulation; equilibrium; attractor; discrete population model
TL;DR:
A 4-dimensional system of nonlinear difference equations tracking allele frequencies and population sizes for a two-patch metapopulation model is studied and the concept of symmetric equilibrium is introduced and related to properties of allelic and genotypic fitness.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2003 journal article
Attractors for discrete periodic dynamical systems
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 286(1), 64–79.
TL;DR:
A structure theorem is established which says that the attractor of a time-periodic dynamical system is the union of attractors of appropriate autonomous maps, and properties that the nonautonomous attractor inherits from the autonomous attractor are discussed.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2003 journal article
Multiple stable periodic solutions in a model for hormonal control of the menstrual cycle
BULLETIN OF MATHEMATICAL BIOLOGY, 65(1), 157–173.
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2002 journal article
Global asymptotic behavior of a two-dimensional difference equation modelling competition
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 52(7), 1765–1776.
author keywords: asymptotic behavior; monotonicity; stability; stable manifold
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2001 journal article
On the structure of attractors for discrete, periodically forced systems with applications to population models
PHYSICA D, 158(1-4), 69–82.
author keywords: periodic forcing; attractors; discrete population models
TL;DR:
A method is presented which shows that if the amplitude of the k-periodic forcing is small enough then the attractor for the forced system is the union of k homeomorphic subsets.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
10. Reduced Inequalities
(OpenAlex)
Source: Web Of Science
Added: August 6, 2018
2000 journal article
A model of gonadotropin regulation during the menstrual cycle in women: Qualitative features
ENVIRONMENTAL HEALTH PERSPECTIVES, 108, 873–881.
author keywords: estradiol; follicle-stimulating hormone; luteinizing hormone; mathematical model; menstrual cycle; progesterone
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
2000 journal article
Dynamical analysis of density-dependent selection in a discrete one-island migration model
MATHEMATICAL BIOSCIENCES, 164(1), 1–15.
author keywords: selection; migration; genotype; density-dependence; bifurcation
MeSH headings : Alleles; Animals; Emigration and Immigration; Genetic Variation / genetics; Geography; Humans; Models, Genetic; Nonlinear Dynamics; Polymorphism, Genetic / genetics; Population Dynamics; Selection, Genetic
TL;DR:
A system of non-linear difference equations is used to model the effects of density-dependent selection and migration in a population characterized by two alleles at a single gene locus, and properties for a genetically important class of equilibria associated with complete dominance in fitness are described.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
1998 journal article
Using stocking or harvesting to reverse period-doubling bifurcations in discrete population models
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 4(2), 163–183.
author keywords: discrete models; period-doubling bifurcations and reversals; pioneer and climax populations
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
1997 journal article
Period-doubling bifurcations for systems of difference equations and applications to models in population biology
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 29(2), 185–199.
author keywords: discrete models; period-doubling bifurcation; Henon map; population genetics; pioneer and climax populations
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
1992 journal article
Dynamical behavior for population genetics models of differential and difference equations with nonmonotone fitnesses
Journal of Mathematical Biology, 30(8), 815.
Source: NC State University Libraries
Added: August 6, 2018
1987 journal article
CONVERGENCE TO EQUILIBRIUM IN A GENETIC MODEL WITH DIFFERENTIAL VIABILITY BETWEEN THE SEXES
JOURNAL OF MATHEMATICAL BIOLOGY, 25(5), 477–490.
MeSH headings : Alleles; Female; Fertility; Genotype; Humans; Male; Mathematics; Models, Genetic; Sex Characteristics; Survival
TL;DR:
A single locus, diallelic selection model with female and male viability differences is studied and every initial genotypic structure converges to an equilibrium structure assuming that no equilibrium has eigenvalues on the unit circle.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Source: Web Of Science
Added: August 6, 2018
1984 journal article
Dynamical behavior of differential equation models of frequency and density dependent populations
Journal of Mathematical Biology, 19(1), 133.
Source: NC State University Libraries
Added: August 6, 2018
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