Stability Theorems for a Mathematical Model SI with Vital Dynamics Structured by Sex for the Infection Free Steady developed by the Ordinary Differential Equations and the Delay Differential Equations respectively
DOI:
https://doi.org/10.17268/sel.mat.2017.02.07Keywords:
Mathematical Epidemiology, Ordinary Differential Equations, Delay Differential Equations, Stationary Points, Local stability, Asintotic EstabilityAbstract
In the present work, a Basic Model SI with Vital Dynamics Structured by Gender developed by the Ordinary Differential Equations (Transmission of contagion is instantaneous), and also developed in the Delay
Differential Equations (Transmission of contagion occurs after a certain period of time), where the Local and Asymptotic Stability Theorem is proposed The Free of Infection point for both models, respectively.
References
Barrios Ginart J., Marrero Severo A., Baguer Díaz-Romañach M., De Arazoza Rodríguez H. (2010). Estimación de parámetros en modelos epidemiológicos deVIH/SIDA. Revista de Matemática: Teoría y aplicaciones. CIMPA - UCR.
Erwin Forde Jonathan. Delay Differential Equation Model in Mathematical Biology. The University of Michigan, (2005).
Driver Rodney David. Ordinary and Delay Differential Equations. Mathl. Comput. Modelling Vol. 24, No. 9, pp. 63-68 (1996).
Gourley. S. A. Y Kuang Yang. A Stage Structured Predator-Prey Model and its dependence on Maturation Delay and Death Rate. J. Math. Biol., 49:188-200 (2004).
Kuang Yang. (2002). Basic Properties of Mathematical Population Models. Department of Mathematics and Statistics, Arizona State University.
López Cruz R. (2006). Structured SI Epidemic Models with Applications to HIV Epidemic. Arizona State University. pp. 27-45.
Mesa Mazo M, Vergao Salazar Juan, Sanchez Botero Claudia, Muoz Loaiza Anibal. (2010). Modelo matemático para la dinámica de transmisión del VIH/SIDA en una población sexualmente activa. Universidad de Quindio, Armenio, Colombia. Rev. Salud Pública 12,308-316.
Pino Romero N. (2013). Modelo matemático para la dinámica de transmisión del VIH/SIDA en una poblacián heterosexual activa en el Perú. Facultad de Ciencias Matemáticas, UNMSM.
Pino Romero N. (2017). An´alisis y Simulación Numérica de un Modelo Matemático SI con Retardo Discreto para las Enfermedades de Transmisión Sexual. Facultad de Ciencias Matemáticas, UNMSM.
Smith, H. (2010). An introduction to delay differential equations with applications to the life sciences (Vol. 57). Springer Science & Business Media.
W. O. Kermack & A. G. Mckendrick. (1927). A contribution to the Mathematical theory of Epidemics Proceedings of the Royal Society of London Series A, 115:700-721.
Published
How to Cite
Issue
Section
License
The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.
