Host model - Vector: Analysis of speed and simulations
DOI:
https://doi.org/10.17268/sel.mat.2018.02.05Keywords:
Epidemiology, SIR model, host model - vector, vital dynamics, Runge - KuttaAbstract
In epidemiological mathematics, the SIR model is well known, as well as the diseases that can be simulated with this model. In the present work starting from a SIR model with vital dynamics, a host-vector model is elaborated, where the transmission of the disease is no longer given by interaction of individuals of the same species, but is carried out by interaction of the susceptible individuals with the infected individuals, of both populations. Two host-vector models (MVH) with vital dynamics are also developed, initially maintaining the population constant, then with variable population and death due to disease.
References
Brauer, F., Driessche , P., Wu , J., editor. Mathemathical Epidemiology, volume 1945 of Lecture Notes in Mathematics. Springer, 2008.
Burden, R. L. and Faires, J. D. Numerical Analysis. BROOKS/COLE CENGAGE learning, USA, 2010.
Elama, J. The basic reproductive number: Bifurcation and stability. Master’s thesis, African Institute for Mathematical Sciences (AIMS), South Africa, Mayo 2009.
Fred,B., Castillo-Chávez, C. and De La Pava, E., editor. Modelos de la propagación de enfermedades infecciosas. Journal of Modelling and Simulation, Cali, Colombia, 2015.
Murray, J. D. Mathematical Biology. I. An introduction. Springer, 2002.
Roberts, M. G. and Heesterbeek, J. A. P. Characterizing the next-generationmatrix and basic reproduction number inecological epidemiology. Journal of Mathematical Biology, Berlin Heidelberg, 2012.
Syafruddin, S. and Salmi, Md. N. A SIR Model for Spread of Dengue Fever Disease (Simulation for South, volume 9. Journal of Modelling and Simulation, England, UK, 2013.
Wahyudin, S., Hirman, R.,Nurul, M., Muhammad, A. and Syafruddin, S. SIR Model Analysis for Transmission of Dengue Fever Disease with Climate Factors Using Lyapunov Function. Journal of Physics: Conference Series, Indonesia, 2018.
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.
