Volume 5, Issue 6, December 2019, Page: 94-99
Global Stability of Critical Points for Type SIS Epidemiological Model
Edgar Ali Medina, Department of Science, Nueva Esparta Nucleus, Universidad de Oriente, Guatamare, Venezuela
Manuel Vicente Centeno-Romero, Department of Mathematics, School of Sciences, Sucre Nucleus, Universidad de Oriente, Cumaná, Venezuela
Fernando José Marval López, Department of Mathematics, School of Sciences, Sucre Nucleus, Universidad de Oriente, Cumaná, Venezuela
Received: Jul. 20, 2019;       Accepted: Aug. 19, 2019;       Published: Dec. 2, 2019
DOI: 10.11648/j.ijtam.20190506.13      View  516      Downloads  131
The construction of mathematical models is one of the tools used today for the study of problems in Medicine, Biology, Physiology, Biochemistry, Epidemiology, and Pharmacokinetics, among other areas of knowledge; its primary objectives are to describe, explain and predict phenomena and processes in these areas. The simulation, through mathematical models, allows exploring the impact of the application of one or several control measures on the dynamics of the transmission of infectious diseases, providing valuable information for decision-making with the objective of controlling or eradicating them. The mathematical models in Epidemiology are not only descriptive but also predictive, helping to prevent pandemics (epidemics that spread through large areas and populations) or by intervening in vaccination and drug acquisition policies. In this article we study the existence of periodic orbits and the general stability of the equilibrium points for a susceptible-infected-susceptible model (SIS), with a non-linear incidence rate. This type of model has been studied in many articles with a very particular incidence rate, here the novelty of the problem is that the aforementioned incidence rate is very general, in this sense this research provides a solution to an open problem. The methodology used is the Dulac technique, proceeding by reduction to the absurdity of the statement to the main test. It shows that the only point of equilibrium is asymptotically stable global. It can be noted that this problem may be subject to discretion or for equations in timescales. This can generate other research.
Periodic Orbits, Global Stability, Equilibrium Points
To cite this article
Edgar Ali Medina, Manuel Vicente Centeno-Romero, Fernando José Marval López, Global Stability of Critical Points for Type SIS Epidemiological Model, International Journal of Theoretical and Applied Mathematics. Vol. 5, No. 6, 2019, pp. 94-99. doi: 10.11648/j.ijtam.20190506.13
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