BIFURCATION ANALYSIS MATHEMATICAL MODEL FOR THE SPREAD OF EXOGENOUS REINFECTION TUBERCULOSIS

  • Rara Sandhy Winanda Department of Mathematics, Faculty of Mathematics and Natural Sciences, Padang State University, Indonesia
  • Defri Ahmad Department of Mathematics, Faculty of Mathematics and Natural Sciences, Padang State University, Indonesia
  • Sovia Helmi Putri Department of Mathematics, Faculty of Mathematics and Natural Sciences, Padang State University, Indonesia
  • Ariana Putri Department of Mathematics, Faculty of Mathematics and Natural Sciences, Padang State University, Indonesia
DOI: https://doi.org/10.30598/barekengvol17iss1pp0075-0084
Keywords: tuberculosis, exogenous reinfection, equilibrium point, bifurcation

Abstract

The spread of tuberculosis can occur in two ways, namely exogenous and endogenous. The spread of tuberculosis exogenously or Exogenous Reinfection of tuberculosis can be observed using a mathematical model. Then an analysis of the mathematical model with a bifurcation approach was carried out. Based on the result, it was found that there was a change in stability properties and the type of equilibrium point in the distribution equation system of exogenous reinfection tuberculosis, where the parameter that occurred bifurcation was , with . When value of  is smaller than zero, the system of differential equations of exogenous reinfection tuberculosis shows an unstable with a saddle point type, when the value of     is equal to zero the system of differential equations cannot be determined its stability, and when  system of differential equations shows asymptotic stability, where there is a change in species. The points are nodes, star nodes, and spirals.

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Published
2023-04-15
How to Cite
[1]
R. Winanda, D. Ahmad, S. Putri, and A. Putri, “BIFURCATION ANALYSIS MATHEMATICAL MODEL FOR THE SPREAD OF EXOGENOUS REINFECTION TUBERCULOSIS”, BAREKENG: J. Math. & App., vol. 17, no. 1, pp. 0075-0084, Apr. 2023.
Issue
Vol 17 No 1 (2023): BAREKENG: Journal of Mathematics and Its Applications
Section
Articles

Copyright (c) 2023 Defri Ahmad, Sovia Helmi Putri, Rara Sandhy Winanda, Ariana Putri

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