Open AccessANALYSIS OF TUBERCULOSIS DYNAMICAL MODEL WITH DIFFERENT EFFECTS OF TREATMENT
Author(s) -
A. H. Permatasari,
Robertus Heri Soelistyo Utomo
Publication year - 2021
Publication title -
journal of fundamental mathematics and applications
Language(s) - English
Resource type - Journals
eISSN - 2621-6035
pISSN - 2621-6019
DOI - 10.14710/jfma.v4i2.12049
Subject(s) - tuberculosis , equilibrium point , lyapunov function , stability (learning theory) , basic reproduction number , mathematics , control theory (sociology) , physics , demography , medicine , computer science , mathematical analysis , population , sociology , differential equation , control (management) , pathology , nonlinear system , quantum mechanics , machine learning , artificial intelligence
A tuberculosis model that integrates pre-infection and active infection stages along with two treatment parameters was studied. The model also considered the death rate due to pre-tuberculosis infection. The basic reproduction ratio was used to investigate the local and global stability of the equilibrium point. The local stability of uninfected equilibrium was analysed using Routh Hurwitz criteria. The existence of endemic equilibrium was given. After we achieved the endemic equilibrium, the global stability of the endemic equilibrium was analyzed using the Lyapunov function. A numerical simulation was studied to illustrate the effect of the treatment on the spread of the tuberculosis disease.