Open AccessStability Analysis of SEIL Tuberculosis Epidemic Model with Logistic Growth in Susceptible Compartment
Author(s) -
Joko Harianto
Publication year - 2021
Publication title -
asm science journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.12
H-Index - 6
eISSN - 2682-8901
pISSN - 1823-6782
DOI - 10.32802/asmscj.2021.733
Subject(s) - equilibrium point , basic reproduction number , stability theory , stability (learning theory) , mathematical economics , epidemic model , mathematics , reproduction , population , tuberculosis , computer science , ecology , biology , physics , demography , mathematical analysis , nonlinear system , medicine , sociology , quantum mechanics , machine learning , differential equation , pathology
This article discusses modifications to the SEIL model that involve logistical growth. This model is used to describe the dynamics of the spread of tuberculosis disease in the population. The existence of the model's equilibrium points and its local stability depends on the basic reproduction number. If the basic reproduction number is less than unity, then there is one equilibrium point that is locally asymptotically stable. The equilibrium point is a disease-free equilibrium point. If the basic reproduction number ranges from one to three, then there are two equilibrium points. The two equilibrium points are disease-free equilibrium and endemic equilibrium points. Furthermore, for this case, the endemic equilibrium point is locally asymptotically stable.