Local Stability of AIDS Epidemic Model Through Treatment and Vertical Transmission with Time Delay

2015 International Conference on Mathematics, its Applications, and Mathematics Education

数学;教育

Cascarilla, Novi W.^1 ; Lestari, Dwi^1

Department of Mathematics Education, Yogyakarta State University, Yogyakarta, Indonesia^1

关键词: Asymptotically stable;    Basic reproduction number;    Disease-free equilibrium;    Endemic equilibrium;    Epidemic modeling;    Local stability;    Nonlinear differential equation;    Vertical transmission;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/693/1/012010/pdf
DOI  :  10.1088/1742-6596/693/1/012010

学科分类：发展心理学和教育心理学

来源: IOP

【 摘 要 】

This study aims to explain stability of the spread of AIDS through treatment and vertical transmission model. Human with HIV need a time to positively suffer AIDS. The existence of a time, human with HIV until positively suffer AIDS can be delayed for a time so that the model acquired is the model with time delay. The model form is a nonlinear differential equation with time delay, SIPTA (susceptible-infected-pre AIDS-treatment-AIDS). Based on SIPTA model analysis results the disease free equilibrium point and the endemic equilibrium point. The disease free equilibrium point with and without time delay are local asymptotically stable if the basic reproduction number is less than one. The endemic equilibrium point will be local asymptotically stable if the time delay is less than the critical value of delay, unstable if the time delay is more than the critical value of delay, and bifurcation occurs if the time delay is equal to the critical value of delay.