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Volume 8, Issue 3, June 2020, Page: 145-157
A Mathematical Model Analysis on the Dynamics of HIV/AIDS with Age Structure and Inflow Immigrants in Ethiopia
Tibebu Tulu Guya, Department of Mathematics, Debre Berhan University, Debre Berhan, Ethiopia
Temesgen Tibebu Mekonnen, Department of Mathematics, Debre Berhan University, Debre Berhan, Ethiopia
Received: Apr. 22, 2020;       Accepted: May 15, 2020;       Published: May 29, 2020
Abstract
In this work we considered a nonlinear deterministic dynamical system to study the dynamics of HIV/AIDS with age structure and different mode of transmissions in Ethiopia. We found that the diseases free equilibrium point and endemic equilibrium points exist and we perform their local stability and global stability analysis using nonlinear stability methods. We found that the basic reproduction number of the considered dynamical system depends on the considered parameters and using real data collected from different health sectors in Ethiopia we found the numerical value of the reproduction number is R_0=1.05>1. This shows that the considered disease spreads in the community. From the sensitivity index of the dynamical system we found that the most sensitive parameter is the transmission rate of unaware infective humans to aware infectiveθ. We also showed that the effect of all parameters on the basic reproduction number using numerical simulation.
Keywords
Age Structure, HIV/AIDS Dynamics, Stability Analysis, Sensitivity Analysis, Numerical Simulation
Tibebu Tulu Guya, Temesgen Tibebu Mekonnen, A Mathematical Model Analysis on the Dynamics of HIV/AIDS with Age Structure and Inflow Immigrants in Ethiopia, American Journal of Applied Mathematics. Vol. 8, No. 3, 2020, pp. 145-157. doi: 10.11648/j.ajam.20200803.16
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