# STABILITY ANALYSIS OF DISEASE FREE EQUILIBRIUM STATE (E_0 ) FOR AN ENDEMIC DETERMINISTIC MODEL FOR HIV/AIDS (Research Paper Sample)

This paper focused on determining the asymptotical stability of the new model which establishes that a disease-free equilibrium state exists and is locally asymptotically stable when the basic reproduction number 0≤R_0<1 and the following threshold conditions (0≤R_1<1, 0≤R_2<1, 0≤R_3<1, 0≤R_4<1 and 0≤R_5<1, 0≤R_6<1, 0≤R_7<1,0≤R_8<1) are satisfied. Results from the model analysis show that the proportion of infected juvenile and adult sub-population in the presence of High Active Antiretroviral Therapy (HAART) drastically reduces to a zero (R_0=0) as compared to the infected age-structured population when treatment rate is low and the net transmission rate is near zero.

source..STABILITY ANALYSIS OF DISEASE FREE EQUILIBRIUM STATE E0 FOR AN ENDEMIC DETERMINISTIC MODEL FOR HIV/AIDS

Victor A. O. and Oduwole, H. K.[Victor Alexander Okhuese, Department of Mathematics, Nasarawa State University, Keffi, NigeriaCorresponding Author’s ] [Department of Mathematics, Nasarawa State University, Keffi, Nigeria]

Abstract

This paper focused on determining the asymptotical stability of the new model which establishes that a disease-free equilibrium state exists and is locally asymptotically stable when the basic reproduction number 0≤R0<1 and the following threshold conditions (0≤R1<1, 0≤R2<1, 0≤R3<1, 0≤R4<1 and 0≤R5<1, 0≤R6<1, 0≤R7<1, 0≤R8<1) are satisfied. Results from the model analysis shows that the proportion of infected juvenile and adult sub-population in the presence of High Active Anteritroviral Therapy (HAART) drastically reduce to a zero (R0=0) as compared to the infected age-structured population when treatment rate is low and the net transmission rate is near zero.

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