Umar Mallam Abdulkarim  , 
    Review of SIR Epidemic Model with Application To Transmission Dynamics of HIV/AIDS in a Proportional Mixing Population,
    Research Journal of Applied Sciences,
    Volume 2,Issue 5,
    2007,
    Pages 595-599,
    ISSN 1815-932x,
    rjasci.2007.595.599,
    (https://makhillpublications.co/view-article.php?doi=rjasci.2007.595.599)
    Abstract: In this study, we examined, the Susceptibles-Infectives-Removed/Recovered, (SIR) epidemic model and applied it to horizontal transmission of HIV/AIDS in a homogeneous mixing population. with additional assumption that AIDS virus does not kill instead;  AIDS-infectives are removed from circulation until death by non disease induced. Also the stability of the equilibrium points are examined via the basic reproductive number of the infection and trace-determinant condition of the Jacobian matrix at the equilibrium point, for a system of non-linear differential equation. The threshold conditions on the model parameters, which allows stability of the disease-free equilibrium and the endemic equilibrium points are derived and their biological interpretations given.
    Keywords: Basic reproductive number;infectivity kernel;HIV;AIDS;transmission rate;stability;vital dynamics;transmission dynamics;disease free-equilibrium point;endemic equilibrium point;transmissibility of the virus;epidemics