MODELING THE EFFECTIVENESS OF CONTROL MEASURES

Abstract

The lungs are a principal target of HIV-associated complications and persons with HIV-infection are at an increased risk for a wide spectrum of opportunistic Pneumonias. In this research an HIV/AIDS and Pneumonia co-infection model is presented and analyzed. The Pneumonia and HIV/AIDS sub-models are also presented and analyzed separately without any intervention strategy. Pneumonia is presented as a S.I.R. (Susceptible Infectious Recovered) simple epidemic model. On the other hand the HIV/AIDS is presented as an S.E.I.A. (Susceptible Exposed Infectious AIDS) model. The HIV/AIDS-only model has a globally asymptotically stable disease-free equilibrium when its corresponding reproduction number is less than unity. We proceed to analyze the full HIV/AIDS-Pneumonia co-infection model. The thresholds and equilibria quantities for the models are determined and stabilities analyzed. Secondly, parameters are used for the numerical simulations of the model system from data for both Pneumonia and HIV/AIDS cases sampled from Kapsabet District Hospital in Nandi County, Kenya for the period 2002 – 2011. Thirdly, the effectiveness of control of Pneumonia through treatment and management of HIV/AIDS epidemic through Education Awareness are studied. The minimum threshold for treatment is 97% and 72% for education computed both analytically and also by numerical simulation of the model system through Runge-Kutta method encoded in MATLAB.