The effect of delayed death in HIV/AIDS models

HIV-infected patients who receive treatment survive for some years after they have acquired the disease. The received treatment causes sustained reduction of viral reproduction by improving the immune function, leading to prolonged progression period to AIDS development. This prolonged progression period has created variability in survival times that affects estimates produced using mathematical models that do not include delay in disease related mortality. This paper investigates the effect of including delay in AIDS death occurrence in HIV/AIDS transmission models. A simple mathematical model with two stages of HIV progression is developed and extended to include time delay in the occurrence of AIDS deaths. Numerical simulations indicate that time delay changes the mortality curves considerably but has less effect on the proportion of infectives. The study highlights the importance of incorporating delay in models of HIV/AIDS for the production of accurate HIV/AIDS estimates.