Mathematical analysis of a delayed HIV/AIDS model with treatment and vertical transmission
Gratien Twagirumukiza, Edouard Singirankabo
Abstract
None can underestimate the importance of mathematical modelling for their role in clarifying dynamics of epidemic diseases. They can project the progress of the disease and demonstrate the result of the epidemic to public health in order to take precautions. HIV attracts global attention due to rising death rates and economic burdens and many other consequences that it leaves behind. Up to date, there is no medicine and vaccine of HIV/AIDS but still many researches are conducted in order to see how to mitigate this epidemic and reduce the death rate or increase the life expectancy of those who are infected. A delayed HIV/AIDS treatment and vertical transmission model has been investigated. The model took into account both infected people from the symptomatics group and asymptomatic group to join AIDS group. We considered that a child can be infected from the mother to an embryo, fetus or childbirth. Those who are infected, it will take them some time to get mature and spread the disease. By using mathematical model, reproduction number, positivity, boundedness, and stability analysis were determined. The results showed that the model is much productive if time delay is considered.