Previous reports show that it is not uncommon for patients to have two viruses at the same time. At the current time, we do not know how to treat co-infections. In order to test the effects of having these concurrent infections, we simulate the two infections using a mathematical model. We use our model to simulate influenza A virus (IAV) coinfected with respiratory syncytial virus (RSV) and parainfluenza virus (PIV) coinfected with human rhinovirus (hRV). Using the model, we can estimate the co-duration of the viruses, the individual duration, and the peak virus amount for both viruses, both with and without drug treatment of the infections to figure out the best treatment strategies for co-infections. We find that sometimes treating one infection can lead to the lengthening of the other infection.