Modified SI Model

Using the data shown in our “Data Selection” section, we wanted to find the numerical values of the parameters encoded in our model. In order to calculate their values, we used a variety of optimization algorithms to minimize the error between our model’s fit and the actual data observed. We made the simplification of our model to exclude the treatment states to reflect the data that was gathered. As such, we implemented our model as:

Our Parameters 

The charts above display the model fit to the first eight data points for both the infected and susceptible data. It can be seen that the model does not fit the data perfectly due to the limited and restrictive nature of the simplified SI model. This simple SI model may not be able to account for the long period of infectivity of HIV, or the social factors that add complexity to the modeling of this disease by impacting data reporting and collection. You can also see the numerical values found for all of the parameters which are consistent with the existing literature.