In my model I have the interaction between parasite and immune repsonse and I want to find a value for the model parameter of death rate of parasite due to immune system killing.
The form of my equation is
${dP \over dt}=- {d P I \over kP+I}$,
P is the parasite and I is the immune cells where $d$ is the death rate ( which I am trying to find) and k is the ratio dependent constant as in here.
Form literature I found a figure that measures the death of parasite over time, which is given as the percentage of parasite that is killed.
1)By fitting a function of the form $1-e^{-dt}$ would I be able to estimate d and does this match with my ODE equation?
Is there any other function or method that I can use to find d?
2) Or because this figure looks exponential, by converting it into logarithmic scale, can I directly read off the slope and obtain d?
3)As in the model I have the parasite and immune cells in numbers, does it matter I am using values from a percentage figure? I am not good with percentages and so I would like to know if I have to convert these percentages to numbers before I can use data on this figure.