I am currently completing an investigation assignment on modelling the growth of a virus inside of the host. There are 3 ODEs that I am using in the system, all determined by change in t. The differential equations I am trying to solve are below:
$/=[1−(/S)]−_**(_3^2/(_3^2+_3^{50}))$
$S/= -[1−(/S)]$
$d/d=−γ$
$d_1/d=/(+_{50})−__1$
$d_2/d=_*_1−_*_2$
$d_3/d=_*_2.$
All values in the system are defined in my program; there is nothing unknown here. So, with relative ease, I created a numerical solution and plotted the graph of I(x) (or any) on matplotlib using python. Below is a table of the first 10 values for all the functions in relation to t:
Note: initial values on first row where t=0.
I wanted to use Euler's integration to create a general (estimated) function for I(x) that I can modify easily and investigate changes in constants for my investigation. How would one go about creating a function for $I(x)$? I have initial values and estimated values, so theoretically, it should be easy. I have watched and read so many perfectly good explanations but none seem to fit my method or purpose. Maybe I am ignorant, it should be noted this is my first experience with non-analytical integrals.
Could someone who understands what they are doing in this field, provide some pointers or steps I should take to ultimately get my function of $I,V,S(x)$ in a closed form (estimated of course), that would be good for an inline investigative paper. Thanks!