You're not plotting the ODE's themselves, but rather the dependent variables that are described by them, a subtle point perhaps. Solving the equations will give you these "plottable" functions. Your attachment shows a variant of the SIR model equations for epidemiology. The Wikipedia page https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology shows a plot of the solution of the "standard form" and also gives lots of references that you'd find very helpful. I would start there. Best.
If you don't want to plot numerical solutions, you still might want to plot the vector field associated to your ODEs' system (for given parameters values). However, I don't know how meaningful this will be in a three-dimensional space.
Ankit's question is on a variation of the SIR epidemiology model, a set of 3 ODEs, each a function of time only. There are many solvers available for this system, some even online.
Dear Ankit, Go to www.civilized.com, get a copy of MLAB, and
enter, solve and graph your ODEs as shown in the PDF story
linked-to below. (You can also fit your ODE model to data
to estimate various parameters, if you wish.)
epidemic model: http://www.civilized.com/pdffiles/epidem.pdf
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