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The symbols are introduced early in the book on page 9 and 10. My confusion is I do not understand how to solve the ODE when P(0) is the dependent variable based on Kpg.

https://books.google.com/books?id=Y8nl4GFx1uIC&pg=PA5&lpg=PA5&dq=a+reduced+mathematical+model+of+the+acute&source=bl&ots=cCcTGLBb49&sig=NJRP0-rd49BJUcGVAAt1SJoTHIw&hl=en&sa=X&ei=4ZoRVerGMsHjoASq8IGoCA&ved=0CFcQ6AEwCA#v=onepage&q=a%20reduced%20mathematical%20model%20of%20the%20acute&f=false The above is the book. The picture is Figure 11 on page 27., which I try to reproduce. The ODE is (2.9)-(2.11) on page 24. The vertical coordinate is marked P0. But in order to solve the ODE systems, I have to set the initial value of P(t), especially I have to use numerical method to solve it . Usually, we set P[0]. But P0 (same as P[0]) depends on Kpg. That means I cannot set it, since it is based on Kpg. Then how could I solve ODE without setting P[0]? Thank you very much.

The book is Mathematical Model of Acute Inflammation and a Full Lung Model of Gas Exchange under Inflammatory Stress. The author is Angela Marie Reynolds. One can find it in google books or the paper on the web. My questions are about page 9 of the book. It listed a lot parameters that I try to understand. I list some of my questions below. 1 kpg is the growth rate of pathogen. P(t) is pathogen level. Should kpg=P'(t)? 2 knp=0.1/P-units/h, which is activation of resting phagocytes(Nr) by pathogen. Is knp=0.1/P(t)? 3 snr=0.08Nr-units/h. I could only find the formula for dNr/dt, which is on page 13. Do I need to solve the ODE system to code snr? Thank you very much.