Primary HIV Infection
by Mike Martin

On this page, you can vary the parameters in a system of three ordinary differential equations that model primary HIV infection.   Let S (t) measure the concentration of healthy T cells, I (t) measure the concentration of infected T cells, and V (t) measurethe concentration of free virus particles.   The model equations are then:


Note that S (0) = S0,   I (0) = I0,   and   V (0) = V0.   The parameter R represents the constant rate that the body produces healthy T cells, T cells die at a rate proportional to the number of cells (D S for healthy cells and D I for infected cells), infected cells die as a result of virus infection with overall rate M I, healthy cells are reduced at the rate B V S and infected cells increase at the same rate, the production rate of virus particles is proportional to the number of infected cells, P I, and the body removes free virus particles at a rate proportional to the concentration of those particles, C V.   Submit real values for all of the parameters to obtain graphical solutions of the system as functions of time.   A numeric solution on the interval [0, T] is produced using Mathematica's numerical ODE solver, NDSolve.   Initial values must be input.

Enter in the value of the parameters and select the plotting bounds, then press the "Plot" button.

R =  

D =  

B =  

M =  

P =  

C =  


S0 =  

I0 =  

V0 =  


T =  


References:

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