(1) Dynamics of CD4 T cells, X(t)

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(1) Dynamics of CD4 T cells, X(t)

• Generated from the thymus at a rate
• is the fraction of cells inhibition by
  AZT
• Loss due to finite lifespan at a rate
• Generated by Antigen(A)-induced proliferation
  at a rate .
• These can be summarized in the differential
  equation

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(2) Dynamics of T cells, Y(t)

• Generated from the thymus at a rate
• Loss due to finite lifespan at a rate
• Generated by Antigen-induced proliferation with
  the help of T cells at rate .
• Thus

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(3) Dynamics of antigen(A)-specific CTLs, C(t)

• Generated from antigen-specific T cells
  with the help of T cells at a rate of
  
• Loss due to natural death at a rate .
• This gives

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(4) Dynamics of antibody-producing B cells, Z(t)

• Generated from bone marrow at a
• rate
• Loss due to natural death at a rate
• Generated by Antigen-induced proliferation with
  the help of T cells at a rate .
• Then

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(5) Dynamics of Antigen, A(t)

• Produced due to vaccination or infection at a
  rate
• Loss due to B cells at a rate .

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Summary

• In summary, the model consists of the equations

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ANALYSIS OF THE MATHEMATICAL MODEL

• The model has been analyzed and found to be
  mathematically stable and therefore suitable for
  computer simulation.