The flowchart shows how the populations of each of the 5 types of cells affect each other (6 types if one includes G, the bone marrow). In order to maintain a constant system size, the bone marrow produces an equal number of cells as those that go to Cell Death.
Example: The change in the initial antiself Bcell population (iBs) is equal to the number of new Initial cells from the bone marrow [ = + k1 * G * SI], minus cells converting from iBs to eBs at a rate k2 [ =  iBs * k2 ], minus iBs to aBs at a rate k3 [ =  iBs * k3], minus the number of initial B cells that die [ =  iBs * k5 ].
In equation form, this statement looks like this:
iBs' = (k1*G* SI)  (iBs*k2)  (iBs*k3)  (iBs*k5);
Now we have a system of equations to calculate the cell population in
each group. It is convenient to think of X' as the (current time step)
variables that we calculate knowing X data (time step 1). The program
executes the equations in the execution order (ExecOrder) as numbered in
the table. However, the most meaningful equations are those where
the bulk of the cell are converted; namely, those listed as ExecOrder #3,
which are listed first. ExecOrder #4, is where antibodies are produced
and removed through decay. Note that these are not cells, and no
cells die as a result of antibody production. Likewise no cells die
when antibodies decay. Antibody in this model are only in the presence
of self (absence of nonself). Finally, in ExecOrder #5 and #6 the
program conveniently calculates the number of self and nonself effector
B cells and the levels of antibodies per determinant for quick analysis.

Variable  Equation  

iBs'  =  iBs + ((N)*SI)  (iBs*k2)  (iBs*k3)  (iBs*k5) + ((M)*SI); 

aBs'  =  aBs + (iBs*k3)  (aBs*k6); 

eBs'  =  eBs + (iBs*k2)  (eBs*k4); 

iBns'  =  iBns + ((N)*(1SI))  (iBns*k2)  (iBns*k5) + (M*(1SI)*(1L)); 

eBns'  =  eBns + (iBns*k2)  (eBns*k4); 

ABs'  =  ABs + (eBs*k7)  (ABs*k8); 

ABns'  =  ABns + (eBns*k7)  (ABns*k8); 
where: (M is an internal variable)  

M  =  Cells Added to the system to initially grow it. Equals 0 once the system reaches Total size (T). 

T'  =  (T + M) = (iBs' + aBs' + eBs' + iBns' + eBns') 

N  =  (As*k6) + (Is*k5) + (Inse*k5) + (eBs*k4) + (ebns*k4);
= cells that die = cells that are reborn = k1*G 
Effector / determinant calculations:  

eBs'/d  =  eBs'/(R*SI); 

eBns'/d  =  eBnse'/(R*(1SI)); 
Antibody / determinant calculations:  

ABs'/d  =  ABs'/(R*SI); 

ABns'/d  =  ABns'/(R*(1SI)); 
Further model notes:
Steady State:
Steady state values can be observed by allowing the system to continue
until the numbers within each cell groups converge on a number and stays
there regardless of additional time steps. It is important to note
that the system is generally allowed sufficient time after the initial
system growth stage to become steady state. At time = 0, it is hardwired
for the bone marrow to output the total number of cells into the system.
These cells then die, transform and/or produce antibodies as mathematically
described above (see image at top of page). Generally it has been
observed that 300 time steps are sufficient for steady state to occur.
As a precaution, it is adjustable by the user, whom may elect to perform
more (or less) time steps.
Antibody production:
Last Modified: November 18, 2003