Zaider Minerbo Model Solution
Equation
The equation of the Zaider-Minerbo model:
$\displaystyle\frac{\partial}{\partial t}A(s,t)=(s-1)[bs-d-h(t)]\displaystyle\frac{\partial}{\partial s}A(s,t)$ |
The solution of this equation will allow us to calculate the
Because we are looking for a solution for which
it can be shown that this is of the form
with
$\Lambda(t)=e^{-\displaystyle\int_0^t[b-d-h(t')]dt'}$ |
With this it can be shown that the
$TCP(t)=\prod_{i=1}^M\left[1-\displaystyle\frac{1}{\left(\Lambda(t)+b\displaystyle\int_0^t\Lambda(u)du\right)}\right]^{v_i}$ |
The
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Simulator Models Poisson and Zaider Minerbo
Html
The following in a simulator that allows to calculate the TCP both under Poisson and Zaider Minerbo assuming two types of cells (birth rate, death, factors
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Correction to the Zaider Minerbo Model
Equation
The Zerider Minerbo model is based on the population equation
however the births can be conditioned by what the generalization of the model can be based on the more general equation:
$\displaystyle\frac{d}{dt}N=f(N)-(d+h(t))N$ |
Where the
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