Birth-death model

From PBDN

In a chemical model, there can be any number of species and reactions. In the birth-death model used in this project, there is just one species, so we can refer to the population without ambiguity. The sole species is also referred to as $A$ .

There are two reactions in this model:

Creation, or synthesis, of one $A$ from the soup
Disappearance, or annihilation, of one $A$ into the soup

The first reaction, synthesis of $A$ , occurs with fixed probability $k$ . The probability of the second reaction, annihilation of $A$ , occurring is directly proportional to the population, $a$ , of $A$ with constant of proportionality $μ$ .

The birth-death model is simple enough that it has an analytical solution. Both the steady-state population, and the variance in the steady-state population, are expected to be $\frac{k}{\mu}$ . In this project, $k$ was fixed at 5 and $μ$ at 0.1, making the expected steady-state values of both the population and its variance equal to 50.

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