Population Groups on a Graph

Abstract

We assume that the states of a graph are occupied by n individuals. We denote by _tN ^°_α the number of individuals in state α at time t. The evolution of the population groups results from the following rules defining the closed graph model. At origin t=0, all n individuals are in state α=0 and all other states are void:

$$ {}_0{N_0}^o = n,{}_0{N_\alpha }^o = 0\left( {\alpha \ne 0} \right). $$

(1)

At any moment τ, any individual in state a can jump to a state β∈α′. The probability that this jump occurs during time interval dt equals _τµ_α→β dτ. Jumps akin to different individuals are independent. No individuals from outside join the graph and no individuals from the graph leave it.