Evolution of parasites - Lycée Val de Durance (Pertuis)

Lycée Val de Durance (Pertuis)
In an isolated environment, we study the relation between a certain type of parasite and their host and how these evolve with time t (continuous or discrete). In our model, parasites deposit eggs on their hosts and when the eggs hatch, the host dies. Denote by H and P the number of hosts and parasites respectively (these can be modelled as a function of t). At each step (unit time), the number of eggs deposited depends on the probability that a parasite and a host meet. One can assume that this probability is proportional to the product H.P of the populations.
We are given fixed values b and d for the birth and death rate of hosts when no parasites are present. Moreover, we let dp be the death rate of the parasites.
Run simulations for given values of b, d and dp and try to determine what happens with the populations H and P in time.