Some species of plants and animals introduced are very invasive
and it is now accepted that they have a significant impact on biodiversity
(competition with other species, release of toxic substances,
genetic disturbance, epidemics, etc.). Some optimization
models were developed in the effective fight against invasive species.
The reader can refer, for example, to the very good article
written by Epanchin-Niell and Hastings (2010). The authors review
studies that address economically optimal control of established
invasive species. They describe three important components for
determining optimal invasion management: invasion dynamics,
costs of control efforts and a monetary measure of invasion damages.
Another interesting reference in connection with this question
is (De Lara and Doyen, 2008), where different biological
models are reviewed.
We present below a simple problem proposed by Hof (1998) to
illustrate the help that operational research can provide to treat
this type of phenomenon. Consider a forest area represented by a
matrix of m n identical square parcels and a parasite present
in some of these parcels. This parasite disperses by neighborhood
and its population is steadily increasing. It is possible to completely
eliminate the parasite from a parcel by performing some