Governmental combat of migration between competing terrorist organisations

Each terrorist organisation is modelled with four coupled differential time equations for the evolution of ideologues, criminal mercenaries, captive participants, and capital sponsoring. Emigration of ideologues may cause unbounded growth of the organisation receiving ideologues. The organisation losing ideologues may reach a stationary state where ideologues are supported by capital sponsors and mercenaries. Emigration of mercenaries may cause the organisation losing mercenaries to experience growth. The organisation receiving mercenaries may lose capital sponsors permanently, allowing for the presence of mercenaries, or capital sponsors may rebound deterring mercenaries. Emigration of ideologues from one organisation to another requires more government intervention into the latter to ensure termination. Emigration of mercenaries from one organisation to another may require more government intervention into the latter, since mercenaries support ideologues. Competing terrorist organisations may facilitate their mutual extinction. Various intervention strategies are considered: the most threatening organisation is eliminated first, aided by competition from the least threatening, after which the remaining organisation is eliminated. The government’s instantaneous and accumulated utilities are analysed through time and compared, depending on emigration, competition, and government intervention strategies.