Terrorism control in the tourism industry

In some countries, for instance Egypt, terrorists try to hurt the country income from the tourism industry by violent actions against tourists. Another example are actions of the Kurds to bring tourism down in the east of Turkey. This paper is a first attempt to model some relevant aspects of these prey-predator relations. The country tries to maximize profits from the tourism industry, where profit is defined as the difference between revenue from the tourism industry and the sum of expenditures on tourism industry investments and expenditures on enforcement associated with reducing terrorism. It turns out that, for reasonable parameter values, the optimal trajectory exhibits a cyclical strategy. The interpretation is that, after starting out with a low number of tourists and terrorists, tourism investments are undertaken to increase tourism. This attracts terrorists reducing the effect of tourism investments. Therefore, investment declines and so does the number of tourists. This makes it less attractive for terrorists to act, so we are back in the original situation, where the whole thing starts again.