We propose mathematical models for the system of slave-maker ants. The system is composed of three species Formica Japonica, Polyergus samuraiand Formica sanguinea. Formica Japonica is a slave, but Polyergus samuraiand Formica sanguineaare slave-makers which utilize Formica Japonicaas slave ants. Although Polyergus samuraialways utilizes Formica Japonica, Formica sanguineastarts to make slaves when its population size is less than a critical value. Moreover, we assume the population dynamics of Formica sanguineaexhibit the Allee effect. We explore the local stability of the equilibria. We consider the condition for Formica sanguineato survive when Formica sanguineaalways makes slaves. It is found that Formica sanguineasurvives independent of the initial value when many slaves exist and the slave-making rate of Formica sanguineais large and when both the carrying capacity and the critical value of Allee effect for Formica sanguineaare small. When the survival conditions for Formica sanguineaare satisfied, the numerical simulation shows that Formica sanguineacan survive through three possible ways. One is the way where all three species can coexist at a positive equilibrium point. The second way is the case where Formica sanguineareaches at carrying capacity, but Formica Japonicaand Polyergus samuraisurvive on their periodic motion. The third is the way where only Formica sanguineacan survive at its carrying capacity.

permanence, host-parasitoid systems, average Liapunov functions, coexistence.