Positive almost periodic solution for a class of Lasota–Wazewska model with infinite delays

By utilizing a fixed theorem in cones, we study the existence of a unique positive almost periodic solution for a generalized Lasota–Wazewska model with infinite delays. Some sufficient conditions which ensure the existence of a unique positive almost periodic solution are derived and it cannot be obtained by the contraction mapping principle. Furthermore, under proper conditions, we establish some criteria to ensure that all solutions of this model converge exponentially to a positive almost periodic solution. An example is provided to illustrate the effectiveness of the proposed result.