Matrix measure on time scales and almost periodic analysis of the impulsive Lasota–Wazewska model with patch structure and forced perturbations

In this paper, a new impulsive Lasota–Wazewska model with patch structure and forced perturbed terms is proposed and analyzed on almost periodic time scales. For this, we introduce the concept of matrix measure on time scales and obtain some of its properties. Then, sufficient conditions are established which ensure the existence and exponential stability of positive almost periodic solutions of the proposed biological model. Our results are new even when the time scale is almost periodic, in particular, for periodic time scales on T=ℝ or T=ℤ. An example is given to illustrate the theory. Finally, we present some phenomena which are triggered by almost periodic time scales.