Periodic solution and almost periodic solution of impulsive Lasota–Wazewska model with multiple time-varying delays

This paper deals with the impulsive Lasota–Wazewska model with multiple time-varying delays. Our results show that the system is uniformly persistent under some appropriate conditions. The sufficient condition for global exponential stability of the system is given. Applying Mawhin’s continuation theorem of coincidence degree, we prove that the periodic system has at least one strictly positive periodic solution. By employing hull theory of impulsive almost periodic system, the existence and uniqueness of strictly positive almost periodic solution of the almost periodic system is obtained. Two examples are provided to illustrate our results.