Periodic solutions, global attractivity and oscillation of an impulsive delay host–macroparasite model

Abstract

In this paper we will consider the nonlinear impulsive delay host–macroparasite model with periodic coefficients. By means of the continuation theorem of coincidence degree, we establish a sufficient condition for the existence of a positive periodic solution M ¯ ( t ) with strictly positive components. Moreover, we establish a sufficient condition for the global attractivity of M ¯ ( t ) and some sufficient conditions for oscillation of all positive solutions about the positive periodic solution M ¯ ( t ) .