Global dynamics for a new high-dimensional SIR model with distributed delay

In this paper, a new high-dimensional SIR epidemic model with double epidemic hypothesis and delays is proposed, which is a high-dimensional system of impulsive functional differential equations with time delays. The linear chain trick technique is employed to prove the upper boundedness of solutions of the impulsive delay differential equations and scaling method techniques for inequalities and classification method are used to study the permanence of the high-dimensional system. We also prove that the ‘infection-free’ periodic solution of the system is globally attractive when R1<1R1<1 and the system is permanent under R2>1R2>1. Moreover, numerical simulation for impulsive and delayed system is presented to illustrate our main conclusions which shows that time delays and pulse vaccination have significant effects on the dynamics behaviors of the model. The feature of the present paper is that the double epidemic hypothesis have different forms of delays to more realistically describe the spread of epidemic though which makes the high-dimensional system more complex.