On [formula omitted]-manifolds stability for impulsive delayed SIR epidemic models

Abstract

In this paper, we study an impulsively extended delayed SIR (Susceptible-Infected-Recovered) epidemic model for the spread of infectious diseases. The impulsive control model is represented by a neural network system with reaction-diffusion terms and impulses at fixed instants of time. The notion of stability of specific manifolds defined by continuous functions is introduced to the model under consideration. Using the Lyapunov impulsive approach, we derive criteria for the global practical exponential stability of the defined manifolds of solutions. Since the stability of manifolds concepts generalize the stability of separate state notions, our results are more general and they extend some existing stability results for non-impulsive and impulsive SIR epidemic models. An example is considered to show the effectiveness of our results.