Dynamics of an SEQIHRS epidemic model with media coverage, quarantine and isolation in a community with pre-existing immunity.

An autonomous deterministic non-linear epidemic model SEQIHRS is proposed for the transmission dynamics of an infectious disease with quarantine and isolation control strategies in a community with pre-existing immunity. The model exhibits two equilibria, namely, the disease-free and a unique endemic equilibrium. The existence and local stability of the disease free and endemic equilibria are explored in terms of the effective reproduction number .