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

Sahu, Govind Prasad; Dhar, Joydip

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 [Formula: see text]. It is observed that media coverage does not affect the effective reproduction number, but it helps to mitigate disease burden by lowering the number of infectious individuals at the endemic steady state and also lowering the infection peak. A new approach is proposed to estimate the coefficient of media coverage. Using the results of central manifold theory, it is established that as [Formula: see text] passes through unity, transcritical bifurcation occurs in the system and the unique endemic equilibrium is asymptotically stable. It is observed that the population level impact of quarantine and isolation depend on the level of transmission by the isolated individuals. Moreover, the higher level of pre-existing immunity in the population decreases the infection peak and causes its early arrival. Theoretical findings are supported by numerical simulation. Sensitivity analysis is performed for [Formula: see text] and state variables at endemic steady state with respect to model parameters.