Nonlinear Epidemic Model With Media Coverage: Stability, Bifurcation, and Control in a Population With Pre-Existing Immunity

Abstract

This paper proposes a deterministic nonlinear epidemic model, $$, incorporating media coverage for the analysis of infectious disease transmission dynamics, considering quarantine and isolation control strategies in a community with pre-existing immunity, and taking into account both asymptomatic and symptomatic infections. The model examines two equilibria: the disease-free equilibrium and a unique endemic equilibrium, investigating their existence and local stability concerning the effective reproduction number, R_e. In addition, global stability analysis of these equilibria is conducted. Media coverage is found to have no effect on R_e but plays a crucial role in mitigating the disease burden by reducing the number of infectious individuals at the endemic steady state and decreasing the infection peak. A new method is introduced to estimate the coefficients of media coverage. Based on the findings of central manifold theory, it is observed that when R_e exceeds unity, a transcritical bifurcation takes place in the system, leading to the asymptotic stability of the endemic equilibrium. Moreover, it is noted that the effectiveness of quarantine and isolation at the population level depends on the transmission rate among isolated and quarantined individuals, while higher pre-existing immunity in the population reduces the infection peak and hastens its occurrence. Theoretical results are validated through simulations, and sensitivity analysis is conducted for the effectiveness of R_e with respect to model parameters.