Mathematical Modeling and Analysis of an Epidemic Model with Quarantine, Latent and Media Coverage (Journal of Nonlinear Modeling and Analysis, 2024)
Epidemic models are very important in today’s analysis of diseases. In this paper, we propose and analyze an epidemic model incorporatingquarantine, latent, media coverage and time delay. We analyze the local stability of either the disease-free and endemic equilibrium in terms of the basicreproduction number $R_0$ as a threshold parameter. We prove that if $R_0 < 1,$ the time delay in media coverage can not affect the stability of the disease-free equilibrium and if $R_0 > 1,$ the model has at least one positive endemicequilibrium, the stability will be affected by the time delay and some conditions for Hopf bifurcation around infected equilibrium to occur are obtainedby using the time delay as a bifurcation parameter. We illustrate our resultsby some numerical simulations such that we show that a proper application ofquarantine plays a critical role in the clearance of the disease, and therefore adirect contact between people plays a critical role in the transmission of thedisease.
Keywords: Epidemic model; Stability; Hopf bifurcation; Delay.