Impact of media information and reinfection in a COVID-19 dynamical model: emergence of periodic orbits through Hopf bifurcation

Abstract

In the current study, we investigate an SIRI compartmental model of COVID-19 incorporating the effect of social media and TV advertisements on the disease transmission of COVID-19 in the presence of reinfection. We have performed basic analysis on the model and studied the basic reproduction number R 0 . The proposed model admits two disease-free equilibria and upto four endemic equilibria under certain parametric restrictions. We have performed local stability analyses via the Routh-Hurwitz criterion. Global asymptotic stability is established for the unique endemic equilibrium, when it exists, via the geometric approach. We have also scrutinized the proposed model for occurrence of the bifurcation phenomena and found that both forward and backward bifurcation transpires for a certain set of parameters. Simultaneously, the proposed model also displays saddle-node bifurcation. When R 0 > 1 , the possibility of numerous endemic equilibria exists. These numerous equilibria exhibit oscillations through Hopf bifurcation leading to rich and complicated dynamics. The model is found to show hysteresis. Effect of levels of media and reinfection on the infected compartment is demonstrated and sensitivity analysis of influential model parameters is carried out. Data fitting is carried out to validate the proposed model by comparison of real data in India and the proposed model. Lastly, numerical simulations are executed for several examples to provide analytical and epidemiological understanding into model behaviour.