| dc.description.abstract |
For a long time, serious public health concerns have been related to the COVID-19 outbreak caused by SARS-CoV-2. Mathematical models are useful in examining the dynamics of the disease transmission, prediction and control when a suitable drug or vaccine is unavailable.
In this study, vaccination and quarantine strategies with mask efficiency, a susceptible, vaccinated, exposed, infected, quarantined and recovered (SVEIQR) compartmental model for COVID-19 is presented. Qualitative properties for the proposed model, such as positivity and boundedness of solutions, existence and uniqueness of solutions and analysis of equilibria will be performed. The control reproduction number is calculated using the next-generation matrix method. Local stability for both disease-free equilibrium (DFE) and disease-endemic equilibrium (DEE) will be tested. With Lyapunov's direct method, the global stability of the model is established. Explicit conditions are obtained to classify different bifurcations, including saddle-node bifurcation, transcritical bifurcation, pitch-fork bifurcation, forward and backward bifurcation. The forward bifurcation phenomenon in the model is demonstrated when the control reproduction number is greater than one. It is also noticed that under the perfect vaccine efficacy, the model exhibits the transcritical bifurcation phenomenon. However, the proposed model will not exhibit the saddle-node and pitch-fork bifurcation.
Furthermore, it is found that an effective vaccination strategy with proper face mask usage is highly necessary to reduce the burden of diseases instead of a quarantine strategy. |
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