Age-structured modeling of COVID-19 dynamics: the role of treatment and vaccination in controlling the pandemic

In addition to non-pharmaceutical interventions, antiviral drugs and vaccination are considered as the optimal solutions to control and eliminate the COVID-19 pandemic. It is necessary to couple within-host and between-host models to investigate the impact of treatment and vaccination. Hence, we propose an age-structured model, where the infection age is used to link the within-host viral dynamics and the disease dynamics at the population level. We conduct a detailed analysis of the local and global dynamics of the model, and the threshold dynamics are completely determined by the basic reproduction number \(\mathcal {R}_0\) ${\mathcal{R}}_0$ . Thus, the disease-free equilibrium is globally asymptotically stable and the disease eventually dies out when \(\mathcal {R}_{0}<1\) ${\mathcal{R}}_0<1$ ; the disease-free equilibrium is globally attractive when \(\mathcal {R}_{0}=1\) ${\mathcal{R}}_0=1$ ; the disease is uniformly persistent, and the unique endemic equilibrium is globally asymptotically stable when \(\mathcal {R}_{0}>1\) ${\mathcal{R}}_0>1$ . The numerical simulation quantitatively studies the impact of the within-host viral dynamics on between-host transmission dynamics. The results show that the combination of antiviral drugs and vaccines can play a key role in mitigating the spread of COVID-19, but it is challenging to eliminate COVID-19 alone. To achieve the complete elimination of COVID-19, we need highly effective antiviral drugs and near-universal vaccine coverage.