Global properties of delayed models for SARS-CoV-2 infection mediated by ACE2 receptor with humoral immunity

The coronavirus disease 2019 (COVID-19) is caused by a new coronavirus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). SARS-CoV-2 infects the epithelial (target) cells by binding its spike protein, S, to the angiotensin-converting enzyme 2 (ACE2) receptor on the surface of epithelial cells. During the process of SARS-CoV-2 infection, ACE2 plays an important mediating role. In this work, we develop two models which describe the within-host dynamics of SARS-CoV-2 under the effect of humoral immunity, and considering the role of the ACE2 receptor. We consider two discrete (or distributed) delays: (ⅰ) Delay in the SARS-CoV-2 infection of epithelial cells, and (ⅱ) delay in the maturation of recently released SARS-CoV-2 virions. Five populations are considered in the models: Uninfected epithelial cells, infected cells, SARS-CoV-2 particles, ACE2 receptors and antibodies. We first address the fundamental characteristics of the delayed systems, then find all possible equilibria. On the basis of two threshold parameters, namely the basic reproduction number, ${\mathrm{\Re }}_0$, and humoral immunity activation number, ${\mathrm{\Re }}_1$, we prove the existence and stability of the equilibria. We establish the global asymptotic stability for all equilibria by constructing suitable Lyapunov functions and using LaSalle's invariance principle. To illustrate the theoretical results, we perform numerical simulations. We perform sensitivity analysis and identify the most sensitive parameters. The respective influences of humoral immunity, time delays and ACE2 receptors on the SARS-CoV-2 dynamics are discussed. It is shown that strong stimulation of humoral immunity may prevent the progression of COVID-19. It is also found that increasing time delays can effectively decrease ${\mathrm{\Re }}_0$ and then inhibit the SARS-CoV-2 replication. Moreover, it is shown that ${\mathrm{\Re }}_0$ is affected by the proliferation and degradation rates of ACE2 receptors, and this may provide worthy input for the development of possible receptor-targeted vaccines and drugs. Our findings may thus be helpful for developing new drugs, as well as for comprehending the dynamics of SARS-CoV-2 infection inside the host.