Analysis of Humoral Immunity SARS-CoV-2 Infection Model with ACE2 Receptor and Latent Phase

Abstract

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is RNA virus which causes the coronavirus disease 2019 (COVID-19). 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. ACE2 is an essential mediating factor in the SARS-CoV-2 infection pathway. In this study, we build a mathematical model for characterizing the dynamics of SARS-CoV-2 within the host while taking into account the impact of humoral immunity and the function of the ACE2 receptor. We incorporate the cells that are latently infected into the model. We consider three distributed delays: (i) delay in development of latently infected epithelial cells, (ii) delay in the latently infected epithelium cells’ activation, and (iii) delay in the maturation of recently released SARS-CoV-2 virions. We first address the fundamental properties of the delayed system, then find all possible equilibria. We demonstrate the existence and stability of the equilibria on the basis of two threshold parameters, namely basic reproduction number (ℜ₀) and humoral immune activation number (ℜ1). By building appropriate Lyapunov functions and applying LaSalle’s invariance principle, we prove the global asymptotic stability for all equilibria. We do numerical simulations to demonstrate the theoretical conclusions. We do sensitivity analysis and determine the most vulnerable parameters. Discussion is had on how the dynamics of the SARS-CoV-2 are affected by ACE2 receptors, humoral immunity, latent phase and time delays. It is shown that vigorous activation of humoral immunity can suppress viral multiplication. We found that, ℜ₀ is influenced by the rates of ACE2 receptor growth and degradation, and this may offer valuable guidance for the creation of potential receptor-targeted vaccinations and medications. Further, it is shown that, increasing time delays can effectively decrease ℜ₀ and then inhibit the SARS-CoV-2 replication. Finally, we showed that, excluding the latently infected cells in the model would result in an overestimation of ℜ₀. Our findings may be useful in understanding the dynamics of SARS-CoV-2 infection in the host as well as in the development of novel therapies.