Global properties of SARS‐CoV‐2 and IAV coinfection model with distributed‐time delays and humoral immunity

Abstract

Severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2) and influenza A virus (IAV) are two respiratory viruses and are similar concerning seasonal occurrence, transmission routes, clinical manifestations, and related immune responses. Recent studies showed that a substantial number of patients infected by SARS‐CoV‐2 were also coinfected with IAV. In this paper, we study the global properties of SARS‐CoV‐2 and IAV coinfection model in vivo. The role of humoral (antibody) immunity in controlling the coinfection is modeled. The model tracks uninfected epithelial cells, latent SARS‐CoV‐2‐infected epithelial cells, latent IAV‐infected epithelial cells, active SARS‐CoV‐2‐infected epithelial cells, active IAV‐infected epithelial cells, free SARS‐CoV‐2 particles, free IAV particles, SARS‐CoV‐2‐specific antibodies and IAV‐specific antibodies. The model includes six distributed‐time delays, two delays for the formation of latent SARS‐CoV‐2‐infected and latent IAV‐infected cells; two delays for the reactivation of latent SARS‐CoV‐2‐infected cells and latent IAV‐infected cells; and two delays for the maturation of new released SARS‐CoV‐2 and IAV virions. The regeneration and death of the uninfected epithelial cells are considered. We first examine the basic qualitative properties of the model, then we calculate all equilibria and prove their global stability. The global stability of equilibria is established using the Lyapunov method. The theoretical findings are demonstrated via numerical simulations. The importance of considering humoral immunity in the coinfection dynamics model is discussed. It is found that without modeling the humoral immunity, the case of IAV and SARS‐CoV‐2 coexistence will not occur. We discuss the effect of time delays on the dynamics of SARS‐CoV‐2 and IAV coinfection. It is noted that increasing the time delay length has similar impact as antiviral therapies.