Global stability of a delayed SARS-CoV-2 reactivation model with logistic growth, antibody immunity and general incidence rate

Abstract

Mathematical models have been considered as a robust tool to support biological and medical studies of the coronavirus disease 2019 (COVID-19). This new disease is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). This paper develop a within-host SARS-CoV-2 dynamics model with logistic growth for healthy epithelial cells, humoral (antibody) immune response and general SARS-CoV-2-target incidence rate. The model is incorporated with four mixed (distributed/discrete) time delays, delay in the formation of latent infected epithelial cells, delay in the formation of active infected epithelial cells, delay in the activation of latent infected epithelial cells, and maturation delay of new SARS-CoV-2 particles. The model is formulated as a system of delay differential equations (DDEs). We establish that the model’s solutions are non-negative and ultimately bounded. We deduce that the model has three equilibria and their existence and stability are perfectly determined by two threshold parameters. We prove the global stability of the model’s equilibria by utilizing the Lyapunov method and applying the LaSalle’s invariance principle. To support and illustrate our theoretical findings we present numerical simulations for the model with a special form of the general incidence rate function. The effect of time delays on the SARS-CoV-2 dynamics is addressed. We observe that increasing time delays values can have the same impact as drug therapies in suppressing viral progression.