Dynamical demeanour of SARS-CoV-2 virus undergoing immune response mechanism in COVID-19 pandemic

Abstract

COVID-19 is caused by the increase of SARS-CoV-2 viral load in the respiratory system. Epithelial cells in the human lower respiratory tract are the major target area of the SARS-CoV-2 viruses. To fight against the SARS-CoV-2 viral infection, innate and thereafter adaptive immune responses be activated which are stimulated by the infected epithelial cells. Strong immune response against the COVID-19 infection can lead to longer recovery time and less severe secondary complications. We proposed a target cell-limited mathematical model by considering a saturation term for SARS-CoV-2-infected epithelial cells loss reliant on infected cells level. The analytical findings reveal the conditions for which the system undergoes transcritical bifurcation and alternation of stability for the system around the steady states happens. Due to some external factors, while the viral reproduction rate exceeds its certain critical value, backward bifurcation and reinfection may take place and to inhibit these complicated epidemic states, host immune response, or immunopathology would play the essential role. Numerical simulation has been performed in support of the analytical findings.

Fig. 1

Graphical explanation regarding the effects of antibody response and CTL response in COVID-19 infection for the intrahost mathematical model (1)

Fig. 2

Best fits of model (1) for SARS-CoV-2 to the viral load data continuous line are the simulation based on (1) and the red circles represent the data from [–34, 45]

Fig. 3

Left panel: the numerical simulation of the system (1). Right panel: the figure represents the existence of endemic equilibrium point

Fig. 4

Forward (left panel) and backward (right panel) bifurcation diagrams of system (1). Red curves represent infection-free equilibrium point and blue curves represent endemic equilibria

Fig. 5

The solution trajectories of the epidemic system (11) for different values of ${\alpha }_1={\alpha }_2=\alpha$ with the set of parameters as in Table 2

Fig. 6

The solution trajectories of the epidemic system (11) for different values of $\beta$ with the set of parameters as enlisted in Table 2

Fig. 7

Left panel: degree of sensitivity of each parameter on ${\mathcal{R}}_0$. Right panel: box-plots illustrating the variation in ${\mathcal{R}}_0$

Fig. 8

Local sensitivity analysis with non-normalization, half-normalization, and full-normalization techniques of ${\mathcal{R}}_0$ with respect to all parameters in computational simulations using MATLAB