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.

Predicting the Cross-Coordinated Immune Response Dynamics in Sars-Cov-2 Infection: Implications for Disease Pathogenesis

“…the broadness of engaged organs and physiological systems to be considered in the models, and the lack of coherent time-series data on the immune response to infection which are required to robustly calibrate the described processes. So far, more than a dozen of mathematical models of SARS-CoV-2 infection have been developed [3][4][5][6][7][8][9][10][11][12][13][14][16][17][18][19][20][21]. They differ enormously in their complexity, ranging from low-dimensional models (e.g., the ODE systems of two to five equations) [4,5,7,11,16]) through medium-size models (about ten equations) [3,6,8,13,14,17,21] up to high resolution models of ODEs (up to 60 equations) [9,10] or hybrid multi-scale models [18,20].…”

“…So far, more than a dozen of mathematical models of SARS-CoV-2 infection have been developed [3][4][5][6][7][8][9][10][11][12][13][14][16][17][18][19][20][21]. They differ enormously in their complexity, ranging from low-dimensional models (e.g., the ODE systems of two to five equations) [4,5,7,11,16]) through medium-size models (about ten equations) [3,6,8,13,14,17,21] up to high resolution models of ODEs (up to 60 equations) [9,10] or hybrid multi-scale models [18,20]. The later can be categorized as "experimental mathematical" models.…”

“…virus spreading and innate immune responses [3,[13][14][15]; • virus spreading and adaptive immune responses [5,6,9,11,16]; • virus spreading and innate/adaptive immune responses [8,12,17];…”

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

“…CTL immune response was included in the SARS-CoV-2 infection model in [20] , [21] , [22] , [23] , [24] , [25] , [26] . Mondal et al [27] developed and analyzed a five-dimensional SARS-CoV-2 dynamics model which includes both CTL and antibody immunities. Ghosh [28] formulated a model that describes the SARS-CoV-2 dynamics with both innate and adaptive immune responses.…”

“…Fractional differential equations (FDEs) were used in studying the SARS-CoV-2 dynamics between hosts [21] , [22] , [23] , [24] and within-host [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] . Ghanbari [25] extended the model presented in [20] by using fractional derivatives.…”