Burden of cytokines storm on prognosis of SARS-CoV-2 infection through immune response: dynamic analysis and optimal control with immunomodulatory therapy

Abstract

Immune responses have a crucial role to play against SARS-CoV-2 virus as the adaptive and innate immune systems of the human body help restoring the body to a healthy stage by annihilating this deadly viral infection. Cytokines also play a significant role in modulating a balance between innate and adaptive immune responses but excess of it can have a detrimental affect on critically ill patients. Therefore, this paper is a novel attempt to formulate a within-host mathematical model showing the impact of cytokines storm on healthy cells. The dynamics of the system is analysed which involves basic reproduction number, steady state solutions and global dynamics for disease-free point and endemic equilibrium using geometric approach. Further, an optimal control problem is discussed considering immunomodulatory therapy (targeting cytokines signaling) as control using linear feedback control method to increase the level of healthy cells, which provides vitality for our system. Through numerical simulations, analytic solutions are validated followed by the curve-fit for the cytokines using real data and an optimization algorithm for optimal fit. Finally, sensitivity analysis for the basic reproduction number and the rate of change of healthy cells using Latin Hypercube Sampling method (LHS) is performed. Our finding suggests that immunomodulatory therapy (tocilizumab) can act as a key component to control cytokines storm for critically ill patients to restore the body to a healthy state.

Macrophage Boolean networks in the time of SARS-CoV-2

“…Notably, this transcription factor (TF) is activated in macrophages which is associated with an pro-inflammatory phenotype ( 31 , 32 ). In reference ( 33 ) the authors developed a compartmentalized system of ODEs by which they assessed how detrimental is cytokine storm for healthy cells. In this last work, they simplified a single equation of all the possible cytokines that can be found in a COVID-19 inflamed lung.…”

“…In this last work, they simplified a single equation of all the possible cytokines that can be found in a COVID-19 inflamed lung. As a result, they concluded that the cytokine storm was the variable to focus with the therapies because it caused a decrease of healthy cells which made the recovery in severe patients harder ( 33 ). Furthermore, in reference ( 34 ) the authors developed a two-step system of ODEs whose variables represented the immune-cytokine and the standard SIV (susceptible-infected-virus) systems.…”

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];…”