# Understanding Neutrophil Dynamics during COVID-19 Infection
###### Abstract  
Infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) results in varied clinical outcomes, with virus-induced chronic inflammation and tissue injury being associated with enhanced disease pathogenesis. To determine the role of tissue damage on immune populations recruitment and function, a mathematical model of innate immunity following SARS-CoV-2 infection has been proposed. The model was fitted to published longitudinal immune marker data from patients with mild and severe COVID-19 disease and key parameters were estimated for each clinical outcome. Analytical, bifurcation, and numerical investigations were conducted to determine the effect of parameters and initial conditions on long-term dynamics. The results were used to suggest changes needed to achieve immune resolution.  
mathematical modelling; neutrophils; COVID-19; SARS-CoV-2; inflammation; resolution; bifurcation analysis; sensitivity analysis +
Footnote †: journal: Medical  
with mild and severe COVID-19 disease [13; 14; 15; 16]. Data in [13] showed elevated levels of proinflammatory (IL-6, IL-2, and IFN-\(\gamma\)) and anti-inflammatory cytokines (IL-10), elevated levels of neutrophils and reduced levels of CD8 T-cells in patients with severe compared to those with mild COVID-19 disease. Similarly, [15] found elevated neutrophils levels, elevated IL-6 levels, and reduced levels of CD8 T-cells and CD4 T-cells in patients with severe or critical compared to those with moderate COVID-19. Elevated anti-inflammatory cytokines levels (IL-10) in severe disease was reported in [16], as well. Last, the neutrophil-to-CD8 T-cell ratio (N8R) has emerged as an early prognosis method for identifying severe COVID-19 disease [13], with high N8R ratio being indicative of severe outcomes [15; 17; 18].  
While data exists for the magnitude of immune cells and proinflammatory mediators in different disease outcomes, little is known about the mechanistic interactions between these populations, and about the role that feedback, interpopulations effects and regulations play on overall disease outcomes. In this paper, we develop a mathematical model of interactions between neutrophils, macrophages, pro- and anti-inflammatory markers and CD8 T-cells and use it to tease out mechanisms responsible for COVID-19 pathogenesis. Previously, mathematical models have investigated human inflammation following physical injury [19; 20; 21], cancer [22; 23], lung infections [10], rheumatoid arthritis [24; 25], atherosclerosis [26], H. pylori [27], diabetes [28], and nonspecific pathogens [29; 30; 31; 32; 33; 34; 35]. Specifically, mathematical modeling of viral infections with pathogens such as influenza [36; 37; 38; 39; 40], hepatitis B [41; 42; 43; 44], SARS-CoV [45; 46], and SARS-CoV-2 [47; 48; 49; 50; 51; 52; 53; 54; 55; 56] have investigated the role of immune responses in disease resolution or inflammation. Some of these studies highlighted the importance of cytokine production and neutrophil function in modulating disease pathogenesis.  
In our study, we do not explicitly model the dynamics of SARS-CoV-2 infection, and instead only model the resulting inflammation. We consider interactions between neutrophils (active and apoptotic), macrophages, proinflammatory mediators, anti-inflammatory mediators and CD8 T-cells. We use the model to investigate the neutrophil responses to tissue damage caused by SARS-CoV-2 infection and to determine the mechanisms leading to resolution or inflammation. Moreover, we fit the model to longitudinal data from mild and severe COVID-19 infections to identify resolution or inflammation-specific parameters, such as the neutrophil-to-CD8 T-cell ratio. These results can inform interventions.