# Understanding Neutrophil Dynamics during COVID-19 Infection
## 5 Discussion  
In this paper, we developed a mathematical model of innate immunity following SARS-CoV-2 infection that describes neutrophils recruitment into the lungs following epithelial tissue damage and investigates their role in inducing disease resolution or in enhancing disease pathogenesis. We studied the model analytically and numerically and determined that it exhibits monostable and bistable kinetics, where the monostable state corresponds to immune resolution and the bistable state corresponds to tradeoff between immune resolution and chronic-inflammation. We fitted the model to immune marker data from patients with mild and severe COVID-19 disease published in [61]. We estimated several key parameters for each clinical outcome group and determined the immune-specific differences between the groups. We examined the effect on the systems' long-term behavior of parameters and initial conditions and used the results to derive markers of chronic-inflammation and immune resolution. Diversity in clinical outcomes following SARS-CoV-2 infection is attributed to heterogeneity in immune responses who, in turn, are influenced by individuals' age, ethnicity, sex and the presence of comorbidities [71]. Delayed and ineffective innate immunity leads to increased neutrophil recruitment in the blood, neutrophil infiltration into the lungs, changes in neutrophil phenotype, and/or formation of neutrophil extracellular traps [3; 12; 72; 73; 74], all of which have been associated with poor disease outcomes. To address the role of neutrophils of different phenotypes, we modeled two neutrophil subpopulations, activated \(n(t)\) and apoptotic \(a(t)\). Using the model, we examined the differences in total neutrophil levels at hospitalization \(n_{0}+a_{0}\), the estimated neutrophil activation rate \(\alpha_{c}\), and the estimated neutrophil apoptosis rate \(\
u\) when the model is fitted to immune population data from mild and severe clinical outcomes. We found higher values for all three markers with initial neutrophils having the biggest increase (2.3-times higher), compared to neutrophil activation (1.5-times higher), and phenotype change (1.3-times higher) in severe cases compared to mild cases. Data fitting indicated that the parameter space corresponding to severe disease outcomes is associated with the bistable kinetics of our model, while the parameter space corresponding to mild clinical outcome is associated with the monostable kinetics of our model (Figure 4). One dimensional bifurcation diagrams with respect to neutrophil recruitment rate \(\alpha_{c}\) (Figure 5) and two-dimensional bifurcation diagrams with respect to \(\alpha_{c}\) and initial activated neutrophils \(n_{0}\) (Figure 7B) showed that lowering neutrophil recruitment and/or the neutrophil activation can lead to immune resolution. One way to accomplish that is by understanding how comorbidities or pre-existing conditions affect neutrophil functionality, recruitment, are inherent dysregulation [75] as done in other diseases [12; 76; 77]. In our model, one way to control neutrophil activity is through recruitment of macrophages \(m(t)\) which, in turn, enhance neutrophil apoptosis at rate \(\phi\). Data fitting showed decreased neutrophil apoptosis rates (12.4-times lower) in severe compared to mild cases. One dimensional bifurcation diagrams with respect to \(\phi\) showed that increasing macrophage induced neutrophil apoptosis can lead to immune resolution (Figure 6). A common feature for severe COVID-19 clinical outcomes is the production of high levels of proinflammatory cytokines (such as IL-6), which in our model were generically combined under the cytokine population \(c\). Paradoxically, IL-10, which is classified as an anti-inflammatory cytokine, is also elevated in severe cases [61]. To determine its role on overall immune dynamics, we considered an anti-inflammatory population \(g(t)\) in our model, modeled its effect on neutrophil phenotype change and on lowering the recruitment of CD8 T-cells, and fitted it to IL-10 data.