A Multicompartment Mathematical Model Based on Host Immunity for Dissecting COVID-19 Heterogeneity
Authors: Wu Jianghua , Mei Heng , Li Jianwei , Zhang Jingpeng , Tang Lu , Du Mengyi , Li Fangting , Hu Yu 
Published: November 2021

Abstract
Background:
As of early August 2021, more than 190 million people have developed coronavirus disease (COVID-19), a pandemic that has killed approximately 4 million people. Caused by acute respiratory syndrome coronavirus 2 (SARS-CoV-2), COVID-19 exhibited a highly variable clinical course, ranging from a high proportion of asymptomatic and mild infections to severe and fatal disease. However, the immunological determinants underlying the heterogeneity of COVID-19 remain to be fully elucidated.
Methods:
To systemically analyze the immunopathogenesis of COVID-19, a multicompartment mathematical model based on both immunological principles and COVID-19-related work performed by the scientific community was built to illustrate the dynamics of host immunity after SARS-CoV-2 infection. We used ordinary differential equations (ODEs) to simulate the time-dependent functions of immunologic variations in the four compartments, which were draining lymph nodes, peripheral blood, lung and distant lymph nodes and spleen. Our model consisted of equations for 109 immunologic variations, which contained 223 parameters. K was used to characterize the adequacy of the SARS-CoV-2-specific naïve T/B cell pool; K I represented the hill coefficient of antigen-presenting cell (APC) differentiation. Further, we used method of pseudo landscape to visualize the effect of APC capacity and the SARS-CoV-2-specific naïve T/B cell pool on clinical outcomes.
Results:
Based on both immunologic knowledge and extensive COVID-19-related work performed by the scientific community, we constructed a knowledge-driven mathematical model that incorporated SARS-CoV-2 infection, bacterial infection, leukocyte chemotaxis, innate immunity and adaptive immunity. The model simulated and predicted the different trajectories of the viral load, bacterial load, immune cells, cytokines and infected epithelial cells in patients with different severities. A higher viral load and longer virus-shedding period were observed in patients with higher severity, along with an increase in SARS-CoV-2-infected lung epithelial cells. The trajectories of both peripheral blood IL-6 and lymphocytes predicted COVID-19 outcomes. Based on the distribution, trafficking and differentiation of immune cells after SARS-CoV-2 infection, we proposed that early-stage lymphopenia is related to lymphocyte chemotaxis. The delayed initiation of both innate and adaptive immunity resulted in elevated SARS-CoV-2 shedding and was a pivotal cause of COVID-19 severity. Spatiotemporally, viral shedding and postviral bacterial infection evoked stronger innate immunity. Viral shedding could be restrained by the rapid initiation of APC, antibody-secreting cell (ASC) and cytotoxic T cell (CTL). Moreover, our model predicted that the insufficient SARS-CoV-2-specific naïve T/B cell pools and inactive APC caused a series of chain reactions, including viral shedding, bacterial infection, sepsis and cytokine storms. Finally, pseudopotential analysis revealed that a high state characterized by severe bacterial infections and cytokine storms was a stable attractor for patients with insufficient SARS-CoV-2-specific naïve T/B cells and inactive APC (Figure 1).
Conclusion:
Overall, our analysis provided a comprehensive view of the dynamics of host immunity after SARS-CoV-2 infection and highlighted that the antigen-specific naïve T/B cell pool and APC ability may essentially determine COVID-19 heterogeneity from an immunological standpoint.
Figure 1 Figure 1.

Disclosures
No relevant conflicts of interest to declare.