Immune response to SARS-CoV-2 in severe disease and long COVID-19

Summary COVID-19 is mild to moderate in otherwise healthy individuals but may nonetheless cause life-threatening disease and/or a wide range of persistent symptoms. The general determinant of disease severity is age mainly because the immune response declines in aging patients. Here, we developed a mathematical model of the immune response to SARS-CoV-2 and revealed that typical age-related risk factors such as only a several 10% decrease in innate immune cell activity and inhibition of type-I interferon signaling by autoantibodies drastically increased the viral load. It was reported that the numbers of certain dendritic cell subsets remained less than half those in healthy donors even seven months after infection. Hence, the inflammatory response was ongoing. Our model predicted the persistent DC reduction and showed that certain patients with severe and even mild symptoms could not effectively eliminate the virus and could potentially develop long COVID.


INTRODUCTION
The emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused an unprecedented ongoing global pandemic known as coronavirus 2019 (COVID-19) (J. F.-W. Chan et al., 2020;Zhou et al., 2020). The disease has heterogeneous characteristics. It may be asymptomatic, induce mild symptoms, or cause critical illness. In the latter case, 10-20% of all symptomatic patients are at elevated risks of multiple organ system involvement and mortality (Gupta et al., 2020;Huang et al., 2020;Zhou et al., 2020). There is limited experimental or clinical evidence that the virus per se is mainly responsible for the heterogeneity of the disease it causes. In contrast, there is growing evidence that the host accounts for the observed variability in disease severity, infection rate, and long-term disease symptoms (Schultze and Aschenbrenner, 2021). Therefore, a better understanding of the innate and adaptive immune response in mild and potentially fatal COVID-19 is crucial for developing diagnostic markers and therapeutic strategies.
Many quantitative methods have been developed to analyze the dynamics of SARS-CoV-2 infection within the host (Almocera et al., 2021;Challenger et al., 2022;Chowdhury et al., 2022;Du and Yuan, 2020;Ejima et al., 2021;Ghosh, 2021;Hernandez-Vargas and Velasco-Hernandez, 2020;Kim et al., 2021;Moses et al., 2021;Nath et al., 2021;Perelson and Ke, 2021;Reis et al., 2021;Sahoo et al., 2020;Voutouri et al., 2021) and some also explicitly considered immune cells (Almocera et al., 2021;Challenger et al., 2022;Chowdhury et al., 2022;Du and Yuan, 2020;Ghosh, 2021;Moses et al., 2021;Reis et al., 2021;Sahoo et al., 2020;Voutouri et al., 2021). The mathematical modeling studies which theoretically show the instability of diseasefree equilibrium and stability of the virus co-existence equilibrium (Almocera et al., 2021;Chowdhury et al., 2022;Ghosh, 2021;Nath et al., 2021) are suggestive of understanding clinically observed longterm symptoms of COVID-19. The development of large-scale models for simulating spatial-temporal dynamics of viral spread and immune response inside lungs (Moses et al., 2021) or incorporating the viral invasion process into epithelial cells, viral dissemination via the bloodstream, and systemic infection and thrombosis (Voutouri et al., 2021) is remarkable. The present study proposes a mathematical model for the immune response to SARS-CoV-2 incorporating the immune cells, related molecules, and their interactions ( Figure 1). It reveals the roles of innate and adaptive immunity and examines the mechanisms of the development of severe COVID-19 in response to age-related risk factors. SARS-CoV-2 has already mutated to evade the immune response. For example, it dysregulates type-I interferon (IFN1) which is a cytokine secreted by infected host cells (Sa Ribero et al., 2020). Here, model simulations were used to assess age-related risk factors (Bastard et al., 2021), e.g., virally mediated suppression effect of IFN1 production by infected epithelial cells and the influences of IFN1-neutralizing autoantibodies.   [Ig]. The typical flow in the immune response depicted in this figure is as follows: The healthy epithelial cells are infected by viral particles and become infected cells. The infected cells produce viral particles, also secreting IFN1 molecules (Sa Ribero et al., 2020). DC cells ingest viral particles and become working as APC R cells. The APC R cells secrete IFN1 molecules (Fitzgerald-Bocarsly and Feng, 2007). The APC R cells migrate toward lymph nodes. The moved APC R cells, namely, APC L cells differentiate CD4 + T 0 cells into Th1 and Tfh cells (Sette and Crotty, 2021), where IFN1 stimulates these developments . The APC L and Th1 cells activate CD8 + T 0 cells, which then differentiate into CTL L cells . The CTL L cells are recruited by IFN1 to migrate toward the sites of infection and the moved CTL L cells, namely, CTL R cells kill infected cells (Sette and Crotty, 2021). The APC L and Tfh cells activate B 0 cells Swain et al., 2012), which differentiate into pB cells, consequently Ig molecules are produced by the pB cells  iScience Article the entire human respiratory system, brain endothelium, and vascular smooth muscle cells (Hamming et al., 2004;Paniz-Mondolfi et al., 2020). Moreover, ACE2 and TMPRSS2 are expressed in esophageal keratinocytes, renal proximal tubules, pancreatic b-cells, and gastrointestinal epithelial cells (Gupta et al., 2020;Paniz-Mondolfi et al., 2020;Puelles et al., 2020;Qi et al., 2020). These facts are consistent with the observation that in certain post-acute sequelae of patients with COVID-19, SARS-CoV-2 maintains chronic symptoms by persisting in certain sites or tissue reservoirs after acute infection (Proal and VanElzakker, 2021). Possibly related to those, the numbers of CD1c + myeloid and plasmacytoid DCs remained low even seven months after SARS-CoV-2 infection whether or not the patients were previously hospitalized (Pé rez-Gó mez et al., 2021). Our model reproduced long-term DC count reduction and showed that ongoing DC-induced inflammation was attributed to persistent viral infection that the host could not remove. The model simulations also predicted that successful elimination of the virus depends on the capacity of the host immune response which is directly related to viral load.

cells ml À1
[CTLR] Population of cytotoxic T lymphocyte at respiratory tracts.

cells ml À1
[Tfh] Population of follicular helper T cells. 0 cells ml À1 [B0] Population of naive B cells 1.0 3 10 3 cells ml À1 (Lee et al., 2009) [pB] Population of plasma B cells. 0 cells ml À1   (Oprea and Perelson, 1996;Vonboehmer and Hafen, 1993) l CD8 Supply rate of susceptible healthy cells. 2.0 3 10 1 cells ml À1 day À1 d CD8 Natural death rate of healthy cells. 2.0 3 10 À2 day À1 (Oprea and Perelson, 1996;Vonboehmer and Hafen, 1993) l B Supply rate of susceptible healthy cells. 2.0 3 10 2 cells ml À1 day À1 d B Natural death rate of healthy cells. 2.0 3 10 À1 day À1 (Chan and Maclennan, 1993;Oprea and Perelson, 1996) p I Infection rate of susceptible healthy epithelial cells 2.0 3 10 À6 day À1 mL copies À1 b I Antibody neutralization rate 5.0 3 10 À3 mL molecules À1 iScience Article load data , and those are denoted as the three vertical lines in Figure 2A. The peak viral load of [V] was attained at $2 days after symptom onset as previously reported by Kim et al. (2021). Figure 2B shows that the immunoglobulin concentration [Ig] time course is consistent with clinically observed data (Yin et al., 2020). The [Ig] increased in response to plasma B cell activation and Ig secretion as seen in Figure 2B. Figure 2C.   Figure 2E). The number of viral particles that have been replicated by infected cells within the host is reduced by natural viral degradation. However, this process is comparatively slow ( Figure 2F). Figure 2G shows In fact, the IFN1 production rate used for the baseline model is equal to 1,000-fold lower in infected cells than APC R (STAR Methods, Table 2). The reason for using these parameters is that experimental studies demonstrate that SARS-CoV-2 possesses several mechanisms to evade the IFN1-mediated immune response (Sa Ribero et al., 2020). However, if a virus lacked these mechanisms (STAR Methods, Table 3), it can be more rapidly cleared from the host as shown by the blue solid line in Figure 2H.

Dendritic cell deficiency persists for >7 months after SARS-CoV-2 infection
DCs play key roles in defending against viral infections. When DCs capture viruses, these functions as APCs, and one of the subsets, plasmacytoid DCs (pDCs), produces abundant IFN1. Whether or not patients with COVID-19 were previously hospitalized, the numbers of their CD1c + myeloid DCs and pDCs were lower than those for healthy donors during the acute infection phase and even 7 months after the initial SARS-CoV-2 infection ( Figure 3A) (Pé rez-Gó mez et al., 2021). Hence, the DCs induce and partially iScience Article sustain ongoing inflammation that can be related to long COVID or PASC (Proal and VanElzakker, 2021). A multisystem inflammatory syndrome in children (MIS-C) had been recognized (Gruber et al., 2020), providing evidence of long-term DC deficiency. Patients with MIS-C had SARS-CoV-2 exposure, mounted an antibody response with similar neutralization capability, and had lower pDC levels than the healthy group. In addition, the levels of non-classical monocytes and a subset of natural killer cells were also reduced in the MIS-C group, thus demonstrating the relationship of these cell populations with the ongoing inflammation in the child participants (Gruber et al., 2020). Our baseline simulation predicted that the number of DCs rapidly decreases during the acute phase and increases thereafter but is nonetheless lower than it was before the infection ( Figure 3B). The simulated proportions of DC reduction in infected patients compared with healthy donors were consistent with those determined by clinical observation ( Figure 3A) (Pé rez-Gó mez et al., 2021). Figure 2C shows that [V] increases after decreasing to a minimum possibly because certain viruses cannot be removed by the host as a consequence of persistent infection. In our baseline simulation, long-term DC deficiency was attributable to persistent SARS-CoV-2 infection, where viral load was often below the detection limit. The simulation result was consistent with the clinical observation that both short-term and long-term COVID-19 symptoms were commonly associated with persistent DC deficiency (Pé rez-Gó mez et al., 2021).

Deficient immune responses might cause severe COVID-19
Attenuation of the immune system during aging is associated with increased susceptibility to various infectious diseases, a decrease in the ability to fight new infections, re-emergence of latent infections, and increases in disease severity. Older people are at a much higher risk of developing severe or fatal COVID-19 than younger people (Sette and Crotty, 2021). We examined the effects of aging on the immune system to understand the risk factors and typical mechanisms related to COVID-19 exacerbation. There are no major differences between young and elderly subjects in terms of the numbers or phenotypes of their DC subsets. In contrast, the ability of DCs to phagocytose antigens, migrate, and prime T cell responses declines with advancing age Sridharan et al., 2011). Thus, we explored how reductions in the following DC functions affect COVID-19 severity: (1) DC transformation into APC, (2) APC migration toward lymph nodes, (3) and (4) CD4 + T 0 differentiation into Th1 and Tfh by APC L , (5) CD8 + T 0 differentiation into CTL L by APC L and Th1, (6) B 0 differentiation into pB by APC L and Th1, and (7) IFN1 production by APC R (STAR Methods, Table 4, Models one and 2).
Congenital and acquired defects in IFN1 signaling can result in severe COVID-19. IFN1 autoantibodies were detected in plasma samples from a large cohort comprising patients with COVID-19 and pre-pandemic controls (Bastard et al., 2021). The incidence of IFN1-neutralizing autoantibodies increasing was particularly evident in subjects >70 years old in the control cohort. Hence, the autoantibodies targeting IFN1 have manifested a common form of acquired immunodeficiency associated with $20% of all COVID-19 fatalities (Bastard et al., 2021). In the present study, we investigated how reductions in IFN1 signaling affect (1) the suppression of viral replication, (2) the migration of APC R and CTL L , (3) and (4) the differentiation of CD4 + T 0 into Th1 and Tfh, and consequently the severity of COVID-19 (STAR Methods, Table 4, Model 3, 4). With advancing age, the number of naive CD8 + T cells decreases by approximately one order of magnitude, whereas the numbers of naive CD4 + T and B cells do not (Westera et al., 2015). Thus, we also examined how age-related reductions in [CD8 + T 0 ] affect the viral load time course (STAR Methods, Table 4, Model 5). . Symbols are viral load data for Singapore patients with COVID-19 Young et al., 2020 iScience Article Reduced APC activity and deficient IFN1 signaling increase [V] immediately after symptom onset and also contribute to higher long-term viral loads ( Figure 4A). The increase in [V] following symptom onset is related to an increase in [I] ( Figure 4B). In contrast, a decrease in [CD8 + T 0 ] by one order of magnitude does not affect [V] immediately after symptom onset but does retard virus removal ( Figure 4A). In this case, the lack of any increase in the maximum [V] is attributed mainly to the lack of increase in the maximum [I] ( Figure 4B).  Figures 4C and 4D. In response to deficient APC activity and neutralization of IFN1 signaling, maximum [I] is higher for the former than the latter, maximum [V] is higher for the latter than the former. Therefore, these results reflect that IFN1 signaling profoundly affects the suppression of viral replication in infected cells.

Figure 2. Baseline model solution for immune response as the function of number of days after SARS-CoV-2 infection (A) Comparison of baseline model solution for viral load [V] calculated from our mathematical model against [V] that Kim et al. determined by fitting a target cell-limited model to viral load data
[V]s for the 90% APC activities and the 50% IFN1 signaling effects overlap each other by chance ( Figure 4A), whereas the other variables do not ( Figures 4B-4F). The higher maximum in [I] for the 80% APC activities ( Figure 4B) was attributed to a raise in viral infection flux that was indirectly mediated by the accumulated effects of reduction in each reaction rate related to APC activities ( Figure S2). Taken together, the foregoing findings indicate that all patients that are partially deficient in innate and/or acquired immunity because of inflammation and (immune) disease are also potentially at high risk of severe or even fatal COVID-19.

The probability of complete SARS-CoV-2 elimination increases with the ability of the immune system to suppress viral replication
The baseline simulation (Figure 2) indicates that numerous patients cannot successfully remove SARS-CoV-2. Furthermore, the linear stable analysis demonstrates that a steady-state with zero viral load is unstable, i.e., the baseline model never reaches the steady-state with zero viral load (Table S1). However, if the viral infection rate p I and the production rate of virus p V were reduced from these values of the baseline model, a steady-state with zero value of [V] was confirmed to be stable (Table S2). In contrast, a steady-state with a finite [V] value in the baseline model was asymptotically stable (Table S3) (Bergmann et al., 2017) (Table S4). The most sensitive parameters to a decrease in [V] were associated with Ig production (p Ig , p pB , and p Tfh ) and APC activation (p APC , a APC , and m APC ) except for parameters related to steady-state concentration of immune cells before viral infection (Table S4). The [V] time courses for six models with several fold increases in the Ig production and/or APC activation parameters (STAR Methods, Table 5) are shown in Figure 5A along with the baseline model. When [V] < 10 À4 , time evolution discontinued and it was assumed that the virus in the model with iScience Article the highest immune capacity was entirely eliminated from the host. Figure 5A shows that long-term [V] and also maximum [V] decreased with increasing parameter values, particularly immune ability. Hence, the maximum [V] asymptotically decreased along with the decrease in steady-state [V] ( Figure 5B). The [V] time courses in these immune-enhanced models deviated from the clinical observation data shown in Figure 2A. These findings suggest that patients cannot completely remove even average SARS-CoV-2 loads that are undergoing replication. Figure 5A also shows that the minimum [V] decreased with increasing those parameter values, namely, the immune ability. Therefore, as the steady-state [V] decreases, the minimum [V] becomes so small that it is effectively zero ( Figure 5C). In this case, the patient is virtually cured as [V] and [I] should stochastically converge to zero. Therefore, for instance, when Ig production and APC activity are sufficiently high, the patient is asymptomatic, if viral replication is suppressed, the virus may have been successfully removed, and the patient is cured. Otherwise, viral infection remains in the host and can progress into long COVID or PASC (Proal and VanElzakker, 2021).

DISCUSSION
SARS-CoV-2 can reach and infect the cells in multiple organs and tissues via hematogenous diffusion from heavily infected airways and lungs (Proal and VanElzakker, 2021). Influenza A virus causes a self-limited acute viral infection in the upper respiratory tract (Miyazawa, 2020). In contrast, ACE2 and TMPRSS2 enable SARS-CoV-2 to infect and penetrate a wide range of host cell types (A. Gupta et al., 2020;Paniz-Mondolfi et al., 2020;Puelles et al., 2020;Qi et al., 2020). Evidence for systemic SARS-CoV-2 infection was provided from the complete autopsies of 44 patients with COVID-19 and demonstrated SARS-CoV-2 distribution, replication, and cell-type specificity throughout the human body. The virus was widely distributed even in deceased patients with asymptomatic to mild COVID-19 (Chertow et al., 2021). In fact, viral replication was detected in multiple extrapulmonary tissues and systemic infection persisted for more than several months.
PASC is being diagnosed in patients with severe acute COVID-19 as well as those with only mild or even no symptoms (Logue et al., 2021). The long-term symptoms observed in patients with PASC may be the consequences of organ and tissue injury caused by SARS-CoV-2 and/or coagulation and inflammation during acute COVID-19 (Del Rio et al., 2020). In contrast, SARS-CoV-2 may remain within certain patients with PASC, thereby causing chronic inflammation and dysfunction in certain organs and tissues. Several studies reported that patients infected with SARS-CoV-2 may not fully clear it for very long periods of time (L. Huang et al., 2021;Liotti et al., 2021;Vibholm et al., 2021). In a trial on 203 post-symptomatic participants with previous RT-PCR-verified SARS-CoV-2 infection, 5.3% of the subjects remained virus-positive even 90 days after recovery (Vibholm et al., 2021). There were no differences between PCR-positive and PCRnegative subjects in terms of SARS-CoV-2-specific Ig. However, the PCR-positive group presented with significantly stronger SARS-CoV-2-specific CD8 + T cell responses (Vibholm et al., 2021).
Dendritic cells (DCs) are components of innate immunity and play key roles in the host SARS-CoV-2 response. Recovery of DC defects after COVID-19 is vital as the normalization of the innate immune system after acute insults are required for appropriate responses to new microbial challenges. However, patients with acute SARS-CoV-2 infection present with substantially reduced DC counts that might not normalize even 7 months after the initial acute SARS-CoV-2 infection (Pé rez-Gó mez et al., 2021) ( Figure 3). The observed long-term decrease in DC number may be explained by the migration of DC cells to inflammatory sites caused by persistent SARS-CoV-2 infection contributing to long COVID. As evidence supporting the persistent viral infection, in addition to long-term pDC deficient, reductions in non-classical monocytes and a subset of natural killer cells have been observed in the MIS-C group (Gruber et al., 2020).
Numerous studies have reported persistent single-strand RNA virus infections (Doi et al., 2016;Ireland et al., 2020;Randall and Griffin, 2017), especially in the CNS (Kristensson and Norrby, 1986). The CNS is iScience Article considered a target for several different persistent viral infections as neurons are post-mitotic single cells that persist throughout the entire lifetime of the host. Thus, neurons may provide a more protective environment for long-term viral persistence than rapidly multiplying cells that can sequester microbial pathogens (Kristensson and Norrby, 1986). As the other well-known case, hepatitis C virus (HCV) also establishes persistent infection by evading the host innate immune response (Patra et al., 2019;Rehermann, 2009). These abundant clinical observations support the potential for the persistence of the SARS-CoV-2 infection to be ongoing in patients with PASC symptoms. In an earlier clinical trial, only $5% of all subjects were positive for SARS-CoV-2 according to RT-PCR nasopharyngeal testing $90 days after infection and there was no apparent transmission to close contacts (Vibholm et al., 2021). Nevertheless, there is no consensus that patients with persistent SARS-CoV-2 infection are not contagious. Persistent SARS-CoV-2 infection and infectivity merit further investigation so that treatments for PASC may be developed and the COVID-19 pandemic may be managed more effectively.

Limitations of the study
Our mathematical model of the host immune response to SARS-CoV-2 demonstrated that age-related risk factors such as a decrease in innate immune cell activity and/or an increase in autoantibody-mediated IFN1 signaling inhibition markedly increased viral load. Our model also predicted persistent reductions in DC abundance and showed that patients with severe and even mild symptoms may develop long COVID-19 as they may not effectively eliminate the virus. However, the foregoing model did not regard memory T iScience Article and B cells. Hence, the mechanisms by which these memory effects including owing to vaccination influence the immune response to SARS-CoV-2 infection and long COVID remain unknown and further investigations including longitudinal observations on prognosis and immune response of unvaccinated and vaccinated patients are essential. Our future studies using mathematical models extended to address these issues are important to further understanding.

STAR+METHODS
Detailed methods are provided in the online version of this paper and include the following:

Simulations
The ODEs (Equations 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 and 16) used in the mathematical model of the immune response to SARS-CoV-2 were solved with the LSODA solver in the COPASI biochemical system simulator (v. 4.28) (Bergmann et al., 2017) to obtain the variable and flux time courses. The timestep that was needed to solve the ODEs was automatically chosen by the integrator in the LSODA solver. The concentrations and model parameters used in the simulations are summarized in the following tables. Baseline model parameters listed in Tables 1 and 2 without references were manually adjusted such that the baseline model simulation reproduced the time courses for the clinically observed viral load ( Figure 2A) and [Ig] ( Figure 2B). Here, a literature value was employed as the initial guessed parameter if it was available from existing literature. Consequently, the baseline simulation was consistent with the clinical data for the DC level 7 months after infection (Pé rez-Gó mez et al., 2021) ( Figure 3). Determination of steady-state solution, linear stability analysis, and sensitivity analysis were also performed with COPASI (Bergmann et al., 2017).