A System Dynamics Model Approach for Simulating

Hyper-inﬂammation in Different COVID-19 Patient Scenarios

Vladimir Estivill-Castro

3 a

, Enrique Hern

andez-Jim

enez

1,2 b

and David F. Nettleton

3 c

Institut d’Investigaci

o Biom

edica de Bellvitge, Barcelona, Spain

Loop Diagnostics S.L., Barcelona, Spain

Department of Information and Communications Technology (DTIC), Universitat Pompeu Fabra, Spain

Keywords:

Simulation of Biological Systems, Case Studies, Immune System Response, Model Construction,

Rule-induction, Machine Learning.

Abstract:

The exceptionally high virulence of COVID-19 and the patients’ precondition seem to constitute primary fac-

tors in how pro-inﬂammatory cytokines production evolves during the course of an infection. We present a

System Dynamics Model approach for simulating the patient reaction using two key control parameters (i)

virulence, which can be “moderate” or “high” and (ii) patient precondition, which can be “healthy”, “not

so healthy” or “serious preconditions”. In particular, we study the behaviour of Inﬂammatory (M1) Alveolar

Macrophages, IL6 and Active Adaptive Immune system as indicators of the immune system response, together

with the COVID viral load over time. The results show that it is possible to build an initial model of the system

to explore the behaviour of the key attributes involved in the patient condition, virulence and response. The

model suggests aspects that need further study so that it can then assist in choosing the correct immunomod-

ulatory treatment, for instance the regime of application of an Interleukin 6 (IL-6) inhibitor (tocilizumab) that

corresponds to the projected immune status of the patients. We introduce machine learning techniques to

corroborate aspects of the model and propose that a dynamic model and machine learning techniques could

provide a decision support tool to ICU physicians.

1 INTRODUCTION

Infectious pandemic corona-virus disease (COVID-

19), caused by severe acute respiratory disease

Corona-virus 2 syndrome (SARS-CoV-2) is rapidly

spreading worldwide (Salehi et al., 2020). In the

case of COVID-19, a worsening has been observed

from 7 to 8 days. However, this only occurs in some

patients; and because of an over-reaction of the im-

mune system (Pedersen and Ho, 2020). During this

pandemic, the challenge is to diagnose those patients

who are not getting worse; and thus free up space for

those who need intensive care when they develop res-

piratory failure due to acute respiratory distress syn-

drome; the main cause of mortality. In a recent retro-

spective, multi-center study of 150 conﬁrmed cases of

COVID-19 in Wuhan, China, the authors suggest that

mortality could be due to hyper-inﬂammatory sep-

sis (Chan et al., 2020).

https://orcid.org/0000-0001-7775-0780

https://orcid.org/0000-0002-8232-8151

https://orcid.org/0000-0002-5852-7716

After a coronavirus infection (COVID19, SARS-

CoV-2), patients with a more unfavourable course

present a higher viremia; this viremia is also more

persistent than those with a more benign course (Les-

cure et al., 2020). This fact will provoke a greater in-

tensity in the inﬂammatory response and involvement

of the different target organs. In clinical practice, we

can monitor the evolution of the immune response by

quantifying IL6, PCR, DD, troponin, LDH, and lym-

phopenia (Pedersen and Ho, 2020). From a concep-

tual point of view, the best therapeutic tool could be

the early and aggressive use of speciﬁc antiviral treat-

ments; but for those patients who evolved in an un-

favourable way, the course of action seems to be an

immunomodulatory treatment with increased health-

care resources (Yao et al., 2020). This care scheme

is currently impossible, we do not have any effective

antiviral treatment or tools that predict the evolution

of patients in the early stages of the clinical picture,

when patients are asymptomatic.

A ﬁrst promising study (Gautret et al., 2020)

showed that patients with COVID-19 treated with hy-

Estivill-Castro, V., Hernández-Jiménez, E. and Nettleton, D.

A System Dynamics Model Approach for Simulating Hyper-inﬂammation in Different COVID-19 Patient Scenarios.

DOI: 10.5220/0010600301410153

In Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2021), pages 141-153

ISBN: 978-989-758-528-9

141

Figure 1: Schematic representation of the Immune System

reaction to COVID.

droxychloroquine and azithromycin cured their infec-

tion and limited the transmission of the virus. How-

ever, a larger study showed limited potential and

alerted of other possible side effects; thus their use

is questionable (FDA cautions against use of hydrox-

ychloroquine or chloroquine for COVID-19 outside

of the hospital setting or a clinical trial due to risk of

heart rhythm problems (FDA, 2020)). Additionally,

Interleukin 6 (IL-6) inhibitor (tocilizumab) had been

suggested for the treatment in COVID-19 (Zhang

et al., 2020b; Choy et al., 2020). However, we still

lack reliable studies and data to verify which patients

will be beneﬁciaries of this treatment. Furthermore,

the IL-6 inhibitor has potential hazards of inducing in-

fectious diseases. Other work is also warranted to de-

termine if these compounds could be useful as chemo-

prophylaxis to prevent virus transmission, especially

for healthcare workers. Currently, some clinical tri-

als have led researchers to claim that the COVID19

studies need new directions. However, there may

also be an inadequate understanding of the key patho-

physiological mechanisms operating in COVID19 pa-

tients. Several other clinical trials of immunomodula-

tory drugs have been initiated, thus corroborating the

concept that immunosuppression has a central role.

The immune response to SARS-CoV-2 is

the main cause of pulmonary pathology and associ-

ated morbidities that lead to death in a proportion

of infected individuals, but this response is highly

variable (Liu et al., 2020). There is limited knowl-

edge of the kinetics, intensity, and diversity of cellu-

lar and humoral immune responses after SARS-CoV-

2 infection (Zhang et al., 2020a; Siracusano et al.,

2020). The innate immune response in patients af-

fected by a SARS-CoV-2 infection is characteristic

of disease outcomes (Merad and Martin, 2020). We

aim to model host immune signatures that can distin-

guish clinical outcomes in patients with COVID-19.

How the immune system reacts in these early stages

of coronavirus infection (COVID19, SARS-CoV-2)

when patients have not developed severe symptoms

has not been well studied (Siracusano et al., 2020).

In Section 2 we present a System Dynamics Model

approach for simulating the patient reaction to viral

infection. In particular, since the exceptionally high

virulence of COVID-19 and the patients’ precondi-

tion seem to constitute primary factors we focus on

using two key control parameters (i) virulence, which

can be “moderate” or “high” and (ii) patient precondi-

tion, which can be “healthy”, “not so healthy” or “se-

rious preconditions”. We aim to reﬂect in the model

the effects of pro-inﬂammatory cytokines produced

and how macrophage polarisation evolves during the

course of an infection. In particular, we focus on sim-

ulating the behaviour of Inﬂammatory (M1) Alveolar

Macrophages, IL6 and Active Adaptive Immune sys-

tem as indicators of the immune system response, to-

gether with the COVID viral load over time. Section 3

presents results of simulations and conﬁrms that it is

possible to build an initial model of the system to ex-

plore the behaviour of the key attributes involved in

the patient condition, virulence and response. Sec-

tion 4 concludes the paper with a discussion of some

speciﬁc aspects of the model and the results, also in

the context of related work.

2 MODEL DEFINITION AND

SIMULATION

We introduce a System Dynamics Model for viral in-

fection of the lungs calibrated with data from clini-

cal studies (Yang et al., 2020; Hotchkiss et al., 2013).

The modelling process, simulations, and optimisation

analyses were performed using Vensim

PLE soft-

ware, version 8, academic license (Ventana Systems,

Harvard, MA, USA). The model consists of inter-

connected “stocks” and “ﬂows” to represent the im-

mune system behaviour in response to a COVID in-

fection. There has been a strong interest in epidemio-

logical models for COVID-19 that study the propaga-

tion of the virus and the potential impact of measures,

such as social distancing, to assist decision-making

for managing transmission, delivery of testing and

other resource management challenges (Currie et al.,

2020). In particular, a freely distributed epidemiolog-

ical model (vensim.com/coronavirus/) has attracted

signiﬁcant social-media attention. We take a rather

orthogonal approach and apply dynamic system mod-

elling to the reaction of the Immune System to viru-

SIMULTECH 2021 - 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

142

lent viruses such as COVID.

One of the fundamental contributions of deﬁning

this model is that it documents the interactions and

potential cause-effect relationships between the many

substances, proteins, and elements of tissue and of the

immune system. A model of this type also highlights

the potential gaps to increase research efforts as well

as the points where a cause-effect relationship can be

altered in search for vaccines or cures.

For instance, there is some understanding about

how a coronavirus uses its S protein to enter into host

cells (mainly latching to ACE-2). There is also some

understanding of the replication processes that hap-

pen afterwards (which involves viral particles germi-

nating into the endoplasmic reticulum-Golgi interme-

diate compartment). Some aspects are also known

about how some new copies of the virus are re-

leased without immediate destruction of the host cell.

Similarly, some microbiology understanding exists

for how the infected cell presents antigen to anti-

gen presentation cells. We remark that the details

for COVID-19 are less known (Li et al., 2020) and

those details now suggest differences between SARS-

CoV and MERS-CoV. Therefore, we will not sim-

ulate the details of antigen presentation here. We

focus on the transitions and activity illustrated in

Figure 1. Figure 2 contains the complete model

with the main control input on the bottom left (vir-

ulence and patient precondition) and 9 main stock-

ﬂows groups which have been designated as A to I.

(see Table 1 for descriptions). A key stock generated

in the model is “viral load” (C) and other key out-

puts are the immune system response (F), lung tis-

sue destruction (coming from A) and macrophages

(coming from E). The rectangles signify a “stock”

(store of something), the circles represent a “rate”,

the hexagons are inputs, arrows are ﬂows, variables

(named source nodes) and the small clouds represent

external source/destination. Table 2 provides a sum-

mary of the event sequence that the stock-ﬂow model

captures.

2.1 Alveolar Macrophages (M1 and M2)

and Viruses: Three Central Stocks

The main player of the immune response in COVID-

19 are the alveolar macrophages (AM) (Merad and

Martin, 2020). These cells detect and respond to

danger signals resulting from pathogen colonization,

growth, and tissue damage. Upon recognition, AM

cells trigger an inﬂammatory response (M1). How-

ever, this reaction must be tightly regulated, as un-

controlled inﬂammation leads to clinical complica-

tions (

Alvarez et al., 2017). One of the most impor-

tant mechanisms to protect a host from excessive in-

ﬂammation is a type of tolerance known as a refrac-

tory state or M2 (Rackov et al., 2016). This protective

mechanism could also become a serious clinical prob-

lem, since an inadequate innate response signiﬁcantly

increases the risk of infections spreading. This cru-

cial process, should never be confused with “immune

paralysis”. The M2 state or refractory state, is char-

acterized by the ability of reduction of the inﬂamma-

tory response (low levels of IL-6) and the increment

of their phagocytosis capacity (Cubillos-Zapata et al.,

2014). Although macrophage polarisation in humans

is arguably a continuum (Atri et al., 2018), we cre-

ate three stocks whose units are “macrophages”.The

interactions of these stocks and their ﬂows is repre-

sented by Group E in Figure 2 and Table 1.

2.2 Lung Tissue Fights Virus Infection

We further our model by incorporating the signals be-

tween tissue cells. Interferon (IFN) is a generic name

for signalling proteins produced and released by in-

fected host cells in response to the presence of several

viruses. The virus-infected cells produce interferon

causing neighbour cells to intensify micro-biological

anti-viral defences.

Thus, our model considers this neighbour defence

system (refer to Group A in Figure 2 and Table 1).

It represents that IFN released by infected lung tis-

sue results in a reduction in the rate by which viruses

transform healthy lung cells to infected cells. We do

not intend to be too detailed in the impact of the virus

with respect to different types of interferon. Sufﬁce to

say that there is some consensus that the IFN response

is high in mild-to-moderate patients, but is reduced in

the severe cases (Hadjadj et al., 2020).

To elaborate the model, we progress to represent

the cytopathic effects and the viral evasion capabil-

ity that appears in viral infections from human coro-

naviruses (SARS-Cov, MERS-CoV and COVID-19).

It is clear that viral evasion contributes to the severity

of the disease, but all the processes that lead to a dys-

regulated immune response and sustained inﬂamma-

tion are not completely understood (Channappanavar

and Perlman, 2017). While there are several common-

alities between the viruses’ mechanisms for evasion

in COVID-19, SARS-CoV and MERS-CoV (Li et al.,

2020), there are also some differences and several de-

tails unknown (Pedersen and Ho, 2020). Therefore,

we consider that our model incorporates all these as-

pects by the viruses impacting on the IFN-immune re-

sponse modelled earlier. That is, we represent the in-

terference the virus performs affecting interferon sig-

nals to neighbour tissue cells. Thus, higher virulence

A System Dynamics Model Approach for Simulating Hyper-inﬂammation in Different COVID-19 Patient Scenarios

143

Figure 2: System Dynamics Model for the Immune system response to COVID. The rectangles signify a “stock” (quantity

existing at a point in time), the circles represent a “rate”, the magenta hexagons are inputs, arrows are ﬂows and the small

clouds represent external source/destination.

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Table 1: Stock-ﬂow groups as deﬁned in Fig 2.

Stock-ﬂow groups & Description Links in-out to other stock-ﬂow group

A : Lung tissue (uninfected →infected → destroyed)

Outgoing link to Flow C, incoming links from {Flow C,Flow E}

B : Interferon strength

Outgoing link to Flow A, incoming link from Flow A.

C : Viral load

Outgoing links to {Flow A, Flow D, Flow E}, incoming link from Flow A

D : PAMPS

Outgoing link to Flow E, incoming link from Flow C

E : Alveolar macrophages (resting → inﬂammatory(M1) → immunosuppressed(M2))

Outgoing links to {Flow F, Flow G}, incoming links from {Flow C, Flow D}

F : Adaptive immune system resting → active Incoming link from Flow E, outgoing link to Flow I

G : IL6 (production → degradation) Outgoing links to Flow H, incoming link from Flow G

H : Delayed IL6 Incoming links from Flow G

I : T-cell Interferon

Incoming links from Flow F

means less effective interferon signals.

The focus of model is to represent the link be-

tween ampliﬁed inﬂammatory response and higher

virus replication (Channappanavar and Perlman,

2017). Therefore, our model represents (refer to

Group C and Group D in Figure 2 and Table 1) the be-

lief that higher viral titters result in an increased viral

Pathogen-Associated Molecular Patterns (PAMPs)

that further dampen IFN signalling and stimulate Pat-

tern Recognition Receptors (PRRs).

2.3 Macrophage Activation

Macrophages detect viruses in many ways. One of

the nasty aspects of coronaviruses such as COVID-

19, SARS-CoV and MERS-CoV, is that they impact

the role of Pattern Recognition Receptors (PRRs)in

the innate immune system response (Li et al., 2020).

For simplicity, we model that PRRs are proteins ex-

pressed by macrophages (although also expressed by

dendritic cells, monocytes, neutrophils and epithelial

cells). They identify two types of molecules.

1. Pathogen-Associated Molecular Patterns

(PAMPs): foreign molecules coming from

microbial pathogens.

2. Damage-Associated Molecular Patterns

(DAMPs): molecules coming from damaged

or dead cells in the host.

As we mentioned, although macrophages exhibit a

range of phenotypes, they can be predominantly sep-

arated into two types (Stout and Suttles, 2004).

• M1 macrophages appear in the early stages of in-

ﬂammation and are activated by four key media-

tors: interferon-γ (IFN-γ), tumour necrosis factor

(TNF), and damage associated molecular patterns

(DAMPs). From these mediator molecules, alve-

olar macrophages create a pro-inﬂammatory re-

sponse that in return produces pro-inﬂammatory

cytokines like Interleukin-6 (IL-6

Interleukin: cytokines made by one leukocyte and acting

• M2 macrophages produce an anti-inﬂammatory

response via the release of Interleukin-4 or

Interleukin-13. They participate in tissue healing.

These two types of macrophages can be con-

verted into each other (Liu et al., 2014). Inter-

feron (IFN)-γ activates resting macrophages as M1

macrophages. When ﬁghting severe viral infections,

more macrophages are recruited by the secretion of

further inﬂammatory mediators (Liu et al., 2014).

Our model represents the migration between these

two types. The model represents the late awakening

of macrophages because of the virus capacity to block

the signals that allow its early detection. It has been

reported that coronaviruses are capable of circum-

venting detection by developing double-membrane

vesicles without PRRs and then replicate in these

vesicles (Li et al., 2020). Alveolar macrophages

are the crucial defence against viruses. Although

macrophages defend against viruses in many ways

(secretion of oxygen metabolites, lysozyme, antimi-

crobial peptides and proteases), our model will focus

on phagocytosis and intracellular killing.

Thus, our model enables to represent the virulence

of the virus by regulating the sensitivity; i.e. the ca-

pacity of its rapid detection. With early detection,

(high sensitivity, low virulence), M1 macrophages

grow quickly in numbers and extinguish the virus

rapidly. The alternative scenario is when the virus can

pass under the radar for a while, resulting in a slow re-

sponse of low numbers of macrophages.

2.4 Macrophages Production of IL-6

We calibrate our model so it matches the observation

that COVID-19 patients suffer from excess inﬂamma-

tion at 9-10 days (Zhou et al., 2020). Cytokines and

chemokines have long been understood to have an im-

portant role in immunity and immunopathology, but

exuberant and deregulated immune responses have

on other leukocytes

A System Dynamics Model Approach for Simulating Hyper-inﬂammation in Different COVID-19 Patient Scenarios

145

Table 2: Event sequence for the model of Figure 2.

Steps in the process represented by the model

Main stock-ﬂow

groups (Table 1)

associated with

chronological steps

Virus present. The virus displays many PAMPS which activate Macrophages M0 to M1.

Model notes: Virus infects a lung cell (lung tissue), interferon is released which alerts neighbouring lung cells. Very low

loads and non aggressive/simple viruses do not progress from this. COVID-19 can pass this stage.

Flow A, Flow C,

Flow D and

Flow E

M1 produces inﬂammatory cytokines like IL-6.

Model notes: Virus passes the interferon alarm of lung cells to their neighbours, and grows by infecting other neighbouring

cells. Viruses may kill or generate copies before killing. Most human cells when infected by viruses generate alarm signals.

COVID-19 can reduce the detectability of these signals released by infected cells.

Flow C, Flow B,

Flow E and

Flow G

M1 starts presenting the virus PAMPS and other antigens to T-cells (CD4 and CD8, and

then T cells start producing Interferon).

Model notes: Macrophages of lung tissue [eventually] detect the virus (generically by PAMPs and PPRS), become active

[turn into predominantly M1] and ﬁght it.

1. For many viruses and small loads the macrophages can kill all and destroy the infection.

2. They themselves raise alarm signals to activate other Macrophages to turn M1 and to produce inﬂammation (release IL-6

and TNS which are pro-inﬂammatory cytokines )

3. This also creates exponential growth in the activation of macrophages of type M1, which if all goes well, can destroy

the virus, and once virus load is down, M1’s turn into M2s, IL-6 comes down and the tissue regenerates because M2’s

repair). Sustained inﬂammation and long time periods of IL-6 is destructive of other organs, sepsis, storm, etc

4. Some of the macrophages are recruited by the release of IL-6 and its propagation in the body from other regions beyond

the infected tissue (the lung)

5. Possibility that COVID-19 can have a stale-mate with a macrophage by infecting it into an abortive infection (the virus

also does not get to reproduce).

Flow E, Flow D

and Flow B

Sub-steps

(see Model Notes):

1 involves Flow C,

Flow E, Flow A

2 involves Flow E,

Flow G, Flow A

3 involves Flow E,

Flow H

4 involves Flow E

Interferon produces M1 and activated CD8 T cells and NK cells to destroy the virus.

Model notes: Several types of lymphocytes are produced rapidly and of all kinds in young people (slowly and with biases for

some types of T-cells). For elderly people, people with diabetes, people with already issues with their immune system [i.e.

lupus] the reinforcements of the adaptive immune system come slow, and/or with biases for some types of T-cells. .

Flow E

M1 becomes M2.

Model notes: Modelled via the immunosuppression rate. Typically, this is regulated via intracellular and genetic regulation

inside M1 macrophage.

Flow E

M2 stops producing inﬂammation (IL-6) and stops presenting

Model notes: This also implies that M2 stops presenting and blocks the T-cell response - because of this cause damage to the

lung. It also increases their phagocytic capacity to eliminate the virus.

Flow E, Flow H

been shown to potentially cause lung damage and de-

creased survival (Pedersen and Ho, 2020). We also

model the observation that, in SARS-CoV-2 infected

individuals, cytokines like IL-6 increase during dis-

ease and decreases during recovery. These cytokines

are especially higher in patients requiring ICU ad-

mission which also exhibit signiﬁcantly higher levels

of fever (Yang et al., 2020). This inﬂammatory cy-

tokine levels were slightly elevated or within the nor-

mal range in moderate cases, but remarkably elevated

in most severe cases. These cytokines are likely pro-

duced by highly inﬂammatory macrophages that have

been implicated in the cytokine storm. The discovery

that several potent cytokines, including IL-6 are in in-

creased concentrations in COVID-19 patients, led to

the concept of blocking them as a treatment to reduce

a cytokine storm (Yao et al., 2020).

However, the behaviour of IL-6 in our model is a

consequence of the macrophages production. There-

fore, the next elaboration of our model is the response

by the innate immune system (refer to Group G and

Group H in Figure 2 and Table 1). In light of

the larger numbers of viruses, M1 macrophages pro-

duce cytokines (including Interleukin-1, IL-6, and

tumour necrosis factor-α), chemokines (including

Interleukin-8), and arachidonic metabolites. How-

ever, among many roles, we focus on IL-6’s effect to

induce inﬂammation (Tanaka et al., 2014). Moreover,

IL-6’s elevated values are consistent in COVID-19 pa-

tients, especially those with severe outcomes (Zhou

et al., 2020; Chen et al., 2020b). IL-6 is believed to be

central to COVID-19 infections resulting in dysfunc-

tional immune response sometimes considered sim-

ilar to sepsis (Hotchkiss et al., 2013) or a so-called

cytokine storm (Chen et al., 2020a). In our model,

we focus on IL-6 production. Again, we are aware

that many other phenomena happen concurrently, in

order for the binding of PAMPs to Toll-Like Recep-

tors (TLRs, which are a type of pattern-recognition

receptors) to eventually result in the activation and

detachment of alveolar macrophages from the alve-

olar epithelial cells, followed with the phagocytosis

of viruses and secretion of Inﬂammatory cytokines

(IL-6). However, for now such detail is not modelled.

What is modelled is a predator-prey approach where

activated (M1) macrophages hunt viruses.

Our model aims to simulate autocrine feedback

loops that amplify inﬂammation (Choy and Rose-

John, 2017). Again, there other innate immune cells

(such as neutrophils and monocytes) that produce and

respond to IL-6 besides macrophages. but we fo-

cus on macrophages since studies have found that for

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146

COVID-19, there is a high incidence of macrophage

inﬁltration (Channappanavar and Perlman, 2017).

2.5 The Adaptive Immune System

In our modeling of the adaptive immune system,

we consider background information relating the key

stocks. For example, the observation that COVID-

19 causes macrophages to become M1 type and pro-

duce the pro-inﬂammatory cytokine IL6 (Pedersen

and Ho, 2020). In its turn, Il-6 promotes lympho-

cyte necrosis (Chen et al., 2020b). The serum con-

centration of IL-6 is negative to blood CD4 and

CD8 T cells (Chen et al., 2020b). COVID-19 infec-

tion can cause T-cell exhaustion, and more notice-

able with patients requiring ICU care (Diao et al.,

2020). In terms of the effect of patient precondi-

tions on the adaptive immune system, smoking and

advanced patient age are key factors (Zhou et al.,

2020; Diao et al., 2020; Feller et al., 2018). T-

cell and B-cell function presents age-dependent de-

fects that can result in an over-production of type 2

cytokines, which in turn results in deﬁcient control

of viral infection and prolonged proinﬂammatory re-

sponses (Zhou et al., 2020). Smoking has been iden-

tiﬁed as a factor that promotes macrophage activation

and the macrophage polarisation for M1 macrophages

over M2 macrophages (Feller et al., 2018). Elderly

patients exhibit lower T-cell numbers, with suggests

that TNF-α could be inducing T-cell depletion (Diao

et al., 2020). For our modelling purposes, we intro-

duce the condition of the patient as an element that

distorts the engagement of the adaptive immune sys-

tem (refer to Group F in Figure 2 and Table 1).

3 RESULTS

Our model offers two key control parameters, virus

virulence and patient preconditions. The virus vir-

ulence (denoted v) is set to 1 or 2, where 1 repre-

sents a virus which is not so virulent, generating many

PAMPs, and not so adept at stealth; 2 indicates a high

virulence with low sensitivity.

The patient pre-condition (denoted p) can be 0, 1

or 2: 0 indicates a very healthy patient whose adaptive

immune system supports the innate immune system

with quick response; 1 indicates a not so healthy pa-

tient where the adaptive immune system is somewhat

slower; 2 indicates a patient with very serious pre-

conditions compromising the response of the adaptive

immune system.

The six possible combinations of virus virulence

and patient pre-conditions described in the design of

Table 3: Six experiments conducted with our model.

Virus virulence 1 1 1 2 2 2

Patient preconditions 0 1 2 0 1 2

Figure 3: Plot of ’Viral Load’ for different virulence and

patient preconditions.

experiment are given in Table 3.

3.1 Results of Simulation

Figure 3 to Figure 5 show the plots for selected key

stocks and rates for the model shown in Figure 2 and

the experiments listed in Table 3. It can be seen that

a healthy patient (patient precondition 0) is able to

overcome a moderate and a high virus virulence. The

macrophages, IL6 and adaptive immune system re-

turn to normal once the virus is overcome. However

for the patient with serious precondition (patient pre-

condition 2) the macrophages, IL6 and adaptive im-

mune system stay high even when the virus virulence

goes down. Also note that the less healthy the pa-

tient, the higher the values for macrophage, IL6 and

immune system.

With reference to Figure 5 (a) (AAIS vs Viral

Load) the log scale on the y-axis reveals an “attractor

type” curve which can be an emergent feature of dy-

namical systems (Dudkowski et al., 2016). It can be

seen that the viral load curves backwards for higher

levels of AAIS (Active Adaptive Immune System).

Note that this tendency is effectively following the

sequence over time. In the case of Viral Load this

makes sense - as the AAIS becomes more progres-

sively activated, there is an inﬂection point around

x-axis value 48 for the v = 1 group and around the

value 60 for the v = 2 group.

A System Dynamics Model Approach for Simulating Hyper-inﬂammation in Different COVID-19 Patient Scenarios

147

Figure 4: Plot of ’IL6’ (a) and ’Active Adaptive Immune System’ (b) vs time for different virulence and patient preconditions.

In the case of Figure 5 (b) (AAIS vs M1), some-

thing similar happens for the healthiest patients (p =

0) as the immune system activates. For the highest

virulence (v = 2) and worst patient condition (p = 2),

M1 continues rising together with AAIS. Now con-

sider the top right quadrant M1 > 45 and AAIS > 700

as a “dangerous region” (the thresholds represent an

initial approximation which would be calibrated as fu-

ture work). The intermediate virulence values and pa-

tient states are located to the left of this region with

clear point (v = 1, p = 1) for a positive infection

outcome (going out of the “dangerous region”). But

v = 1, p = 2 (worst patient type) is heading into the

dangerous region, whereas v = 2, p = 1 is relatively

static but also close to the dangerous region together

with the two highest risk patient types.

3.2 Interpretation, Conﬁrmation and

Limitations

We interpret the displayed phenotype to have the fol-

lowing vivo relevance: a poor inﬂammatory capacity

situation (High Virulence (id = 2) and Healthy Patient

precondition (id=0) represented by the green lines in

Figures 3 to 5) has impaired antigen presentation and

would possibly either inhibit or alter the development

of an adaptive response (AAIS). Moreover, an inter-

mediate controlled level of M1 macrophages (black,

grey and red lines, Figure 5(b)) reduce their inﬂam-

matory cytokines like IL-6. Such condition would

contribute to protection against septic shock, and in-

creased phagocytosis that would allow efﬁcient vi-

ral clearance. In support of this, M2 macrophages

have been related to decreased antigen presentation

and impaired T-cell proliferation as well as reduced

production of IFN. These observations underline the

importance of the interaction between the antigen-

presenting cells like M1 macrophages and the T-cells

during infections. Finally, the higher inﬂammatory

situation (blue lines in Figures 3 to 5) increases M1

and T-cell with more lag, and a lesser increasing

slope; therefore they are much less efﬁcient in elimi-

nating the viral load.

Table 4 shows the correlations between all the

stocks from the model of Figure 2. Correlations

over 0.7 are highlighted, and high values can be

seen between M1, IL6 and the Active adaptive im-

mune system. Also, high values can be seen be-

tween M2 and Infected/destroyed lung tissue and In-

terferon strength. Apart from Time, Resting Alveolar

has the most correlations greater than 0.7 with other

stocks. The complete dataset was used to calculate

the correlations and generate a PART rule-model ap-

pearing in Table 6. This rule model is set to predict

IL6, was trained on a random sample of 50% of the

data and tested on the remaining 50%. PART is a

highly effective rule-induction algorithm (Frank and

Witten, 1998) and the Weka (Hall et al., 2009) imple-

mentation of a variation on Quinlan’s C4.5 (Quinlan,

1993). This approach to build decision trees (or deci-

sion lists (Frank and Witten, 1998)) which uses Shan-

non’s information theory to calculate an information

gain to rank the best attribute candidates to include

in the rules. The composition of the antecedents and

consequents of the rules for predicting IL6 can give

us useful information about what are the most rele-

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148

Figure 5: Plot of ’Active Adaptive Immune System’ vs ’Viral Load’ (a) and ’Inﬂammatory M1 Alveolar Macrophages” (b)

for different virulence and patient preconditions.

Table 4: Correlations between model stocks.

Time (hours)

Virulence

Patient precondition

Viral load

Inﬂammatory (M1) Alveolar

Macrophages

IL6

Active Adaptive Immune System

Immunosuppressed (M2) Alveolar

macrophages

Resting Alveolar Macrophages

Delayed IL6

Un-Infected Lung Tissue

Infected Lung Tissue

Destroyed Lung Tissue

Interferon Strength

PAMPs

Resting Adaptive Immune System

T-cell Interferon

Time (hours) 1 0 0 -0.37 0.71 0.71 0.74 0.95 -0.92 0.72 -0.65 -0.62 -0.6 0.8 0.25 -0.77 0.76

virulence 0 1 0 0.39 -0.03 -0.03 -0.41 -0.05 0.04 -0.03 -0.13 0.04 0.04 0.08 -0.46 0.42 -0.41

Patient precondition 0 0 1 0.07 0.36 0.36 0.23 -0.14 -0.13 0.34 -0.03 0.01 0.01 0.01 0.06 -0.19 0.16

Viral load -0.37 0.39 0.07 1 -0.37 -0.38 -0.62 -0.41 0.43 -0.42 -0.26 0.41 0.47 0.1 -0.04 0.6 -0.58

Inﬂammatory (M1) Alveo-

lar Macrophages

0.71 -0.03 0.36 -0.37 1 1 0.75 0.62 -0.9 1 -0.6 -0.6 -0.58 0.66 0.5 -0.64 0.57

IL6 0.71 -0.03 0.36 -0.38 1 1 0.76 0.62 -0.9 1 -0.59 -0.6 -0.59 0.65 0.49 -0.65 0.58

Active Adaptive Immune

System

0.74 -0.41 0.23 -0.62 0.75 0.76 1 0.65 -0.78 0.78 -0.38 -0.56 -0.56 0.52 0.4 -0.96 0.93

Immunosuppressed (M2)

Alveolar macrophages

0.95 -0.05 -0.14 -0.41 0.62 0.62 0.65 1 -0.9 0.63 -0.64 -0.69 -0.68 0.78 0.34 -0.67 0.65

Resting Alveolar

Macrophages

-0.92 0.04 -0.13 0.43 -0.9 -0.9 -0.78 -0.9 1 -0.91 0.69 0.72 0.7 -0.8 -0.47 0.73 -0.68

Delayed IL6 0.72 -0.03 0.34 -0.42 1 1 0.78 0.63 -0.91 1 -0.58 -0.6 -0.59 0.65 0.47 -0.67 0.6

Un-Infected Lung Tissue

-0.65 -0.13 -0.03 -0.26 -0.6 -0.59 -0.38 -0.64 0.69 -0.58 1 0.44 0.37 -0.97 -0.64 0.3 -0.25

Infected Lung Tissue

-0.62 0.04 0.01 0.41 -0.6 -0.6 -0.56 -0.69 0.72 -0.6 0.44 1 0.99 -0.52 -0.35 0.52 -0.48

Destroyed Lung Tissue

-0.6 0.04 0.01 0.47 -0.58 -0.59 -0.56 -0.68 0.7 -0.59 0.37 0.99 1 -0.46 -0.3 0.52 -0.48

Interferon Strength

0.8 0.08 0.01 0.1 0.66 0.65 0.52 0.78 -0.8 0.65 -0.97 -0.52 -0.46 1 0.58 -0.47 0.43

PAMPs

0.25 -0.46 0.06 -0.04 0.5 0.49 0.4 0.34 -0.47 0.47 -0.64 -0.35 -0.3 0.58 1 -0.25 0.17

Resting Adaptive Immune

System

-0.77 0.42 -0.19 0.6 -0.64 -0.65 -0.96 -0.67 0.73 -0.67 0.3 0.52 0.52 -0.47 -0.25 1 -0.99

T-cell Interferon

0.76 -0.41 0.16 -0.58 0.57 0.58 0.93 0.65 -0.68 0.6 -0.25 -0.48 -0.48 0.43 0.17 -0.99 1

A System Dynamics Model Approach for Simulating Hyper-inﬂammation in Different COVID-19 Patient Scenarios

149

Table 5: Two sample rules for predicting IL6.

Rule 1 IF Inﬂammatory (M1) Alveolar Macrophages > 16.289

THEN IL6 =

0.1 × Inﬂammatory (M1) Alveolar Macrophages

+ 0.0021 × Immunosupressed (M2) Alveolar macrophages

- 0.1056 [763/0.931%]

Rule 2 IF Inﬂammatory (M1) Alveolar Macrophages ≤ 1.381

THEN IL6 =

-0.0001 × Viral Load

+ 0.1025 × Inﬂammatory (M1) Alveolar Macrophages

- 0.0101 × Delayed IL6

- 0.0001 × T-cell Interferon

+ 0.0019 [410/1.095%]

vant attributes to include in the model as proposed by

the rule-induction algorithm.

From the complete model deﬁnition it can be

seen that in the antecedent of the ﬁrst three rules,

“Inﬂammatory (M1) Alveolar Macrophages” is in-

cluded. Rule 4 also uses Active Adaptive Immune

System as well as M1. Rule 5 uses T-cell Interferon

in the antecedent. In the antecedents, Rule 6 has

“Time (Hour)” and “Active Adaptive Immune Sys-

tem”, Rule 7 has “Viral Load” and Rule 8 has “Time

(Hour)”. On the other hand, the consequents of all

the rules use mainly the following stocks: “Viral

Load”, “Time (Hour)”, “M1”, “Active Adaptive Im-

mune System” and “Delayed IL6”. It can be seen that

Rule 1 and Rule 2 have the most corresponding cases,

with 763 and 410, respectively. Rule 6 to Rule 9

have relatively much fewer cases associated. From

the overall rule model (Appendix-Table 6), it can be

concluded that “M1” and Active “Adaptive Immune

System” are key stocks for predicting IL6.

The scope of the simulation is limited, for exam-

ple, by ﬁxing one of the key control parameters (i.e.

viral load) while varying the other (patient precondi-

tions). In this way we see the behaviour of the im-

mune system through Figure 3, Figure 4 and Figure 5.

On the other hand, the viral load does not vary for

different patient preconditions and in vivo, we would

expect a weaker patient to allow the virus load to be

greater.

4 DISCUSSION

The results show that it is possible to build an ini-

tial model of the system to explore the behaviour

of the key attributes involved in the patient condi-

tion, virulence and response. From the perspec-

tive of dynamic models, our results show that, with

the few elements we have incorporated (relative to

the many other players known to be involved), the

system has many bifurcations and the behaviour is

far from stable. In particular, such bifurcations in-

spire aspects that need further study. From the per-

spective of control theory, signiﬁcant more informa-

tion is required to exercise control of the inﬂamma-

tory response by selecting medication depending on

a modelled individualised classiﬁcation of the poten-

tial outcome for each patient. The immune control

of the excessive inﬂammatory response is called re-

fractory state (RS); this mechanism is characterized

by a signiﬁcant reduction in the inﬂammatory capac-

ity (IL-6) of innate immune cells like macrophages to

a subsequent Pathogen-Associated Molecular Pattern

(PAMP) challenge (L

opez-Collazo and del Fresno,

2013; Agrawal et al., 2015). However, this state

is not restricted to bacterial sepsis but has been ob-

served for a number of pathologies such as acute

pulmonary syndrome, cystic ﬁbrosis, and even can-

cer (L

opez-Collazo et al., 2010). While refractory

state (RS) has been thought of as a protective mech-

anism against septic shock and ischemia, its immune

regulation was associated with non-controlled hyper-

inﬂammatory status in COVID-19. Similarly, in acute

pulmonary syndromes and cystic ﬁbrosis, RS relates

to an increased susceptibility to nosocomial infec-

tions (Biswas and Lopez-Collazo, 2009). Several

studies have also shown some common mechanistic

paradigms in RS across different diseases (L

opez-

Collazo and del Fresno, 2013). In addition to this, RS

in cystic ﬁbrosis shows impaired antigen presentation,

however it also displays a potent phagocytic activ-

ity. In cancer, tumor-associated macrophages (TAMs)

show an immunosuppressive phenotype similar to RS

macrophages. TAMs show decreased production of

inﬂammatory cytokines like IL-6 but upregulation of

anti-inﬂammatory cytokines (Cubillos-Zapata et al.,

2014). This was explained by a defective NF-kB ac-

tivation, overexpression of p50 NF-kB homodimers,

and a functional TRIF pathway (Biswas and Lopez-

Collazo, 2009).

Taken together, the SARS-CoV-2-induced cy-

tokine storm is associated with disease severity and

outcome. Understanding immune dysregulation in

patients with COVID-19 not only provides a bet-

ter understanding of the pathogenesis of SARS-CoV-

2, but also identiﬁes targets for immune therapeu-

tics (Merad and Martin, 2020). While antiviral agents

are currently being explored, the use of antiviral

agents alone may not be sufﬁcient to stop the cytokine

storm, lung destruction, and respiratory distress in pa-

tients who presented late after infection. Targeted im-

munomodulation that reduces cytokine storm can im-

prove lung inﬂammation and hopefully reduce mor-

tality (Avenda

no Ortiz et al., 2017). Other studies of

SIMULTECH 2021 - 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

150

the viral factors driving immune dysregulation may

provide insights into the conformation of vaccine re-

sponses to protective immunity (Zhang et al., 2020a).

Advances in immunology and our understanding of

the pathophysiological basis of sepsis provides ex-

citing new therapeutic opportunities (

Alvarez et al.,

2017; Hotchkiss et al., 2013; Rackov et al., 2016;

Shalova et al., 2015). We postulate that immunother-

apy will have a wide range of beneﬁcial effects on

COVID19, and could be an important advance in

infectious disease. Recently, interleukin 6 receptor

(IL-6R) monoclonal antibody (tocilizumab)-directed

COVID-19 therapy has been used in a clinical trial in

China (No.ChiCTR2000029765) and the US (Clini-

calTrials.gov Identiﬁer: NCT04322773) Such therapy

has been incorporated into COVID-19 management

guidelines generated in China based on the concept of

“cytokine storm” in COVID-19 pneumonia. Here, we

explore the role of interleukin 6 (IL-6) in COVID-19

patients that could help the physician to recommend

tocilizumab increasing the efﬁcacy of this monoclonal

antibody-directed therapy. Our results highlight the

paramount need for future studies examining subsets

and functions of both innate and adaptive immune

cells at different time points, such as early during the

asymptomatic viremic stage, during respiratory dis-

tress, and after recovery. This may identify mecha-

nisms that lead to immune dysregulation in patients

who have different susceptibilities to the disease, such

as children versus the elderly. We now have a better

understanding of the IL-6 change and cytokine storm

in COVID-19 pneumonia, but more data are needed

on treatment options that improve survival.

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APPENDIX

The datasets generated and analyzed for this

study can be found in the Github available at:

github.com/vladestivillcastro/SIMULTECH2021.

We also have available tables that provide details

as follows.

Stocks: stock, equation and units.

Flows: ﬂow, equation and units.

Auxiliary Variables: auxiliary variables, equation

and units.

Constants ID, parameters, value, units.

Table 6: Learned rules.

Rule 1 IF Inﬂamatory (M1) Alveolar Macrophages > 16.289

THEN IL6 =

0.1 × Inﬂamatory (M1) Alveolar Macrophages

+ 0.0021 × Immunosupressed (M2) Alveolar macrophages

- 0.1056 [763/0.931%]

Rule 2 IF Inﬂamatory (M1) Alveolar Macrophages ≤ 1.381

THEN IL6 =

-0.0001 × Viral Load

+ 0.1025 × Inﬂamatory (M1) Alveolar Macrophages

- 0.0101 × Delayed IL6 - 0.0001 × T-cell Interferon

+ 0.0019 [410/1.095%]

Rule 3 IF Inﬂamatory (M1) Alveolar Macrophages > 10.592

THEN IL6 =

-0.0002 × Time (Hour) - 0.0015 ×Viral Load

+ 0.0833 × Inﬂamatory (M1) Alveolar Macrophages

- 0 × Active Adaptive Immune System

+ 0.0001 × Resting Alveolar Macrophages

+ 0.1664 × Delayed IL6

- 0.5716 [89/0.318%]

Rule 4 IF Active Adaptive Immune System > 9.922

Inﬂamatory (M1) Alveolar Macrophages > 6.424

THEN IL6 =

-0.0001 × Time (Hour) - 0.0048 × Viral Load

+ 0.1134 × Inﬂamatory (M1) Alveolar Macrophages

- 0.0003 × Active Adaptive Immune System

- 0.0008 × Immunosupressed (M2) Alveolar macrophages

+ 0.0011 × Resting Alveolar Macrophages

- 0.1284 × Delayed IL6 + 0.0015 × TcellInterferon

- 5.0631 [69/0.096%]

Rule 5 IF TcellInterferon > 0.517

THEN IL6 =

-0.0003 × Time (Hour) - 0.0019 × Viral Load

+ 0.0992 × Inﬂamatory (M1) Alveolar Macrophages

+ 0.0001 × Active Adaptive Immune System

+ 0.1282 [79/2.143%]

Rule 6 IF Time (Hour) > 1.5 and Active Adaptive Immune System ≤ 7.841

THEN IL6 =

-0.0003 × Time (Hour) - 0.0103 × Viral Load + 0.7211 [11/1.317%]

Rule 7 IF Viral Load ≤ 0.999

THEN IL6 =

+ 0.9887 [4/0%]

Rule 8 IF Time (Hour) > 1

THEN IL6 =

+ 0.9597 [4/4.369%]

Rule 9 IF

THEN IL6 =

+ 3 [2]

A System Dynamics Model Approach for Simulating Hyper-inﬂammation in Different COVID-19 Patient Scenarios

153