Figure 1.
Functional diagram of the immune response to a virus targeting macrophages.
Interactions between macrophages and virus (1) result in macrophage activation by either phagocytosis (2a, amplified by antiviral cytokines and inhibited by immuno-modulatory cytokines) or macrophage infection (2b, amplified by immuno-modulatory cytokines and inhibited by antiviral cytokines) releasing viral particles (3b). The activated macrophages initiate the adaptive response (4a–c). and
orient the adaptive response towards the cellular response (4a), whereas immuno-modulatory cytokines orient the response towards the humoral and regulatory responses (4b–c). The cellular response and the natural killers are responsible for the destruction of infected cells by cytolysis (7 & 10, respectively). The humoral response is responsible for the viral neutralisation through antibodies (6). The recruitment of susceptible macrophages and natural killers is amplified by the pro-inflammatory cytokines (8a & 8b, respectively). Cytokines are produced by activated macrophages (3d), natural killers (9) and adaptive cells (4a–c). These syntheses are regulated by various cytokines.
Figure 2.
Conceptual model: state variables and flows without regulations.
The state variables consist of: the free viral particles (); the susceptible (
), phagocyting (
), latent (
) and excreting (
) macrophages; the natural killers (
); the cellular (
), humoral (
) and regulatory (
) adaptive cells; the pro-inflammatory cytokines (
,
&
; grouped in the box), the innate antiviral cytokines (
&
) and the immuno-regulatory cytokines (
,
,
&
). The flows represented are: the inoculation of free viral particles (
); the recruitment of susceptible macrophages (
); the activation of natural killers (
) and cells of the adaptive response (
); the decay of the free viral particles (
), the macrophages (
*), the natural killers (
), the adaptive cells (
) and the cytokines (
); the macrophage state changes, i.e. phagocytosis (
and
), infection (
) and transient excretion (
and
); the excretion of free viral particles by infected macrophages (
) and the cytokine syntheses by activated immune cells (
*). For the sake of readability, the cytokine and cell regulations and not drawn and some parameter notations (marked with *) are simplified.
Table 1.
Model parameters.
Figure 3.
Susceptible macrophage dynamics with cytokine regulations.
The state variables represented are: the free viral particles (); the susceptible (
), phagocyting (
) and latent (
) macrophages; the pro-inflammatory cytokines (
&
), the innate antiviral cytokines (
&
) and the immuno-regulatory cytokines (
,
,
&
). All processes that impact the susceptible macrophages are included: recruitment (
), decay (
, simplified notation), phagocytosis (
and
) and infection (
); their positive and negative regulations by cytokines are also drawn.
Figure 4.
Generalised sensitivity indices (GSI) for the three outputs of interest.
A: Viral titer (
). B: Cumulative number of phagocyting macrophages
(
). C: Percentage of infected macrophages among all macrophages
(
). Total GSI (bars) are represented for an output-dependent selection of influential parameters. For each parameter, the total GSI is split into main parameter effect (black bar) and the sum of two-parameter interactions involving the parameter (grey bar).
corresponds to the fraction of output variance explained by the parameters. NB: As the two-parameter interactions are counted for both parameters, the sum of the total GSI is higher than 100%.
Table 2.
Definition of the host susceptibility and strain virulence scenarios.
Figure 5.
Immune and infection dynamics for variable host susceptibility and strain virulence.
Evolution of twelve variables (panels A to L) during the first 30 days of infection (unless specified). A: Viral titer (, during 120 days). B: Phagocyting macrophages (
). C: Infected macrophages (
). D: Pro-inflammatory cytokines (
). E: Innate antiviral cytokines (
). F–I: Immuno-regulatory cytokines (F:
, G:
, H:
and I:
). J: Adaptive cellular effectors (
). K: Adaptive humoral effectors (
). L: Adaptive regulatory effectors (
). For each variable, the left plot corresponds to scenarios SB
SA, in which the antiviral cytokine synthesis is higher (S0
SB, red) or lower (S0
SA, magenta) than in the reference scenario (S0, black). The right plot corresponds to scenarios S1
S2, in which the macrophage permissiveness is lower (S0
S1, green) or higher (S0
S2, blue) than in the reference scenario (S0, black). Low susceptibility and virulence levels correspond to scenarios which promote the antiviral cytokine synthesis (red) and scenarios with low macrophage permissiveness (green). High susceptibility and virulence levels correspond to scenarios which promote the immuno-modulatory cytokine synthesis (magenta) and scenarios with high macrophage permissiveness (blue) Scenarios are defined in Table 2.
Table 3.
Generalised sensitivity indices and influence of the key parameters on the three outputs of interest.
Table 4.
Summary of the virus and immune dynamics for variable host susceptibility and strain virulence.
Figure 6.
Linear regressions between the infection duration and immune components of interest.
The immune components selected are the area under the curve (AUC) of A: infected macrophages (), B: innate antiviral cytokines (
), D: pro-inflammatory cytokines (
), and E: phagocyting macrophages (
); and the relative AUC of C:
and F:
. Two regressions were performed for each component: (i) for scenarios SB
SA (dark red), in which the antiviral cytokine synthesis is higher (S0
SB, red dots) or lower (S0
SA, magenta dots) than in the reference scenario; (ii) for scenarios S1
S2 (dark blue), in which the macrophage permissiveness is lower (S0
S1, green dots) or higher (S0
S2, blue dots) than in the reference scenario. Scenarios are defined in Table 2.