# Towards a Multiscale Model of Acute HIV Infection

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## Abstract

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^{+}T cell dynamics in blood.

## 1. Introduction

^{+}T cell immune responses in Lymph Nodes (LN) [18,19], the NF-κB signaling pathway [20] and immune processes in lymph nodes [21,22]. The gained experience led to the formulation of some more general principles for developing and computationally implementing integrative models of immune responses [16,23,24]. A recent study integrating the spatial structure of the T cell zone of lymph nodes and the dynamics of T cell responses in HIV infection has quantified the effect of the destruction of the Fibroblastic Reticular Cell (FRC) network on T cell reactivity [25]. The aim of our study is: (1) to formulate a multi-scale mathematical model of HIV infection; (2) to implement the model computationally following a hybrid approach; and (3) to calibrate the model by estimating the parameter values enabling one to reproduce the “standard” dynamics of HIV infection in blood during the acute phase of primary infection.

^{+}T cells [4]. Both cell types play a key role in the regulation of immune responses by producing cytokines, such as IL-2 and interferons. The activation state of CD4

^{+}T cells has a strong effect on the replication of the virus [26]. Naive resting CD4

^{+}T cells do not support HIV replication, whereas activated cells are the major source of newly-secreted virus particles. HIV selectively infects and destroys memory CD4

^{+}T cells in lymphoid tissues. After mucosal infection, some period of local replication and amplification takes place, finally resulting in the migration of the infected cells to the draining lymph nodes and, from there, to the rest of the body [26]. Dendritic cells (DC), which are highly efficient Antigen-Presenting Cells (APC), play a key role in disseminating HIV from mucosal tissues to the draining lymph nodes [27]. Intravenous infection leads to fast direct dissemination of the virus to all lymphoid organs. In these organs, the productive infection is initially observed in the T cell zone. The development of AIDS occurs when the level of mucosal CD4

^{+}T cells drops to 5%–10% of their normal homeostatic level. Although about half of the gut-associated lymphoid tissue CD4

^{+}T cells is depleted after acute infection [28], the prolonged maintenance of CD4

^{+}T cells is explained by an increased turnover of the cells resulting from a chronic immune activation [26].

^{+}T Lymphocytes (CTL) [28]. The infection is characterized by the production of up to ${10}^{10}$ new virus particles per day [27]. The viral load drops from ∼1–5 × ${10}^{6}$ viral copies/mL to a steady state of ∼3 ×${10}^{4}$ viral copies/mL [28]. It is remarkable that despite massive HIV-specific CTL responses (up to $19\%$), a full control of HIV viremia is not achieved. The magnitude and rapidity of the CD8

^{+}T cell response correlate with the viral set point [29]. The set point is a strong predictor of the rate of the progression to AIDS [27]. The failure of HIV-specific CTLs to control HIV infection is attributed to functional defects of these cells associated with apoptosis [29,30]. The development of CTL responses in lymphoid organs is much less characterized than those in the peripheral blood [28]. Therefore, relating the immune processes in LNs to those in peripheral blood is important for a deeper understanding of the control of HIV infection.

## 2. Methods

#### 2.1. Multiscale Framework

#### 2.1.1. Cell Displacement

#### 2.1.2. Cell Division and Differentiation

^{+}T cells and three levels for CD8

^{+}T cells. If a differentiated cell has enough IL-2, then it divides and gives two mature daughter cells. Finally, differentiated cells leave the lymph node. In the simulations, this means that they are removed from the computational domain. The overall cell fate regulation is determined by a hierarchy of the gene activation thresholds for signaling coming via TCR, IL-2, IFNa and Fas receptors, as shown in Figure 3. Different activation thresholds uncouple the distinct modes of cellular responses depending on the cytokine levels and intracellular signaling, yielding context-specific functional responses [39].

#### 2.2. Biological Assumptions

- HIV enters the lymph node with infected antigen-presenting cells. These cells secrete HIV and transmit it to uninfected (both HIV-specific and non-specific) CD4
^{+}T cells by cell-cell interaction; - Each APC or CD4
^{+}T cell is determined by an intracellular viral RNA concentration (${H}_{i}$). The cell is considered to be infected if ${H}_{i}$ reaches some threshold level ${h}_{0}$. HIV upregulates the concentration of caspase, which can result in cell apoptosis; - The CD8
^{+}T cells produce FasL, as well as other apoptosis-inducing factors. They also activate the caspase cascade through direct cell-cell contact with infected cells resulting in target cell apoptosis. These two mechanisms only affect infected CD4^{+}T cells and not uninfected cells; - HIV impairs the immune response by reducing the number of CD4
^{+}T cells in the lymph node. These cells are killed by cytotoxic CD8^{+}T cells or by the virus itself. As a result, fewer mature helper CD4^{+}T cells are left, and less IL-2 and type I IFN are produced. This leads to a decrease in the survival and differentiation of CD8^{+}T cells, which ultimately results in the relapse of the infection.

- 1.
- ${V}_{Blood}\left(t\right)$, the viral load in blood;
- 2.
- ${N}_{CD4,inf}\left(t\right)$, the abundance of infected CD4
^{+}T cells in blood; - 3.
- ${N}_{CD4,un}\left(t\right)$, the abundance of uninfected CD4
^{+}T cells in blood; - 4.
- ${N}_{CD8,ef}\left(t\right)$, the abundance of HIV-specific effector CD8
^{+}T cells in blood.

- 5.
- ${n}_{APC}(\mathbf{x},t)$, the density of APCs in the T cell zone of LN, uninfected or infected;
- 6.
- ${n}_{CD4,un}(\mathbf{x},t)$, the density of uninfected CD4
^{+}T cells in the T cell zone of LN; and ${n}_{CD4,inf}(\mathbf{x},t)$, the density of infected cells; - 7.
- ${n}_{CD8}(\mathbf{x},t)$, the density of CD8
^{+}T cells in the T cell zone of LN; - 8.
- ${H}_{e}(\mathbf{x},t)$, the concentration of free HIV in the T cell zone;
- 9.
- ${I}_{e}(\mathbf{x},t)$, the concentration of IL-2 in the T cell zone;
- 10.
- ${C}_{e}(\mathbf{x},t)$, the concentration of type I IFN in the T cell zone;
- 11.
- ${F}_{e}(\mathbf{x},t)$, the concentration FasL in the T cell zone.

- 12.
- ${H}_{i}\left(t\right)$, the intracellular concentration of viral genomes in the i-th cell;
- 13.
- ${I}_{i}\left(t\right)$, the intracellular concentration of IL-2-induced signaling molecules in the i-th cell;
- 14.
- ${C}_{i}\left(t\right)$, the intracellular concentration of type I IFN-induced signaling molecules in the i-th cell;
- 15.
- ${w}_{i}\left(t\right)$, the intracellular concentration of FasL-induced signaling molecules in the i-th cell.

## 3. The Model of Acute HIV Infection

#### 3.1. Blood Compartment

^{+}T cells are generated in the course of the antiviral immune response occurring in LN. The concentration of the cells in blood results from their migration from LN via efferent lymphatic vessels to blood and further to peripheral tissues. A simple description of the above processes is provided by the equation:

^{+}T cells in blood and ${T}_{CD8,LN}$ is the density of HIV-specific CD8

^{+}T cells in LNs,

- 1.
- ${k}_{1}$, rate of T cell production and release into the body: $1.8$ ${\mathrm{h}}^{-1}$;
- 2.
- ${k}_{2}$, death rate of T cells in the body: $0.12$ ${\mathrm{h}}^{-1}$;
- 3.
- ${k}_{3}$, elimination rate of the infected cells by T cells $1.8\times {10}^{-6}$ ${\mathrm{h}}^{-1}$;
- 4.
- a, a growth rate parameter of infected cells: $0.00024$ ${\mathrm{h}}^{-1}$;
- 5.
- h, a parameter in the growth function of infected cells: $0.006$ ${\mathrm{h}}^{-1}$.

- 6.
- ${k}_{LN,Blood}$, migration rate constant of CD8
^{+}T cells from LN to blood. The fraction of HIV-specific CTLs in acute HIV infection can reach 10% of the total number of CD8^{+}T cells, i.e., about 100 cell/$\mathsf{\mu}$L [11]. Therefore, the value of ${k}_{LN,Blood}$ should be within the range 0.004–0.04 ${\mathrm{h}}^{-1}$; - 7.
- ${k}_{CD8}$, the disappearance rate of HIV-specific effector CD8
^{+}T cells from blood [11]: ${k}_{CD8}$ = 0.0013 ${\mathrm{h}}^{-1}$.

^{+}T cells in blood (${N}_{CD4,inf}$). We describe the dynamics of the infected cells in blood by the equation:

^{+}T cells in the lymph node,

- 8.
- a, the accumulation rate constant of HIV-infected CD4
^{+}T cells in blood due to the migration of cells from LNs and other peripheral tissues: the reference value 0.1 ${\mathrm{h}}^{-1}$ suggested in [1] was tuned to 0.35 ${\mathrm{h}}^{-1}$; - 9.
- h, the inverse of the threshold of infected T cells density in LN that leads to 50% reduction of the maximal accumulation rate of the infected cells in blood: 1/100 ${\mathrm{cell}}^{-1}$·$\mathsf{\mu}$L;
- 10.
- ${k}_{CD8,CD4}$, the elimination rate of HIV-infected CD4
^{+}T cells by CTL-mediated killing. We used the value estimated in [9] ${k}_{CD8,CD4}\sim $ 0.0004 $\mathsf{\mu}$L/(cell·h). For a strong $CD{8}^{+}$ T cell response, this value reaching 10% of the total CTL population in blood, this value will ensure the elimination rate of the infected cells from blood of about 1 per day; - 11.

- 12.
- λ, the influx rate of CD4
^{+}from the lymph nodes: 0.45 ($\mathsf{\mu}$L·h)^{−1}; - 13.
- ${h}_{1}$, the inverse of the threshold of uninfected T cells density in LN that leads to 50% reduction of the maximal accumulation rate of the uninfected cells in blood: 1/200 ${\mathrm{cell}}^{-1}$·$\mathsf{\mu}$L;
- 14.
- ${k}_{CD4,inf-un}$, the infection rate of the CD4
^{+}T cells in blood: 0.00042 ($\mathsf{\mu}$L·h)^{−1}; - 15.
- ${k}_{CD4,un}$, the death rate of uninfected CD4
^{+}T cells in blood: $3.3\times {10}^{4}$ ${\mathrm{h}}^{-1}$.

- 16.
- k the influx of HIV from LNs to blood was estimated in [40]. Taking into account the volume differences of our computational domain (0.001 $\mathsf{\mu}$L) and the unit of blood volume $\mathsf{\mu}$L, we used the following value ${k}_{V,LN-Blood}\sim $ 100 virion/($\mathsf{\mu}$L·h);
- 17.

#### 3.2. Population Dynamics of Infection in LN

#### 3.2.1. Free HIV

^{2}/h, with the geometric mean taken to be the baseline value $0.01$ mm

^{2}/h.

^{+}T cells. The production depends on the intracellular concentration of HIV DNA in a threshold manner; once the DNA level is above a certain value in the activated cell, the secretion starts to take place. Virus production is presented by the source term ${W}_{{H}_{i}}$,

^{+}T cell is taken to be ${\rho}_{HIV}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}5\times {10}^{2}$ virion/(cell·h) [11]. The clearance rate of free virus is taken to be about ${d}_{HIV}$ = 0.5 ${\mathrm{h}}^{-1}$ [11].

#### 3.2.2. HIV Infection in Target Cells

^{+}T cells. We suppose that the number of infected APCs CD4

^{+}T cells entering the lymph node and the concentration of proviral HIV DNA inside of them depend on the level of HIV infection. The proportion of the infected APCs and HIV-specific CD4

^{+}entering the lymph node corresponds to the actual level of HIV of infection divided by $20\times {10}^{6}$ virion/$\mathsf{\mu}$L. The concentration of intracellular HIV DNA is equal to the infection level divided by $5\times {10}^{3}$ virion/$\mathsf{\mu}$L. HIV infects the CD4

^{+}T cells in the lymph node, resulting potentially in the apoptosis of activated cells. Otherwise, the virus stays latent inside of the cell. Furthermore, infected APCs do not induce the differentiation of CD4

^{+}T cells. To describe the number of the integrated proviral HIV DNA D by (${H}_{i}$) in each CD4 T cell or APC, we use the equation:

- ${\beta}_{1}$, the infection rate constant for susceptible cells by free virus. It can be evaluated using the estimates in [44]: ${\beta}_{1}=5.6\times {10}^{-5}$ $\mathsf{\mu}$L/(virion·h);
- ${\beta}_{2}$, specifies the maximal production rate of HIV DNA in the activated cell. We used the following estimate ${\beta}_{2}=5\times {10}^{2}$ virion/(cell·h) [11];
- ${\omega}_{IFN}$, specifies the protective effect of type I interferon on HIV DNA growth in the activated cell. The following estimate [45] is used to reproduce a 50% reduction in the viral DNA synthesis rate due to the availability of type I IFN: ${\omega}_{IFN}$ = 467 $\mathsf{\mu}$L/pg;
- ${\beta}_{3}$, the probability that a susceptible cell is infected when it contacts infected cells was estimated in [44] to be ${\beta}_{3}=0.19$.

#### 3.3. Cytokine Fields in LN

#### 3.3.1. IL-2

^{+}T cells. Its spatial distribution is described by the reaction-diffusion equation:

^{+}T cells; and the last term in the right-hand side of this equation describes its consumption and degradation. The production rate ${W}_{IL}$ is determined by mature CD4

^{+}T cells. We consider each such cell as a source term with a constant production rate ${\rho}_{IL}$ at the area of the cell. Let us note that we do not take into account explicitly consumption of IL-2 by immature cells in order not to introduce an additional parameter. Implicitly, this consumption is taken into account in the degradation term. The following estimates of the parameters were used:

- ${\rho}_{IL2}$, the secretion rate of IL-2 by a single CD4
^{+}T cell: $7\times {10}^{5}$ molec/h; - ${d}_{IL2}$, the degradation rate of extracellular IL-2: 0.5 ${\mathrm{h}}^{-1}$.

#### 3.3.2. Type I IFN

- ${\rho}_{IFN}$, the secretion rate of type I IFN by single activated APC (plasmacytoid dendritic cell): $1.6\times {10}^{4}$ molec/h;
- ${d}_{IFN}$, the degradation rate of extracellular type I IFN: 0.012 ${\mathrm{h}}^{-1}$.

^{3}/h. Initial and boundary conditions for both concentrations IL-2 and IFN are taken to be zero. As before, the production rate ${W}_{IFN}$ equals ${\rho}_{IFN}$ at the area filled by APC cells and zero otherwise.

#### 3.3.3. FasL

^{+}T cells:

^{2}/h. The production rate of FasL by activated T cells can be estimated from the data in [46] to be around ${\rho}_{FasL}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}2\times \phantom{\rule{3.33333pt}{0ex}}{10}^{3}$–$4.5\times \phantom{\rule{3.33333pt}{0ex}}{10}^{4}$ (molecules/(cell·h) [46] with the geometric mean value of $9.5$ molecules/(cell·h). The degradation rate constant of the soluble FasL is assumed to range from 0.3 ${\mathrm{h}}^{-1}$ (characteristic of the decay rate of Fas receptor [18]) through 0.5 ${\mathrm{h}}^{-1}$ (estimated degradation rate of extracellular IL-2 [47]) to 14 ${\mathrm{h}}^{-1}$ [46], and we used the geometric mean value ${d}_{FasL}=$ 2 ${\mathrm{h}}^{-1}$.

#### 3.4. Intracellular Regulation of Cell Fate

#### 3.4.1. IL-2 Signaling

- ${n}_{T}$, the number of IL-2 molecules internalized by T cells via IL-2 receptors: 2000–5000 per T cell, with ${n}_{T}=5000$ used in simulations;
- ${I}_{i}^{*}$, the saturation concentration of IL-2 for T cell division in vitro: $6\times {10}^{10}$ molec/mL for $5\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{4}$ cells/mL.

#### 3.4.2. Type 1 IFN Signaling

- C1
- If the concentration of activation signals induced by type I IFN, ${C}_{i}$, is greater than some critical level ${C}_{i}^{*}$ at the beginning of the cell cycle and that of ${I}_{i}$ is smaller than the critical level ${I}_{i}^{*}$ at the end of the cell cycle, then the cell will differentiate, resulting in a mature cell.
- C2
- If the concentration of activation signals induced by IL-2, ${I}_{i}$, is greater than some critical level ${I}_{i}^{*}$ at the end of the cell cycle, then the cell will divide, producing two more mature cells.
- C3
- If ${C}_{i}<{C}_{i}^{*}$ at the beginning of cell cycle and ${I}_{i}<{I}_{i}^{*}$ at the end of cell cycle, then the cell will die by apoptosis and will be removed from the computational domain.

#### 3.4.3. FasL Signaling

- ${\gamma}_{1}$, the rate of pro-apoptotic signals accumulation because of the viral replication. As the death rate of the infected CD4 T cells is $1.3$ ${\mathrm{h}}^{-1}$, then we used it to quantify the cytopathic effect of the intracellular HIV DNA on the cell. It can be further scaled depending on the choice of the threshold ${w}^{*}$. The latter was estimated in [12], and we set it $2.0$ M;
- ${\gamma}_{2}$, specifies the FasL-Fas-induced caspase accumulation rate. It was estimated to be ${\gamma}_{4}=0.24$ ${\mathrm{h}}^{-1}$ in [12];
- ${\gamma}_{3}$, the killing rate of infected cells by effector CTL. It has been indicated in [46] that once in contact with a target cells, the CTL can program them to undergo apoptosis within 5 min. This value results in the following estimate for the impact of CTL on death likelihood ${\gamma}_{3}=8.3$ ${\mathrm{h}}^{-1}$;
- ${\gamma}_{4}$, the caspase degradation rate is taken from [18] ${\gamma}_{4}=0.23$ ${\mathrm{h}}^{-1}$.

#### 3.5. Population Dynamics of Immune Response in LN

## 4. Numerical Simulation Results

^{+}and CD8

^{+}T cells being 2:1 and the number of APCs ranging from 30–300 cells. The maximal number of HIV-specific T cells in the computational domain is assumed to be ∼$3\times {10}^{2}$. This corresponds to ∼$10\%$ of the lymph node space that can be occupied by T cells.

^{+}and CD8

^{+}T cells are periodically introduced to the middle of the domain when there is available space.

#### 4.1. Dynamics of APCs, CD4^{+} and CD8^{+} T Cells in LN

^{+}T cells over the first 30 days after a few infected APCs appear in LN.

^{+}T cell response as reproduced in Figure 5. It is characterized by a sequence of ongoing bursts in the expansion and contraction of CTLs. The strength of the cytotoxic T cell response is enough to limit the spread of infection and to reduced the number of infected APCs and CD4

^{+}T cells from Days 15–20 by four-fold.

^{+}and CD8

^{+}) is detailed in Figure 6. The responses are dynamically regulated by the cytokine and HIV distribution in the computational domain.

#### 4.2. HIV and Cytokine Fields in LN

^{+}T cells (black), infected CD4

^{+}T cells (orange), naive CD8

^{+}T cells (white), three maturity levels of differentiated CD8

^{+}T cells (blue) and two maturity levels of uninfected CD4

^{+}T cells (yellow).

^{+}T cells secrete HIV as shown in Figure 7 in blue. Mature CD4

^{+}T cells produce IL-2, whose concentration in the extracellular matrix is shown by the level of green; see Figure 8. Activated APCs produce type I IFN shown in red in Figure 9. Finally, the distribution of the apoptosis-inducing ligands is depicted in Figure 10. The simulations clearly indicate that the cytokines and HIV distributions are non-homogeneous and not identical. The relative shifts and differences underlie the existence of compartments differing in the preferential fate of immune cells (division vs. differentiation vs. death) and the niche for infection continuation (domain with a low interferon level).

#### 4.3. Systemic Dynamics of HIV Infection in Blood

^{+}T cells and infected and CD4

^{+}T cells is presented in Figure 12.

^{+}T cells’ response developing in LN. The HIV-specific CD8

^{+}T cells migrate to blood, as shown in Figure 13. The restoration of naive uninfected CD4

^{+}T cells is only partial and takes longer.

^{+}T cells during the initial acute phase of infection. These are determined by the specified and calibrated processes of infection spread and immune response development that occur in LN according to the biological schemes implemented in the model equations.

^{+}T cells from lymph node to blood (${k}_{LN,Blood}$) affects the dynamics of the observed characteristics of HIV infection. A variation by $\pm 11$% of the rate from its reference values has a strong impact on the dynamics of viral load and reduction in the blood number of uninfected CD4

^{+}T cells.

## 5. Discussion

^{+}T cell dynamics in blood [4,51]. Further refinement of the model and parameter estimates requires data on virological and immunological characteristics of HIV-infected individuals at the earliest stage of infection similar to those that have started to be gathered recently [51,52].

- the spatial dynamics of cells and cytokines in LNs is considered in a 2D regular domain;
- the model is restricted to primary acute HIV infection and concomitant cytotoxic T cell responses;
- intracellular regulation of cell fate by multiple cytokine signaling is described via a hierarchy of activation thresholds;
- HIV infection is considered in LN and blood compartments.

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

HIV | Human Immunodeficiency Virus |

LN | Lymph Mode |

FRC | Fibroblastic Reticular Cell |

APC | Antigen-Presenting Cell |

IL-2 | Interleukin 2 |

IFN | Type I Interferon |

FasL | Fas Ligand |

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**Figure 2.**Scenarios of virus modes of infection of CD4 T cells. (

**A**) Free virus infection of resting CD4 T cells resulting in a latent infection; (

**B**) interaction between infected APC and uninfected CD4 T lymphocytes resulting in a productive infection; (

**C**) cell-to-cell spread of HIV from infected to uninfected CD4 T lymphocytes resulting in a productive infection upon activation by HIV antigen-presenting APC.

**Figure 3.**Scheme of the cell fate regulation via TCR, IL-2, IFNa and Fas receptor-mediated signaling in naive T cells to adaptively program the balance of growth-differentiation and death.

**Figure 4.**(

**left**) The dynamics of the population of HIV-infected APCs in the lymph node; (

**right**) The dynamics of the population of HIV-infected CD4

^{+}T cells in the lymph node.

**Figure 6.**The dynamics of populations of naive and mature HIV-specific CD4

^{+}(black curve) and CD8

^{+}(blue curve) T cells in the lymph node.

**Figure 7.**Snapshots of the simulation in which the concentration of HIV (in virions/$\mathsf{\mu}$L) is shown in blue color gradient. Different cell types are represented as follows: uninfected APCs (green), infected APCs (red), naive uninfected CD4

^{+}T cells (black), infected CD4

^{+}T cells (orange), naive CD8

^{+}T cells (white), three maturity levels of differentiated CD8

^{+}T cells (blue) and two maturity levels of uninfected CD4

^{+}T cells (yellow). (

**top**) Three days after the virus transmission; (

**bottom**) 12 days after virus transmission.

**Figure 8.**Snapshots of the simulation in which the concentration of IL-2 (in molecules/$\mathsf{\mu}$L) is shown in green gradient. For cell notations, the same color code as in Figure 7 is used. (

**top**) Three days after the virus transmission; (

**bottom**) 12 days after virus transmission.

**Figure 9.**Snapshots of the simulation in which the concentration of type I interferon (in molecules/$\mathsf{\mu}$L) is shown in red color gradient. For cell notations, the same color code as in Figure 7 is used. (

**top**) Three days after the virus transmission; (

**bottom**) 12 days after virus transmission.

**Figure 10.**Snapshots of the simulation in which the concentration of FasL (in molecules/$\mathsf{\mu}$L) is shown in yellow color gradient. For cell notations, the same color code as in Figure 7 is used. (

**top**) Three days after the virus transmission; (

**bottom**) 12 days after virus transmission.

**Figure 11.**(

**left**) The viral load in blood (virion/$\mathsf{\mu}$L); (

**right**) The HIV concentration in the lymph node over time.

**Figure 12.**Dynamics of infection in blood. (

**left**) The population of uninfected CD4

^{+}T cells (cell/$\mathsf{\mu}$L); (

**right**) The population of infected CD4

^{+}T cells (cell/$\mathsf{\mu}$L).

**Figure 13.**Dynamics of immune response in blood. The population of HIV-specific CD8

^{+}T cells over time (cell/$\mathsf{\mu}$L).

**Figure 14.**Sensitivity analysis for blood. The effect of the variation of the rate of CD8

^{+}T cell migration from lymph node to blood (${k}_{LN,Blood}$) by ± 11%. (

**left**) Viral load (virion/$\mathsf{\mu}$L); (

**right**) Infected CD4

^{+}T cells (cell/$\mathsf{\mu}$L).

**Figure 15.**Sensitivity analysis for blood. The effect of the variation of the rate of CD8+ T cell migration from lymph node to blood (${k}_{LN,Blood}$) by ± 11%. (

**left**) Uninfected CD4

^{+}T cells (cell/$\mathsf{\mu}$L); (

**right**) HIV-specific CD8

^{+}T cells (cell/$\mathsf{\mu}$L).

**Figure 16.**Three single runs of the model from the same starting conditions showing the effect of randomness on the dynamics of infected CD4

^{+}T cells in blood (cell/$\mathsf{\mu}$L).

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**MDPI and ACS Style**

Bouchnita, A.; Bocharov, G.; Meyerhans, A.; Volpert, V.
Towards a Multiscale Model of Acute HIV Infection. *Computation* **2017**, *5*, 6.
https://doi.org/10.3390/computation5010006

**AMA Style**

Bouchnita A, Bocharov G, Meyerhans A, Volpert V.
Towards a Multiscale Model of Acute HIV Infection. *Computation*. 2017; 5(1):6.
https://doi.org/10.3390/computation5010006

**Chicago/Turabian Style**

Bouchnita, Anass, Gennady Bocharov, Andreas Meyerhans, and Vitaly Volpert.
2017. "Towards a Multiscale Model of Acute HIV Infection" *Computation* 5, no. 1: 6.
https://doi.org/10.3390/computation5010006