Dynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a review
DD YNAMIC MODEL OF
HIV
INFECTION WITH IMMUNE SYSTEMRESPONSE OF T- LYMPHOCYTES , B-
CELLS AND DENDRITICCELLS : A REVIEW
A P
REPRINT
Miguel Ramos-Pascual A BSTRACT
A dynamic model of non-lineal time-dependent ordinary differential equations (ODE) has beenapplied to the interactions of a HIV infection with the immune system cells. This model has beensimplified into two compartments: lymph node and peripheral blood. The model includes CD4T-lymphocytes in several states (quiescent Q, naive N and activated T), cytotoxic CD8 T-cells, B-cellsand dendritic cells. Cytokines and immunoglobulins specific for each antigen (i.e. gp41 or p24)have been also included in the model, modelling the atraction effect of CD4 T-cells to the infectedarea and the reduction of virus concentration by immunoglobulins. HIV virus infection of CD4T-lymphocytes is modelled in several stages: before fusion as HIV-attached (H) and after fusionas non-permissive / abortively infected (M), and permissive / latently infected (L) and permissive /actively infected (I). These equations have been implemented in a C++/Python interface application,called Immune System app, which runs Open Modelica software to solve the ODE system through a4th order Runge-Kutta numerical approximation. Results of the simulation show that although HIVvirus concentration in both compartments is lower than − virus/ µL after t=2 years, quiescentlymphocytes reach an equilibrium with a concentration lower than the initial conditions, due to thelatency state, which serves as a reservoir in time of virus production. As a conclusion, this model canprovide reliable results in other conditions, such as antiviral therapies. K eywords HIV-1 · CD4 lymphocyte · CD8 lymphocyte · B-cell · dendritic cells · immunoglobulins · cytokines Viral spread is focus of multiple research and modelling in many fields of computerised medicine and biology. Severalapproaches have been carried out to estimate virus and immune system cells concentrations with time, in whichdifferential equations systems have provided efficient and reliable results [1]. Each model includes in more or lessdetail the interaction of immune system cells with the virus, simplifiying the human body in several compartments(lymphatic system, peripheral blood, neural system or specific tissues, such as skin, epithelium cells, muscles or bones)and several states of the immune cells (quiescent, naive, activated or cytotoxic) [2] [3].Since 80’s Human Immunodeficiency Virus (HIV) has extended worldwide as a viral pandemics which in the worstcases revokes into AIDS (Acquired Immune Deficiency Syndrome), a syndrome characterised by a considerablereduction of CD4 lymphocytes levels and consequently the apparition of secondary oportunistic diseases [4] [5] [6]HIV infection is mainly treated with specific antiviral treatments, as Highly Active Antiretroviral Therapy (HAART), inorder to mantain viral loads in undetectable or low concentration levels [7]. No vaccine against HIV has been stilldeveloped, although multiple research studies are on-going world-wide [8] [9] .ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a review
Perelson‘s model is a set of non-lineal time-dependent ordinary differential equations (ODE) widely used in inmunologyfor modeling in a simplified way the host-cell and virus interactions [1]. Several mathematical models have extendedthis approach for including for instance cell-to-cell transmissions or infection rates [2]. These models have simplifiedthe reaction of the inmune system, situating the analysis in the worst-case scenario, compared with other researchstudies [3]Perelson’s model can be extended to multiple compartments, in order to increase the accuracy of results. An extendedmodel in immunology includes two compartments, circulatory and lymphatic system, simplified in two blocks: lymphnodes and peripheral blood. Bone marrow compartment is normally represented with a continuous production rate λ ofcellsFigure 1: Scheme of Immune System: (1) Bone marrow, (2) lymph node and (3) peripheral blood. Virus infection V isproduced in peripheral blood compartment 2ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a review Lymphatic organs are generally divided into primary organs (bone marrow and thymus) and secondary organs (lymphnodes, spleen, tonsil, appendix). In bone marrow, there are pluripotent lymphopoietic stem cells (SCs), which duringreplication, differentiate into T-cell/B-cell precursors. T-cell precursor cells emigrate to the thymus to maturate intonaive CD4 or CD8 T-cells.Figure 2: (1) Antigen-presenting-cell (APC) phagocytes a HIV virion and process antigens, (2) migrates to the lymphnodes and (3) presents antigen to T-helper cells (naive CD4 or CD8) through MHC (major-histocompatibility complex),activating CD4 and CD8 T cells (Image produced with https://app.biorender.com)Figure 3: HIV infection of a CD4 T-lymphocyte in three different states: (1) abortively infected (non-permissive) (2)actively infected (permissive) and (3) latently infected (permissive) (Image produced with https://app.biorender.com)3ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a review
CD4 T-lymphocytes are cycling continuously through the lymphatic system and peripheral blood in a quiescent state Q ( G / G state of virus replication), characterised by low size, low metabolic rates, low levels of transcription and verylong periods of survival, until they encounter an antigen-presenting cell (APC), mainly dendritic cells ( Z ). These cellspresent the antigen to the CD4 T-lymphocytes through the MHCII (major-histocompatibility complex II), activatingthem ( T ). In a similar way, CD8 T-cells activate into cytotoxic CD8 T-cells when encounter an APC (see fig 2) [10] Itis important to remark that T-lymphocytes are activated by APC, that is, activated dendritic cells ( Z + ) with specificantigens (i.e. gp41, p24, gp120, p17 or p31).In a first step, HIV virus attaches to the CD4 co-receptor during infection, and then fuses into the cell. This stateof lymphocyte before fusion has been called HIV-attached CD4 T-lymphocyte ( H ). After attachment, HIV gp120spike connects with another co-receptor (CCR5/CXCR4) and then fuses into host-cell. Once virus membrane andcapside have merged, reverse-transcription takes place and virus genome is integrated in host-cell nucleous. Provirusremains in a latent state until transcription starts, in a process which is still unknown. This state is called latentlyinfected T-lymphocyte ( L ). Then, once transcription has started, they become actively infected CD4-T lymphocytes ( I ),producing next virus progenie until CD4-T lymphocyte collapses.In quiescent T-cells, virus replication fails during reverse-transcription because host-cell detection is activated. CD4-Tlymphocyte becomes abortively infected or non-permissive to infection ( M ) [11, 10]. Inflammatory cytokines (C)are released from abortively infected cells during pyroptosis, in particular chemokines (IL-1 β ), attracting moreCD4-T lymphocytes from other areas. Cytokines released during pyroptosis cannot accumulate in blood as in lymphnodes, being unable to attract other immune cells. Therefore, cytokines accumulate only in lymphoid organs [12, 13, 14].As described in some research studies, HIV virus replication is more permissive in activated than quiescent T-cells,although there are divergent opinions about the reasons. As observed in fig. 3, both processes (permissive andnon-permissive infection) are in a certain way similar, because they bring CD4-T lymphocyte to collapse, releasing newvirus when infection is permissive or a cytokine storm when is no-permissive. This suggests that HIV virus productionand cytokine release can be related processes, or initiated by the same cell subprocess.4ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a reviewIn lymph node, equations are expressed for CD4 T-lymphocytes, considering that there is a fraction of circulating CD4T-cells which are leaving quiescent state for duplicaton ( N q ), in which infection is not possible, as ∂Q ∂t = (cid:104) λ q − k a V Q − k z Z +1 Q − µ q Q (cid:105) + ∂N q ∂t (1) ∂T ∂t = − k a V T + k z Z +1 Q + σ t (1 + γC ) T − µ t T (2) ∂N q ∂t = r n Q (cid:34) − (cid:80) j ( CD j Q av (cid:35) − µ q N q (3)where the sum of all CD4 T-lymphocytes is expressed as (cid:88) j ( CD j = Q + T + N q + H + L + I + M (4)where Q = CD4-T lymphocytes (quiescent)T = CD4-T lymphocytes (activated) N q = CD4-T lymphocytes (naive)H = CD4-T lymphocytes (HIV-attached)L = CD4-T lymphocytes (latently infected)I = CD4-T lymphocytes (actively infected)M = CD4-T lymphocytes (abortively infected)and λ q is the production of lymphocytes in the thymus from CD4 T-cell precursors, k a is the rate of virus attachmentto CD4 T-lymphocytes, k z is the rate of activation of T-lymphocytes from quiescent state after antigen presentation byactivated dendritic cells ( Z + ), γ is the efficiency of cytokines on infection, µ q is the decay rate of quiescent T cells and µ t is the decay rate of activated T cells.When HIV virus infects a CD4 T-lymphocyte, HIV virion attachs to CD4 co-receptor on host-cell surface as ∂H ∂t = k a V ( Q + T ) − ( k f + µ q ) H (5)where k f is the rate of virus fusion into CD4 T-cell.Once the virus has fused into an activated T-lymphocyte and reverse transcription has occurred successfully, CD4T-lymphocytes stay in a latent state with the provirus integrated in the host-cell genome, until it activates and startsreplication, that is ∂L ∂t = Lk f k r H − ( k b + µ t ) L (6) ∂I ∂t = (1 − L ) k f k r H + k b L − ( αE +1 + µ i ) I (7)where L is the fraction of permissive infections leading to latency, k b is the activation rate from latent state, k r is thereverse-transcription and integration rate, α is the killing rate of infected CD4 T-cells by effector or cytotoxic CD8T-lymphocytes and µ i is the decay rate of infected T-cells.5ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a reviewIn the case of infection is not permissive and reverse-transcription and integration fail, abortively infected T-lymphocyteand released cytokines are expressed as ∂M ∂t = k f (1 − k r ) H − µ m M (8) ∂C ∂t = ρ ( µ m − µ q ) M − µ c C (9)where ρ is the cytokine production rate per abortively infected cell, µ m is the decay rate of abortively infected cells and µ c is the decay rate of cytokines.Virus production is expressed as ∂V ∂t = πI − ( c + (cid:15)G ) V − k a V ( Q + T ) − k m V Z − D V + D V (10)where π is the virus production rate, c is the clearance rate in the lymph node, (cid:15) is the efficiency of inmunoglobulins invirus clearance by opsonization and NK cells recruiting and D and D are the transport rate of virus from blood tolymph node, and viceverse. CD8-T lymphocytes, which are circulating through lymph nodes and peripheral blood, are activated in the presence ofactivated and infected lymphocytes into effector CD8+T cells (cytotoxic), with a maximum activation rate of p E , andhalf-maximal saturation constants of θ and η , that is ∂E ∂t = (cid:104) λ e − p E (cid:16) I I + θ (cid:17)(cid:16) T T + η (cid:17) − µ e E (cid:105) + ∂N e ∂t (11) ∂N e ∂t = r e E (cid:34) − E + N e + E +1 E av (cid:35) − µ e N e (12) ∂E +1 ∂t = p E (cid:16) I I + θ (cid:17)(cid:16) T T + η (cid:17) − µ p E +1 (13)where µ e and µ p are the decay rates of CD8+T lymphocytes. In a similar way, activated dendritic cells migrate from the infection place to the lymph nodes to present antigens to theT-cells, ∂Z ∂t = (cid:104) λ z − ( k m V + µ z ) Z (cid:105) + ∂N z ∂t (14) ∂N z ∂t = r z Z (cid:34) − Z + N z + Z +1 Z av (cid:35) − µ z Z (15)6ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a review ∂Z +1 ∂t = k m V Z + σ z Z +2 − ( σ z + µ d ) Z +1 (16)where k m is the rate of activation and migration of dendritic cells, σ z is the diffusion of DC into peripheral blood and µ z is the decay rate of dendritic cells. B-cells differentiate in the bone marrow and migrate to the lymphoid organs as inmature B cells, which maturate intonaive mature B cells, circulating through the blood and lymph nodes. After the presence of antigen, these B cellsdevelop into plasma B cells, which produce antibodies, or memory B cells, long-lived cells which can be activated inseconday response to antigen.HIV virus antigens (i.e. glycoproteins, viral envelope/matrix) produce thymus dependent antibody response, requiringhelper T cells to synthesize antibodies of more than one isotype (IgM plus IgG, IgA or IgE), what is called a polyclonalresponse. The interaction of T-helper cells and B cells takes place in the germinal centers of secondary lymphoid organs(as lymph nodes).In the presence of antigen and a simultaneous signal received from T-helper cell, B cells activate as ∂B ∂t = (cid:104) λ b − ( ξT + µ b ) B (cid:105) + ∂N b ∂t (17) ∂N b ∂t = r b B (cid:34) − B + B +1 + N b B av (cid:35) − µ b N b (18) ∂B +1 ∂t = ξT B − µ y B +1 (19)where λ b is the production rate of B-cells in the lymph node, ξ is the activation rate of B cells for a specific antigen, µ b is the decay rate of B cells and µ y is the decay rate of plasma B cells.Once activated, B cells produce immunoglobulins as ∂G ∂t = φB +1 − ( (cid:15)V + µ g ) G (20)where φ is the production rate of immunoglobulins per activated B cell and µ g the decay rate of inmunoglobulins.A specific response from B-cells is expected from different activated T-lymphocytes by specific antigens or proteins (i.e.gp41, p24, gp120, p17 or p31). For example, immunoglobulins specific for p24 protein will be produced by plasmaB-cells activated by activated T-lymphocytes with p24 protein. In peripheral blood compartment, equations are expressed similarly as in lymph node. As an observation, the majorityof T-cell lymphocytes circulating through the peripheral blood are in a quiescent state [10]7ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a review
Let us consider one of the equations of the system of ODE (Ordinary Differential Equations), expressed in integral formas T ( t ) = T ( t ) + (cid:90) tt (cid:2) − k a V T + k z Z +1 Q + σ t (1 + γC ) T − µ t T (cid:3) dt (21)and after applying the Runge-Kutta method of 4th order, we arrive to the recursive solution T n +1) = T n + 16 (cid:2) k n + 2 k n + 2 k n + k n (cid:3) (22)where k n +1) = h (cid:104) − k a V n T n + k z Z +1 n Q n + σ t (1 + γC n ) T n − µ t T n ] (23) k n +1) = h (cid:104) − k a ( V n + k n / T n + k n /
2) + k z ( Z +1 n + k n / Q n + k n / σ t (1 + γ ( C n + k n / T n + k n / − µ t ( T n + k n / (cid:105) (24) k n +1) = h (cid:104) − k a ( V n + k n / T n + k n /
2) + k z ( Z +1 n + k n / Q n + k n / σ t (1 + γ ( C n + k n / T n + k n / − µ t ( T n + k n / (cid:105) (25) k n +1) = h (cid:104) − k a ( V n + k n )( T n + k n ) + k z ( Z +1 n + k n )( Q n + k n )+ σ t (1 + γ ( C n + k n ))( T n + k n ) − µ t ( T n + k n ) (cid:105) (26)and h is the step height, that is, t n +1 = t n + h , and each k in is refered to the function in parenthesis.In a similar way, we arrive recursively to the solutions Q n +1 , H n +1 , L n +1 , I n +1 , M n +1 , C n +1 , E n +1 , P n +1 , Y n +1 , Z n +1 , D n +1 and V n +1 .No time delay has been considered in the simulations, as normally HIV virus cycle from incorporation to next virusprogenie release is around 24h in normal conditions [15] The dynamic model of HIV infection and immune system response has been modelled and simulated with Python andOpen Modelica. A Python script calls to Open Modelica in order to obtain the solutions of the differential equationsystems (peripheral blood and lymph node) and then plot them graphically. Open Modelica allows the definition of aseries of simulation parameters which define the dynamic model and solve the system of ODE by 4th order Runge-Kuttamethod.
The concentration of CD4-T cells in peripheral blood variates around 200-1500 cells/ µL , depending on the sample andthe state of inmuno-depressed system [16, 17]. In a health individual, a normal concentration is around 1000 cells/ µ L.The concentration of CD8-T cells in peripheral blood is around 500 cells/ µ L, which are activated into effector CD8-Tcells after antigen-presenting-cells (APC) 8ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a reviewIn lymph node, CD4-T cell concentration is also variable, as the concentration of CD8-T cells of around 10 % innon-infected indiviuals, that is 500 cells/ µ L [18].Infection rate k i is calculated as k i = k a k f k r , where k a is the attachment rate to the CD4 receptor, k f is the fusion ratewith the CCR5/CRCX4 co-receptors and k r is the reverse-transcription and integration rate.The initial conditions have been established as the solutions of the steady state system, for the immune system T-cells(CD4 and CD8), B-cells and dendritic cells. The ratio CD4:CD8 has been established as the average value in normalconditions, 3.7 (range from 2 to 11) Table 2 presents the initial conditions of the simulation, with a step height h = 0 . days. Table 1: Initial conditions of the immune system (t=0)Parameter Lymph node Blood Units DescriptionQ µL − CD4-T lymphocytes (naive)E µL − CD8-T lymphocytes (naive)B µL − B-cells (naive)Z µL − Dendritic cells (inmatute)T µL − CD4-T lymphocytes (activated)H µL − CD4-T lymphocytes (HIV-attached)L µL − CD4-T lymphocytes (latently infected)I µL − CD4-T lymphocytes (actively infected)M µL − CD4-T lymphocytes (abortively infected)P µL − CD8-T lymphocytes (cytotoxic)Y µL − B-cells (plasma)D µL − Dendritic cells (activated)C µL − CytokinesG µL − ImmunoglobulinsTable 2: HIV concentrations at infection (t=365 days)Parameter Lymph node Blood Units DescriptionV µL − HIV virions9ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a reviewTable 3: Parameters of the immune system used in the simulationsParameter Description Mean Units Reference Q av Average population of CD4 T-cell (lymph node) 50000 cell µL − fitted P av Average population of CD8 T-cell (lymph node) 5400 cell µL − fitted B av Average population of B-cell (lymph node) 10000 cell µL − fitted Z av Maximum number of dendritic cells (lymph node) 1000 cells µL − fitted Q av Average population of CD4 T-cell (blood) 1000 cell µL − fitted P av Average population of CD8 T-cell (blood) 270 cell µL − fitted B av Average population of B-cell (blood) 200 cell µL − fitted Z av Maximum number of dendritic cells (blood) 40 cells µL − fitted λ Q CD4 T-cell rate of supply from thymus (lymph node) 50 cell µL − day − [1] λ P CD8 T-cell rate of supply from thymus (lymph node) 55 cell µL − day − [1] λ B B-cell rate of supply from thymus (lymph node) 100 cell µL − day − [1] λ Z Dendritic cell rate of supply from thymus (lymph node) 10 cell µL − day − [1] λ Q CD4 T-cell migration rate (blood) 2 cell µL − day − [1] λ P CD8 T-cell migration rate (blood) 2 cell µL − day − [1] λ B B-cell migration rate (blood) 2 cell µL − day − [1] λ Z Dendritic cell migration rate (blood) 2 cell µL − day − [1] r q CD4 T-cell growth rate (quiescent) 0 day − [1] r n CD4 T-cell growth rate (naive) 0.03 day − fitted r e CD8 T-cell growth rate (naive) 0.03 day − fitted r b B-cell growth rate (naive) 0.03 day − [19] r z Dendritic cell growth rate (immature) 0.03 day − fitted r t CD4 T-cell growth rate (activated) 0.5 day − [1] r p CD8 T-cell growth rate (activated) 0.5 day − fitted r y B-cell growth rate (activated) 0.5 day − [19] r d Dendritic cell growth rate (mature) 0.5 day − fitted µ q Decay rate of quiescent CD4 T-cell 0.01 day − fitted µ t Decay rate of activated CD4 T-cell 0.01 day − [13] µ m Decay rate of abortively infected CD4 T-cell 1 day − [13] µ i Decay rate of actively infected CD4 T-helper cell 1 day − [13] µ e Decay rate of CD8 T-cell 0.01 day − [13] µ p Decay rate of CD8 T-cell (cytotoxic) 0.01 day − [13] µ z Decay rate of dendritic cells 0.0037 day − [20] µ d Decay rate of dendritic cells (activated) 0.024 day − [20] µ b Decay rate of B-cells 0.01 day − [21] µ c Decay rate of cytokine (lymph node) 2 day − [22] µ c Decay rate of cytokine (peripheral blood) 10 day − [22] µ g Decay rate of immunoglobulins 0.03 day − [21] k m Activation and migration rate of DC 1.5e-1 cell virion − day − [23] k z Activation rate of T-cells from quiescent state by DC 1e-6 day − fitted σ z Diffusion of DC from blood to lymph node 1000 day − fitted σ z Diffusion of DC from lymph node to blood 1 day − fitted ρ Cytokine production rate 15 molecules cell − [13] γ Efficiency of cytokines on infection 0.2 µL molecule − [13] α Killing rate of CD8+T cells 10 µL cell − day − [13] p E Max activation rate of CD8+T cells 0.1 cells µL − day − [13] θ Half max saturation of CD8+T cells 0.05 cells µL − [13] η Half max saturation of CD4+T cells on CD8+T cell activation 500 cells µL − [13] ξ Probability of simultaneous activation Tcell/Bcell/antigen 0.01 - fitted φ Production rate of antibodies per activated B-cell 2000 s − [24] (cid:15) Efficiency of Ig in virus clearance by macrophages 1e-15 - fitted10ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a reviewTable 4: Parameters of the HIV cycle replication used in the simulationsParameter Description Mean Units Reference k i Infection rate 2.4e-5 µL virion − day − [1] k a Attachment rate to CD4 T-cell 5e-3 µL virion − day − fitted k f Fusion rate in CD4 T-cell 1e-1 µL virion − day − fitted k r Reverse-transcription and integration rate in CD4 T-cell 5e-2 µL virion − day − fitted k b Activation rate from latently infected state 5e2 µL virion − day − [1] L Fraction of permissive infections leading to latency 5e-2 - fitted π Virus burst size per infected cell 100 virion cell − day − [25] c Virus clearance rate 3 day − [20] D Viral diffusion rate (blood to lymph) 0.1 day − [13] D Viral diffusion rate (lymph to blood) 0.2 day − [13]11ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a review Figure 4 shows the maximum values of immune cells obtained with the immune system application, after an initialinfection in the peripheral blood of 1 virion/ µL at t=1 year.As observed in figures 5 to 18, immune system response cell concentrations reach an equilibrium after initial infection,with a maximum value at t=0. Although virus concentration is < 10 − virion/ µL after t>2 years, quiescent T-cells ( Q )are considerably lower than initial conditions ( Q =25000 cells/ µL and Q =1000 cells/ µL ), due to the fact that virus iscontinuously producing new virions from a latency state.Figure 4: Immune System app: Maximum values of inactivated, activated and infected states of immune system cellsand HIV virus particles 12ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a reviewFigure 5: Infectious HIV free-virus concentration ( V ) after infection at t=1 year (lymph node)Figure 6: Infectious HIV free-virus concentration ( V ) after infection at t=1 year (peripheral blood)13ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a reviewFigure 7: Quiescent CD4 T-lymphocytes ( Q ) concentration after infection at t=1 year (lymph node)Figure 8: Quiescent CD4 T-lymphocytes ( Q ) concentration after infection at t=1 year (peripheral blood)14ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a reviewFigure 9: Activated CD4 T-lymphocytes ( T ) concentration after infection at t=1 year (lymph node)Figure 10: Activated CD4 T-lymphocytes ( T ) concentration after infection at t=1 year (peripheral blood)15ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a reviewFigure 11: HIV-attached CD4 T-lymphocytes ( H ) concentration after infection at t=1 year (lymph node)Figure 12: HIV-attached CD4 T-lymphocytes ( H ) concentration after infection at t=1 year (peripheral blood)16ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a reviewFigure 13: Activated dendritic cells ( Z +1 ) concentration after infection at t=1 year (lymph node)Figure 14: Plasma B-cells ( Y ) concentration after infection at t=1 year (lymph node)17ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a reviewFigure 15: Inflammatory cytokines ( C ) concentration after infection at t=1 year (lymph node)Figure 16: Inflammatory cytokines ( C ) concentration after infection at t=1 year (peripheral blood)18ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a reviewFigure 17: Total immunoglobulins ( G ) concentration after infection at t=1 year (lymph node)Figure 18: Total immunoglobulins ( G ) concentration after infection at t=1 year (peripheral blood)19ynamic model of HIV infection with immune system response of T-lymphocytes, B-cells and dendritic cells: a review The dynamic model presents in detail the immune system response against a HIV virus infection in the peripheralblood compartment: activation of dendritic cells (DC), migration to the lymph node, activation of CD4 T-cells, CD8T-cells and B-cell, with the production of inflammatory cytokines atracting more CD4 T-cells to the infection place andimmunoglobulins to attach to the virus particles. The HIV virus infects CD4 T-cells in several stages, from attachment,fusion, reverse-transcription, integration and virus budding. CD4 T-cells can be permissive or non-permissive toinfection, resulting in two states: abortively infected T-cells ( M ), latently infected ( L ) and actively infected T-cells ( I ).All these states can be modelled through a system of ordinary differential equations (ODE) which have been solvedwith numerical methods.Although the dynamic model provides reliable results with an impulse infection in the peripheral blood (initial condi-tions), there are several aspects of the modelling still unknown, such as the attachment, fusion and reverse-transcriptionrates, which has been fitted. Furthermore, activated cells and immunoglobulins have been simulated to only one antigentarget (glycoprotein gp41). 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