Lentiviruses, which cause arthritis-encephalitis and maedi-visna in goats and sheep, respectively, cause persistent infections in these animals. The viruses replicate productively at low levels in macrophages in diseased organs such as the "maedi lung" and nonproductively in other cell types such as leukocytes in peripheral blood. Nonproductive infections become productive during in vitro cultivation of the cells. This study showed that monocytes were the only cells in the peripheral blood leukocytes of an infected animal in which virus was detected and that virus activation occurred only when these cells matured into macrophages. Only a minute fraction of cultured monocytes matured into macrophages, and viral infectivity was associated exclusively with this fraction. Antiglobulin-coated glass wool fragments were lethal for monocyte macrophages because of toxic phagocytosis, but had no effect on B or T lymphocytes. The simultaneous addition of the glass fragments and leukocytes to culture dishes resulted in no macrophage maturation and no virus production. The addition of the fragments to virus-producing macrophages caused the death of the cells and a decline in virus production. Virus production in less avidly phagocytic cells was unaffected by the glass. Thus, although macrophages may be permissive for virus replication, one mechanism for restricted virus expression in vivo may be physiological factors controlling the maturation of these cells.

The immune system can remember, sometimes for a lifetime, the identity of a pathogen. Understanding how this is accomplished has fascinated immunologists and microbiologists for many years, but there is still considerable debate regarding the mechanisms by which long-term immunity is maintained. Some of the controversy stems from a failure to distinguish between effector and memory cells and to define their roles in conferring protection against disease. Here the current understanding of the cellular basis of immune memory is reviewed and the relative contributions made to protective immunity by memory and effector T and B cells are examined.

This study evaluated whether T-cell memory reflects increased precursor frequencies of specific long-lived T cells and/or a low-level immune response against some form of persistent antigen. Antivirally protective CD8+ T-cell memory was analyzed mostly in the original vaccinated host to assess the role of antigen in its maintenance. T-cell mediated resistance against reinfection was measured in the spleen and in peripheral solid organs with protocols that excluded protection by antibodies. In vivo protection was compared with detectable cytotoxic T-lymphocyte precursor frequencies determined in vitro. In the spleen, in vitro detectable cytotoxic T-lymphocyte precursor frequencies remained stable independently of antigen, conferring resistance against viral replication in the spleen during reinfection. In contrast, T-cell mediated resistance against reinfection of peripheral solid organs faded away in an antigen-dependent fashion within a few days or weeks. We show that only memory T cells persistently or freshly activated with antigen efficiently extravasate into peripheral organs, where cytotoxic T lymphocytes must be able to exert effector function immediately; both the capacity to extravasate and to rapidly exert effector function critically depend on restimulation by antigen. Our experiments document that the duration of T-cell memory protective against peripheral reinfection depended on the antigen dose used for immunization, was prolonged when additional antigen was provided, and was abrogated after removal of antigen. We conclude that T-cell mediated protective immunity against the usual peripheral routes of reinfection is antigen-dependent.

This study documents that virus-specific CTL can persist indefinitely in vivo. This was accomplished by transferring Thy-1.1 T cells into Thy-1.2 recipient mice to specifically identify the donor T cell population and to characterize its antigenic specificity and function by using a virus-specific CTL assay. Thy-1.1+ T cells from mice previously immunized with lymphocytic choriomeningitis virus (LCMV) were transferred into Thy-1.2 mice persistently infected with LCMV. The transferred LCMV-specific CTL (Thy-1.1+ CD8+) eliminate virus from the chronically infected carriers and persist in the recipient mice in small numbers, comprising only a minor fraction of the total T cells. Upon re-exposure to virus, these long-lived "resting" CD8+ T cells proliferate in vivo to become the predominant cell population. These donor CD8+ T cells can be recovered up to a year post-transfer and still retain antigenic specificity and biological function. They kill LCMV infected H-2-matched cells in vitro and can eliminate virus upon transfer into a second infected host. In addition, these long-lived CD8+ T cells appear not to be dependent on help from CD4+ T cells, since depletion of CD4+ T cells has minimal or no effect on their biological properties (proliferation, CTL response, viral clearance). These donor CTL also exhibit an immunodominance over the host-derived LCMV-specific CTL response. When both host and donor T cells are present, the donor CTL response is dominant over the potential CTL response of the cured carrier host. Taken together, these results suggest that virus-specific CTL can persist for the life span of the host as memory cells.

Phenotypically and functionally, the early steps of T cell differentiation are not well characterized. In addition, the effector T cell stage shares several phenotypic characteristics with memory T cells, which has made the analysis of T cell memory difficult. In this study, we have investigated in vitro and in vivo the differentiation of naive CTL into effector and memory CTL as a function of cell division using lymphocytic choriomeningitis virus-specific TCR-transgenic spleen cells labeled with the vital dye carboxyfluorescein diacetate, succinimidyl ester. The following major points emerged. 1) During the first nine cell divisions, the investigated cell surface markers were strongly modulated. 2) The TCR was stepwise down-regulated during viral infection. 3) Cytotoxic effector function was acquired within one cell division and was retained during the next four to five divisions. 4) In vitro, CTL reached a CD44highCD62L+ memory phenotype after 6-10 cell divisions and required restimulation to exert effector function. 5) Lymphocytic choriomeningitis virus memory mice contained two distinct memory populations: a CD44highCD62L- population, predominately located in the spleen and exerting rapid effector function, and a CD44highCD62L+ population found in the spleen and the lymph nodes, which had lost immediate effector function. This finding suggests that two types of memory CTL exist. The correlation between CD62L expression, effector function, and Ag persistence is discussed.

This note presents closed-form formulas for determining the critical points of general n-dimensional differential equations. The formulas do not require commutating the eigenvalues of the Jacobian of a system. Based on the Hurwitz criterion, explicit necessary and sufficient conditions are obtained. Particular attention is focused on Hopf and double Hopf bifurcations. A model of induction machine is presented to show the application of the results.

In this paper, we propose and analyze a delayed HIV-1 model with CTL immune response and virus waning. The two discrete delays stand for the time for infected cells to produce viruses after viral entry and for the time for CD8+ T cell immune response to emerge to control viral replication. We obtain the positiveness and boundedness of solutions and find the basic reproduction number R0. If R0 < 1, then the infection-free steady state is globally asymptotically stable and the infection is cleared from the T-cell population; whereas if R0 > 1, then the system is uniformly persistent and the viral concentration maintains at some constant level. The global dynamics when R0 > 1 is complicated. We establish the local stability of the infected steady state and show that Hopf bifurcation can occur. Both analytical and numerical results indicate that if, in the initial infection stage, the effect of delays on HIV-1 infection is ignored, then the risk of HIV-1 infection (if persists) will be underestimated. Moreover, the viral load differs from that without virus waning. These results highlight the important role of delays and virus waning on HIV-1 infection.

The CD8+ lymphocyte response is a main component of host immunity, yet it is difficult to quantify its contribution to the control of persistent viruses. Consequently, it remains controversial as to whether CD8+ cells have a biologically significant impact on viral burden and disease progression in infections such as human immunodeficiency virus-1 and human T-lymphotropic virus type I (HTLV-I). Experiments to ascertain the impact of CD8+ cells on viral burden based on CD8+ cell frequency or specificity alone give inconsistent results. Here, an alternative approach was developed that directly quantifies the impact of CD8+ lymphocytes on HTLV-I proviral burden by measuring the rate at which HTLV-I-infected CD4+ cells were cleared by autologous CD8+ cells ex vivo. It was demonstrated that CD8+ cells reduced the lifespan of infected CD4+ cells to 1 day, considerably shorter than the 30 day lifespan of uninfected cells in vivo. Furthermore, it was shown that HTLV-I-infected individuals vary considerably in the rate at which their CD8+ cells clear infected cells, and that this was a significant predictor of their HTLV-I proviral load. Forty to 50 % of between-individual variation in HTLV-I proviral load was explained by variation in the rate at which CD8+ cells cleared infected cells. This novel approach demonstrates that CD8+ cells are a major determinant of HTLV-I proviral load. This assay is applicable to quantifying the CD8+ cell response to other viruses and malignancies and may be of particular importance in assessing vaccines.

A within-host viral infection model with both virus-to-cell and cell-to-cell transmissions and three distributed delays is investigated, in which the first distributed delay describes the intracellular latency for the virus-to-cell infection, the second delay represents the intracellular latency for the cell-to-cell infection, and the third delay describes the time period that viruses penetrated into cells and infected cells release new virions. The global stability analysis of the model is carried out in terms of the basic reproduction number R0. If R0≤1, the infection-free (semi-trivial) equilibrium is the unique equilibrium and is globally stable; if R0>1, the chronic infection (positive) equilibrium exists and is globally stable under certain assumptions. Examples and numerical simulations for several special cases are presented, including various within-host dynamics models with discrete or distributed delays that have been well-studied in the literature. It is found that the global stability of the chronic infection equilibrium might change in some special cases when the assumptions do not hold. The results show that the model can be applied to describe the within-host dynamics of HBV, HIV, or HTLV-1 infection. Copyright © 2015. Published by Elsevier Inc.

A.S. Perelson, D.E. Kirschner and R. De Boer (Math. Biosci. 114 (1993) 81) proposed an ODE model of cell-free viral spread of human immunodeficiency virus (HIV) in a well-mixed compartment such as the bloodstream. Their model consists of four components: uninfected healthy CD4(+) T-cells, latently infected CD4(+) T-cells, actively infected CD4(+) T-cells, and free virus. This model has been important in the field of mathematical modeling of HIV infection and many other models have been proposed which take the model of Perelson, Kirschner and De Boer as their inspiration, so to speak (see a recent survey paper by A.S. Perelson and P.W. Nelson (SIAM Rev. 41 (1999) 3-44)). We first simplify their model into one consisting of only three components: the healthy CD4(+) T-cells, infected CD4(+) T-cells, and free virus and discuss the existence and stability of the infected steady state. Then, we introduce a discrete time delay to the model to describe the time between infection of a CD4(+) T-cell and the emission of viral particles on a cellular level (see A.V.M. Herz, S. Bonhoeffer, R.M. Anderson, R.M. May, M.A. Nowak [Proc. Nat. Acad. Sci. USA 93 (1996) 7247]). We study the effect of the time delay on the stability of the endemically infected equilibrium, criteria are given to ensure that the infected equilibrium is asymptotically stable for all delay. Numerical simulations are presented to illustrate the results.

Despite significant advances in our understanding of the immune response to persistent viruses like human T-cell lymphotropic virus type I (HTLV-I), many important questions remain unanswered. Mathematical modelling enables us to interpret and synthesise diverse experimental data in new ways and thus can contribute to our understanding. Here, we review recent advances in mathematical modelling of HTLV-I infection and illustrate how mathematics has enabled us to identify factors that determine an individual's viral burden and risk of developing HTLV-I-associated diseases.

We examine a model for the interaction of HIV with CD4+ T cells that considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. Using this model we show that many of the puzzling quantitative features of HIV infection can be explained simply. We also consider effects of AZT on viral growth and T-cell population dynamics. The model exhibits two steady states, an uninfected state in which no virus is present and an endemically infected state, in which virus and infected T cells are present. We show that if N, the number of infectious virions produced per actively infected T cell, is less a critical value, Ncrit, then the uninfected state is the only steady state in the nonnegative orthant, and this state is stable. For N > Ncrit, the uninfected state is unstable, and the endemically infected state can be either stable, or unstable and surrounded by a stable limit cycle. Using numerical bifurcation techniques we map out the parameter regimes of these various behaviors. oscillatory behavior seems to lie outside the region of biologically realistic parameter values. When the endemically infected state is stable, it is characterized by a reduced number of T cells compared with the uninfected state. Thus T-cell depletion occurs through the establishment of a new steady state. The dynamics of the establishment of this new steady state are examined both numerically and via the quasi-steady-state approximation. We develop approximations for the dynamics at early times in which the free virus rapidly binds to T cells, during an intermediate time scale in which the virus grows exponentially, and a third time scale on which viral growth slows and the endemically infected steady state is approached. Using the quasi-steady-state approximation the model can be simplified to two ordinary differential equations the summarize much of the dynamical behavior. We compute the level of T cells in the endemically infected state and show how that level varies with the parameters in the model. The model predicts that different viral strains, characterized by generating differing numbers of infective virions within infected T cells, can cause different amounts of T-cell depletion and generate depletion at different rates. Two versions of the model are studied. In one the source of T cells from precursors is constant, whereas in the other the source of T cells decreases with viral load, mimicking the infection and killing of T-cell precursors.(ABSTRACT TRUNCATED AT 400 WORDS)