Measles Infection Dose Responses: Insights from Mathematical Modeling.

How viral infections develop can change based on the number of viruses initially entering the body. The understanding of the impacts of infection doses remains incomplete, in part due to challenging constraints, and a lack of research. Gaining more insights is crucial regarding the measles virus (MV). The higher the MV infection dose, the earlier the peak of acute viremia, but the magnitude of the peak viremia remains almost constant. Measles is highly contagious, causes immunosuppression such as lymphopenia, and contributes substantially to childhood morbidity and mortality. This work investigated mechanisms underlying the observed wild-type measles infection dose responses in cynomolgus monkeys. We fitted longitudinal data on viremia using maximum likelihood estimation, and used the Akaike Information Criterion (AIC) to evaluate relevant biological hypotheses and their respective model parameterizations. The lowest AIC indicates a linear relationship between the infection dose, the initial viral load, and the initial number of activated MV-specific T cells. Early peak viremia is associated with high initial number of activated MV-specific T cells. Thus, when MV infection dose increases, the initial viremia and associated immune cell stimulation increase, and reduce the time it takes for T cell killing to be sufficient, thereby allowing dose-independent peaks for viremia, MV-specific T cells, and lymphocyte depletion. Together, these results suggest that the development of measles depends on virus-host interactions at the start and the efficiency of viral control by cellular immunity. These relationships are additional motivations for prevention, vaccination, and early treatment for measles.

Quantification of CD4 Recovery in Early-Treated Infants Living With HIV.

BACKGROUND: Perinatally HIV-acquired infants benefit from an early antiretroviral treatment initiation. Thanks to a short viral exposure time, their immune system can be maintained or reconstituted, allowing a "normal" immune development. METHODS: In this study, we mathematically modeled and quantified individual CD4+ T-cell reconstitution of a subset of 276 children who started treatment within 6 months of age and achieved sustained viral suppression. Considering natural age differences in CD4+ T-cell dynamics, we fitted distances to age-matched healthy reference values with a linear model approaching an asymptote. RESULTS: Depleted CD4+ percentages (CD4%) and CD4+ counts (CD4ct) restored healthy levels during treatment. CD4ct recovered with a median rate of 4 cells/µL/d, and individual recovery rates were correlated negatively with their initial CD4ct. CD4 values at onset of treatment decrease with age, whereas recovery times and levels seem to be age-independent. CD4 recovery correlates positively with viral suppression, and the stabilization of CD4 levels usually occurs after viral suppression. CD4 levels stabilize within 3-13 months after treatment initiation. The recovery dynamics of the CD4% is comparable with those of the CD4ct. CONCLUSIONS: In early-treated children with successful viral suppression, the CD4 depletion is typically mild and CD4+ T cells tend to "fully" recover in numbers.

Control theory helps to resolve the measles paradox.

Measles virus (MV) is a highly contagious respiratory morbillivirus that results in many disabilities and deaths. A crucial challenge in studying MV infection is to understand the so-called 'measles paradox'-the progression of the infection to severe immunosuppression before clearance of acute viremia, which is also observed in canine distemper virus (CDV) infection. However, a lack of models that match in vivo data has restricted our understanding of this complex and counter-intuitive phenomenon. Recently, progress was made in the development of a model that fits data from acute measles infection in rhesus macaques. This progress motivates our investigations to gain additional insights from this model into the control mechanisms underlying the paradox. In this paper, we investigated analytical conditions determining the control and robustness of viral clearance for MV and CDV, to untangle complex feedback mechanisms underlying the dynamics of acute infections in their natural hosts. We applied control theory to this model to help resolve the measles paradox. We showed that immunosuppression is important to control and clear the virus. We also showed under which conditions T-cell killing becomes the primary mechanism for immunosuppression and viral clearance. Furthermore, we characterized robustness properties of T-cell immunity to explain similarities and differences in the control of MV and CDV. Together, our results are consistent with experimental data, advance understanding of control mechanisms of viral clearance across morbilliviruses, and will help inform the development of effective treatments. Further the analysis methods and results have the potential to advance understanding of immune system responses to a range of viral infections such as COVID-19.

Oncolytic virus therapy benefits from control theory.

Oncolytic virus therapy aims to eradicate tumours using viruses which only infect and destroy targeted tumour cells. It is urgent to improve understanding and outcomes of this promising cancer treatment because oncolytic virus therapy could provide sensible solutions for many patients with cancer. Recently, mathematical modelling of oncolytic virus therapy was used to study different treatment protocols for treating breast cancer cells with genetically engineered adenoviruses. Indeed, it is currently challenging to elucidate the number, the schedule, and the dosage of viral injections to achieve tumour regression at a desired level and within a desired time frame. Here, we apply control theory to this model to advance the analysis of oncolytic virus therapy. The control analysis of the model suggests that at least three viral injections are required to control and reduce the tumour from any initial size to a therapeutic target. In addition, we present an impulsive control strategy with an integral action and a state feedback control which achieves tumour regression for different schedule of injections. When oncolytic virus therapy is evaluated in silico using this feedback control of the tumour, the controller automatically tunes the dose of viral injections to improve tumour regression and to provide some robustness to uncertainty in biological rates. Feedback control shows the potential to deliver efficient and personalized dose of viral injections to achieve tumour regression better than the ones obtained by former protocols. The control strategy has been evaluated in silico with parameters that represent five nude mice from a previous experimental work. Together, our findings suggest theoretical and practical benefits by applying control theory to oncolytic virus therapy.

Quantifying the Dynamics of HIV Decline in Perinatally Infected Neonates on Antiretroviral Therapy.

BACKGROUND: Mathematical modeling has provided important insights into HIV infection dynamics in adults undergoing antiretroviral treatment (ART). However, much less is known about the corresponding dynamics in perinatally infected neonates initiating early ART. SETTING: From 2014 to 2017, HIV viral load (VL) was monitored in 122 perinatally infected infants identified at birth and initiating ART within a median of 2 days. Pretreatment infant and maternal covariates, including CD4 T cell counts and percentages, were also measured. METHODS: From the initial cohort, 53 infants demonstrated consistent decline and suppressed VL below the detection threshold (20 copies mL) within 1 year. For 43 of these infants with sufficient VL data, we fit a mathematical model describing the loss of short-lived and long-lived infected cells during ART. We then estimated the lifespans of infected cells and the time to viral suppression, and tested for correlations with pretreatment covariates. RESULTS: Most parameters governing the kinetics of VL decline were consistent with those obtained previously from adults and other infants. However, our estimates of the lifespan of short-lived infected cells were longer than published values. This difference may reflect sparse sampling during the early stages of VL decline, when the loss of short-lived cells is most apparent. In addition, infants with higher pretreatment CD4 percentage or lower pretreatment VL trended toward more rapid viral suppression. CONCLUSIONS: HIV dynamics in perinatally infected neonates initiating early ART are broadly similar to those observed in other age groups. Accelerated viral suppression is also associated with higher CD4 percentage and lower VL.

Time to Viral Suppression in Perinatally HIV-Infected Infants Depends on the Viral Load and CD4 T-Cell Percentage at the Start of Treatment.

BACKGROUND: Interventions aiming for an HIV cure would benefit from rapid elimination of virus after the onset of antiretroviral therapy (ART), by keeping the latent HIV reservoir small. SETTING: We investigated HIV suppression in 312 perinatally infected infants starting ART within 6 months after birth from the EPPICC (European Pregnancy and Paediatric HIV Cohort Collaboration). METHODS: To better understand kinetic differences in HIV suppression among infants, we investigated their individual viral load (VL) decay dynamics. We identified VL decay patterns and determined times to viral suppression (TTS). For infants with strictly declining VLs (n = 188), we used parameter fitting methods to estimate baseline VLs, decay rates, and TTS. We subsequently identified the parameters determining TTS by linear modeling. RESULTS: The majority of infants suppress HIV VL after the onset of ART. Some children experienced a long TTS due to an "erratic" VL decay pattern. We cannot exclude that this is partly due to treatment complications and subsequent treatment changes, but these children were characterized by significantly lower CD4 percentages (CD4%) at start of treatment compared with those with a "clean" VL decline. Focusing on this "clean" subset, the TTS could be predicted by mathematical modeling, and we identified baseline VL and CD4% as the major factors determining the TTS. CONCLUSIONS: As VL steeply increases and CD4% constantly decreases in untreated HIV-infected infants, the progression of an HIV infection is largely determined by these 2 factors. To prevent a further disease progression, treatment should be initiated early after contracting HIV, which consequently shortens TTS.

Prediction of the containment of HIV infection by antiretroviral therapy - a variable structure control approach.

It is demonstrated that the reachability paradigm from variable structure control theory is a suitable framework to monitor and predict the progression of the human immunodeficiency virus (HIV) infection following initiation of antiretroviral therapy (ART). A manifold is selected which characterises the infection-free steady-state. A model of HIV infection together with an associated reachability analysis is used to formulate a dynamical condition for the containment of HIV infection on the manifold. This condition is tested using data from two different HIV clinical trials which contain measurements of the CD4+ T cell count and HIV load in the peripheral blood collected from HIV infected individuals for the six month period following initiation of ART. The biological rates of the model are estimated using the multi-point identification method and data points collected in the initial period of the trial. Using the parameter estimates and the numerical solutions of the model, the predictions of the reachability analysis are shown to be consistent with the clinical diagnosis at the conclusion of the trial. The methodology captures the dynamical characteristics of eventual successful, failed and marginal outcomes. The findings evidence that the reachability analysis is an appropriate tool to monitor and develop personalised antiretroviral treatment.

Modelling and Simulation of the Dynamics of the Antigen-Specific T Cell Response Using Variable Structure Control Theory.

Experimental and mathematical studies in immunology have revealed that the dynamics of the programmed T cell response to vigorous infection can be conveniently modelled using a sigmoidal or a discontinuous immune response function. This paper hypothesizes strong synergies between this existing work and the dynamical behaviour of engineering systems with a variable structure control (VSC) law. These findings motivate the interpretation of the immune system as a variable structure control system. It is shown that dynamical properties as well as conditions to analytically assess the transition from health to disease can be developed for the specific T cell response from the theory of variable structure control. In particular, it is shown that the robustness properties of the specific T cell response as observed in experiments can be explained analytically using a VSC perspective. Further, the predictive capacity of the VSC framework to determine the T cell help required to overcome chronic Lymphocytic Choriomeningitis Virus (LCMV) infection is demonstrated. The findings demonstrate that studying the immune system using variable structure control theory provides a new framework for evaluating immunological dynamics and experimental observations. A modelling and simulation tool results with predictive capacity to determine how to modify the immune response to achieve healthy outcomes which may have application in drug development and vaccine design.