Modelling HIV immune response and validation with clinical data

System Complexity in Influenza Infection and Vaccination: Effects upon Excess Winter Mortality

Unexpected outcomes are usually associated with interventions in complex systems. Excess winter mortality (EWM) is a measure of the net effect of all competing forces operating each winter, including influenza(s) and non-influenza pathogens. In this study over 2400 data points from 97 countries are used to look at the net effect of influenza vaccination rates in the elderly aged 65+ against excess winter mortality (EWM) each year from the winter of 1980/81 through to 2019/20. The observed international net effect of influenza vaccination ranges from a 7.8% reduction in EWM estimated at 100% elderly vaccination for the winter of 1989/90 down to a 9.3% increase in EWM for the winter of 2018/19. The average was only a 0.3% reduction in EWM for a 100% vaccinated elderly population. Such outcomes do not contradict the known protective effect of influenza vaccination against influenza mortality per se—they merely indicate that multiple complex interactions lie behind the observed net effect against all-causes (including all pathogen causes) of winter mortality. This range from net benefit to net disbenefit is proposed to arise from system complexity which includes environmental conditions (weather, solar cycles), the antigenic distance between constantly emerging circulating influenza clades and the influenza vaccine makeup, vaccination timing, pathogen interference, and human immune diversity (including individual history of host-virus, host-antigen interactions and immunosenescence) all interacting to give the observed outcomes each year. We propose that a narrow focus on influenza vaccine effectiveness misses the far wider complexity of winter mortality. Influenza vaccines may need to be formulated in different ways, and perhaps administered over a shorter timeframe to avoid the unanticipated adverse net outcomes seen in around 40% of years.

Designing a Predictive Model for Antiretroviral Regimen at the Antiretroviral Therapy Center in Chiro Hospital, Ethiopia

Nowadays, the huge amount of patient's data significantly increases with respect to the time in repositories and data mining is increasingly used as an emerging research area in medical fields for extracting useful and previously unknown insights/patterns from the repository data. These unknown patterns/hidden insights can help in discovering new knowledge hidden in these data repositories. From the observation, different ARV regimens were ordered for different patients. However, combination of these drugs causes different side effects on the patients. It has been observed that there was a lack of predictive studies and designed models available in hospitals specifically ART Centers that accurately determine or classify the patient's ARV regimen to TDF + 3TC + EFV, TDF + 3TC + NVP, AZT + 3TC + ATV/R, AZT + 3TC + LPV/R, TDF + 3TC + LVP/R, TDF + 3TC + ATV/R, 8888, and ABC + 3TC + LPV/R. In order to solve these kinds of problems, we built an accurate classifier system or model using parameters like Patient Age, Patient Encounter Day, Patient Encounter Month, Patient Encounter Year, Patient Weight, Patient CD4 Count Adult, Patient TB Screen, Patient Following WHO Stage, Patient CD4 Percent Child, Patient Regimen Specify, Patient Regimen, and so on. The general objective of this research was predictive modeling for the patient's ARV regimen class through data mining techniques so as to improve them. The study used the CRIPS-DM methodology to find and interpret patterns in repositories. A decision tree (J48 and Random Forest) algorithm was used for classification. Using all tested classifiers, the investigation of the study shows that the total accuracy was more than 60%. On the other hand, among different classifications, class H (ABC + 3TC + LPV/R) has shown the worst prediction. But it was revealed that the J48 classifier relatively produces higher classification accuracy for the D (AZT-3TC-NVP) regimen. Here, classification depended on the selected parameters, which revealed that prediction accuracy value differed among all classifiers and the selected attributes. Finally, the study concluded that data mining can be used as a significant technique to discover patient regimen based on salient affecting factors with 96.1% precision achieved. Ensemble learning resolves the categorizing models of greater anticipating performance with different learning algorithms. This model aligned with sentimental investigation to magnify the appearances of the dataset either from the social media or from primary data collection. The empirical investigation with different parameters shows the detailed improvement of their learning methods.

Mathematical modeling of N-803 treatment in SIV-infected non-human primates

Immunomodulatory drugs could contribute to a functional cure for Human Immunodeficiency Virus (HIV). Interleukin-15 (IL-15) promotes expansion and activation of CD8⁺ T cell and natural killer (NK) cell populations. In one study, an IL-15 superagonist, N-803, suppressed Simian Immunodeficiency Virus (SIV) in non-human primates (NHPs) who had received prior SIV vaccination. However, viral suppression attenuated with continued N-803 treatment, partially returning after long treatment interruption. While there is evidence of concurrent drug tolerance, immune regulation, and viral escape, the relative contributions of these mechanisms to the observed viral dynamics have not been quantified. Here, we utilize mathematical models of N-803 treatment in SIV-infected macaques to estimate contributions of these three key mechanisms to treatment outcomes: 1) drug tolerance, 2) immune regulation, and 3) viral escape. We calibrated our model to viral and lymphocyte responses from the above-mentioned NHP study. Our models track CD8⁺ T cell and NK cell populations with N-803-dependent proliferation and activation, as well as viral dynamics in response to these immune cell populations. We compared mathematical models with different combinations of the three key mechanisms based on Akaike Information Criterion and important qualitative features of the NHP data. Two minimal models were capable of reproducing the observed SIV response to N-803. In both models, immune regulation strongly reduced cytotoxic cell activation to enable viral rebound. Either long-term drug tolerance or viral escape (or some combination thereof) could account for changes to viral dynamics across long breaks in N-803 treatment. Theoretical explorations with the models showed that less-frequent N-803 dosing and concurrent immune regulation blockade (e.g. PD-L1 inhibition) may improve N-803 efficacy. However, N-803 may need to be combined with other immune therapies to countermand viral escape from the CD8⁺ T cell response. Our mechanistic model will inform such therapy design and guide future studies.

Immune therapy may be a critical component in the functional cure for Human Immunodeficiency Virus (HIV). N-803 is an immunotherapeutic drug that activates antigen-specific CD8⁺ T cells of the immune system. These CD8⁺ T cells eliminate HIV-infected cells in order to limit the spread of infection in the body. In one study, N-803 reduced plasma viremia in macaques that were infected with Simian Immunodeficiency Virus, an analog of HIV. Here, we used mathematical models to analyze the data from this study to better understand the effects of N-803 therapy on the immune system. Our models indicated that inhibitory signals may be reversing the stimulatory effect of N-803. Results also suggested the possibilities that tolerance to N-803 could build up within the CD8⁺ T cells themselves and that the treatment may be selecting for virus strains that are not targeted by CD8⁺ T cells. Our models predict that N-803 therapy may be made more effective if the time between doses is increased or if inhibitory signals are blocked by an additional drug. Also, N-803 may need to be combined with other immune therapies to target virus that would otherwise evade CD8⁺ T cells.

Viral Infection Dynamics Model Based on a Markov Process with Time Delay between Cell Infection and Progeny Production

Many human virus infections including those with the human immunodeficiency virus type 1 (HIV) are initiated by low numbers of founder viruses. Therefore, random effects have a strong influence on the initial infection dynamics, e.g., extinction versus spread. In this study, we considered the simplest (so-called, ‘consensus’) virus dynamics model and incorporated a delay between infection of a cell and virus progeny release from the infected cell. We then developed an equivalent stochastic virus dynamics model that accounts for this delay in the description of the random interactions between the model components. The new model is used to study the statistical characteristics of virus and target cell populations. It predicts the probability of infection spread as a function of the number of transmitted viruses. A hybrid algorithm is suggested to compute efficiently the system dynamics in state space domain characterized by the mix of small and large species densities.

Prediction of PD-L1 inhibition effects for HIV-infected individuals

The novel therapies with immune checkpoint inhibitors hold great promises for patients with chronic virus infections and cancers. This is based mainly on the partial reversal of the exhausted phenotype of antigen-specific cytotoxic CD8 T cells (CTL). Recently, we have shown that the restoration of HIV-specific T cell function depends on the HIV infection stage of an infected individual. Here we aimed to answer two fundamental questions: (i) Can one estimate growth parameters for the HIV-specific proliferative responsiveness upon PD-L1 blockade ex vivo? (ii) Can one use these parameter estimates to predict clinical benefit for HIV-infected individuals displaying diverse infection phenotypes? To answer these questions, we first analyzed HIV-1 Gag-specific CD8 T cell proliferation by time-resolved CFSE assays and estimated the effect of PD-L1 blockade on division and death rates, and specific precursor frequencies. These values were then incorporated into a model for CTL-mediated HIV control and the effects on CTL frequencies, viral loads and CD4 T cell counts were predicted for different infection phenotypes. The biggest absolute increase in CD4 T cell counts was in the group of slow progressors while the strongest reduction in virus loads was observed in progressor patients. These results suggest a significant clinical benefit only for a subgroup of HIV-infected individuals. However, as PD1 is a marker of lymphocyte activation and expressed on several lymphocyte subsets including also CD4 T cells and B cells, we subsequently examined the multiple effects of anti-PD-L1 blockade beyond those on CD8 T cells. This extended model then predicts that the net effect on HIV load and CD4 T cell number depends on the interplay between positive and negative effects of lymphocyte subset activation. For a physiologically relevant range of affected model parameters, PD-L1 blockade is likely to be overall beneficial for HIV-infected individuals.

Multi-scale immunoepidemiological modeling of within-host and between-host HIV dynamics: systematic review of mathematical models

OBJECTIVE

The objective of this study is to conduct a systematic review of multi-scale HIV immunoepidemiological models to improve our understanding of the synergistic impact between the HIV viral-immune dynamics at the individual level and HIV transmission dynamics at the population level.

BACKGROUND

While within-host and between-host models of HIV dynamics have been well studied at a single scale, connecting the immunological and epidemiological scales through multi-scale models is an emerging method to infer the synergistic dynamics of HIV at the individual and population levels.

METHODS

We reviewed nine articles using the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) framework that focused on the synergistic dynamics of HIV immunoepidemiological models at the individual and population levels.

RESULTS

HIV immunoepidemiological models simulate viral immune dynamics at the within-host scale and the epidemiological transmission dynamics at the between-host scale. They account for longitudinal changes in the immune viral dynamics of HIV+ individuals, and their corresponding impact on the transmission dynamics in the population. They are useful to analyze the dynamics of HIV super-infection, co-infection, drug resistance, evolution, and treatment in HIV+ individuals, and their impact on the epidemic pathways in the population. We illustrate the coupling mechanisms of the within-host and between-host scales, their mathematical implementation, and the clinical and public health problems that are appropriate for analysis using HIV immunoepidemiological models.

CONCLUSION

HIV immunoepidemiological models connect the within-host immune dynamics at the individual level and the epidemiological transmission dynamics at the population level. While multi-scale models add complexity over a single-scale model, they account for the time varying immune viral response of HIV+ individuals, and the corresponding impact on the time-varying risk of transmission of HIV+ individuals to other susceptibles in the population.

Impact of disease, drug and patient adherence on the effectiveness of antiviral therapy in pediatric HIV

INTRODUCTION

Maintaining effective antiretroviral treatment for life is a major problem in both resource-limited and resource-rich countries. Despite the progress observed in paediatric antiretroviral therapy, approximately 12% of children still experience treatment failure due to drug resistance, inadequate dosing and poor adherence. We explore the current status of antiretroviral therapy in children with focus on the interaction between disease, drug pharmacokinetics and patient behavior, all of which are strongly interconnected and determine treatment outcome. Areas covered: An overview is provided of the viral characteristics and available drug combinations aimed at the prevention of resistance. In this context, the role of patient adherence is scrutinized. A detailed assessment of factors affecting adherence is presented together with the main strategies to enhance treatment response in children. Expert opinion: Using modeling and simulation, a framework for characterizing the forgiveness of non-adherence for specific antiretroviral drugs in children is proposed in which information on pharmacokinetics, pharmacokinetic-pharmacodynamic relationships and viral dynamics is integrated. This approach represents an opportunity for the simplification of dosing regimens taking into account the interaction between these factors. Based on clinical trial simulation scenarios, we envisage the possibility of assessing the impact of variable adherence to antiretroviral drug combinations in HIV-infected children.

A Dynamical Modeling Approach for Analysis of Longitudinal Clinical Trials in the Presence of Missing Endpoints

Randomized longitudinal clinical trials are the gold standard to evaluate the effectiveness of interventions among different patient treatment groups. However, analysis of such clinical trials becomes difficult in the presence of missing data, especially in the case where the study endpoints become difficult to measure because of subject dropout rates or/and the time to discontinue the assigned interventions are different among the patient groups. Here we report on using a validated mathematical model combined with an inverse problem approach to predict the values for the missing endpoints. A small randomized HIV clinical trial where endpoints for most of patients are missing is used to demonstrate this approach.

Modeling Immune Response to BK Virus Infection and Donor Kidney in Renal Transplant Recipients

In this paper we develop and validate with bootstrapping techniques a mechanistic mathematical model of immune response to both BK virus infection and a donor kidney based on known and hypothesized mechanisms in the literature. The model presented does not capture all the details of the immune response but possesses key features that describe a very complex immunological process. We then estimate model parameters using a least squares approach with a typical set of available clinical data. Sensitivity analysis combined with asymptotic theory is used to determine the number of parameters that can be reliably estimated given the limited number of observations.

Uncertainty quantification in modeling HIV viral mechanics

We consider an in-host model for HIV-1 infection dynamics developed and validated with patient data in earlier work [7]. We revisit the earlier model in light of progress over the last several years in understanding HIV-1 progression in humans. We then consider statistical models to describe the data and use these with residual plots in generalized least squares problems to develop accurate descriptions of the proper weights for the data. We use recent parameter subset selection techniques [5,6] to investigate the impact of estimated parameters on the corresponding selection scores. Bootstrapping and asymptotic theory are compared in the context of confidence intervals for the resulting parameter estimates.

Information content in data sets for a nucleated-polymerization model

We illustrate the use of statistical tools (asymptotic theories of standard error quantification using appropriate statistical models, bootstrapping, and model comparison techniques) in addition to sensitivity analysis that may be employed to determine the information content in data sets. We do this in the context of recent models [S. Prigent, A. Ballesta, F. Charles, N. Lenuzza, P. Gabriel, L.M. Tine, H. Rezaei, and M. Doumic, An efficient kinetic model for assemblies of amyloid fibrils and its application to polyglutamine aggregation, PLoS ONE 7 (2012), e43273. doi:10.1371/journal.pone.0043273.] for nucleated polymerization in proteins, about which very little is known regarding the underlying mechanisms; thus, the methodology we develop here may be of great help to experimentalists. We conclude that the investigated data sets will support with reasonable levels of uncertainty only the estimation of the parameters related to the early steps of the aggregation process.

Immuno-modulatory strategies for reduction of HIV reservoir cells

Antiretroviral therapy is able to suppress the viral load to below the detection limit, but it is not able to eradicate HIV reservoirs. Thus, there is a critical need for a novel treatment to eradicate (or reduce) the reservoir in order to eliminate the need for a lifelong adherence to antiretroviral therapy, which is expensive and potentially toxic. In this paper, we investigate the possible pharmacological strategies or combinations of strategies that may be beneficial to reduce or possibly eradicate the latent reservoir. We do this via studies with a validated mathematical model, where the parameter values are obtained with newly acquired clinical data for HIV patients. Our findings indicate that the strategy of reactivating the reservoir combined with enhancement of the killing rate of HIV-specific CD8+ T cells is able to eradicate the reservoir. In addition, our analysis shows that a targeted suppression of the immune system is also a possible strategy to eradicate the reservoir.

Optimal Design of Non-equilibrium Experiments for Genetic Network Interrogation

Many experimental systems in biology, especially synthetic gene networks, are amenable to perturbations that are controlled by the experimenter. We developed an optimal design algorithm that calculates optimal observation times in conjunction with optimal experimental perturbations in order to maximize the amount of information gained from longitudinal data derived from such experiments. We applied the algorithm to a validated model of a synthetic Brome Mosaic Virus (BMV) gene network and found that optimizing experimental perturbations may substantially decrease uncertainty in estimating BMV model parameters.

Model Comparison Tests to Determine Data Information Content

In the context of inverse or parameter estimation problems we demonstrate the use of statistically based model comparison tests in several examples of practical interest. In these examples we are interested in questions related to information content of a particular given data set and whether the data will support a more complicated model to describe it. In the first example we compare fits for several different models to describe simple decay in a size histogram for aggregates in amyloid fibril formation. In a second example we investigate whether the information content in data sets for the pest Lygus hesperus in cotton fields as it is currently collected is sufficient to support a model in which one distinguishes between nymphs and adults. Finally in a third example with data for patients having undergone an organ transplant, we question whether the data content is sufficient to estimate more than 5 of the fundamental parameters in a particular dynamic model.

Experimental Design for Vector Output Systems

We formulate an optimal design problem for the selection of best states to observe and optimal sampling times for parameter estimation or inverse problems involving complex nonlinear dynamical systems. An iterative algorithm for implementation of the resulting methodology is proposed. Its use and efficacy is illustrated on two applied problems of practical interest: (i) dynamic models of HIV progression and (ii) modeling of the Calvin cycle in plant metabolism and growth.

A comparison of computational efficiencies of stochastic algorithms in terms of two infection models

In this paper, we investigate three particular algorithms: a stochastic simulation algorithm (SSA), and explicit and implicit tau-leaping algorithms. To compare these methods, we used them to analyze two infection models: a Vancomycin-resistant enterococcus (VRE) infection model at the population level, and a Human Immunodeficiency Virus (HIV) within host infection model. While the first has a low species count and few transitions, the second is more complex with a comparable number of species involved. The relative efficiency of each algorithm is determined based on computational time and degree of precision required. The numerical results suggest that all three algorithms have the similar computational efficiency for the simpler VRE model, and the SSA is the best choice due to its simplicity and accuracy. In addition, we have found that with the larger and more complex HIV model, implementation and modification of tau-Leaping methods are preferred.

Multiple endemic states in age-structured SIR epidemic models

SIR age-structured models are very often used as a basic model of epidemic spread. Yet, their behaviour, under generic assumptions on contact rates between different age classes, is not completely known, and, in the most detailed analysis so far, Inaba (1990) was able to prove uniqueness of the endemic equilibrium only under a rather restrictive condition. Here, we show an example in the form of a 3x3 contact matrix in which multiple non-trivial steady states exist. This instance of non-uniqueness of positive equilibria differs from most existing ones for epidemic models, since it arises not from a backward transcritical bifurcation at the disease free equilibrium, but through two saddle-node bifurcations of the positive equilibrium. The dynamical behaviour of the model is analysed numerically around the range where multiple endemic equilibria exist; many other features are shown to occur, from coexistence of multiple attractive periodic solutions, some with extremely long period, to quasi-periodic and chaotic attractors. It is also shown that, if the contact rates are in the form of a 2x2 WAIFW matrix, uniqueness of non-trivial steady states always holds, so that 3 is the minimum dimension of the contact matrix to allow for multiple endemic equilibria.

Modelling and optimal control of immune response of renal transplant recipients

We consider the increasingly important and highly complex immunological control problem: control of the dynamics of immunosuppression for organ transplant recipients. The goal in this problem is to maintain the delicate balance between over-suppression (where opportunistic latent viruses threaten the patient) and under-suppression (where rejection of the transplanted organ is probable). First, a mathematical model is formulated to describe the immune response to both viral infection and introduction of a donor kidney in a renal transplant recipient. Some numerical results are given to qualitatively validate and demonstrate that this initial model exhibits appropriate characteristics of primary infection and reactivation for immunosuppressed transplant recipients. In addition, we develop a computational framework for designing adaptive optimal treatment regimes with partial observations and low-frequency sampling, where the state estimates are obtained by solving a second deterministic optimal tracking problem. Numerical results are given to illustrate the feasibility of this method in obtaining optimal treatment regimes with a balance between under-suppression and over-suppression of the immune system.

Host immune responses that promote initial HIV spread

The host inflammatory response to HIV invasion is a necessary component of the innate antiviral activity that vaccines and early interventions seek to exploit/enhance. However, the response is dependent on CD4+ T-helper cell 1 (Th1) recruitment and activation. It is this very recruitment of HIV-susceptible target cells that is associated with the initial viral proliferation. Hence, global enhancement of the inflammatory response by T-cells and dendritic cells will likely feed viral propagation. Mucosal entry sites contain inherent pathways, in the form of natural regulatory T-cells (nTreg), that globally dampen the inflammatory response. We created a model of this inflammatory response to virus as well as inherent nTreg-mediated regulation of Th1 recruitment and activation. With simulations using this model we sought to address the net effect of nTreg activation and its specific functions as well as identify mechanisms of the natural inflammatory response that are best targeted to inhibit viral spread without compromising initial antiviral activity. Simulation results provide multiple insights that are relevant to developing intervention strategies that seek to exploit natural immune processes: (i) induction of the regulatory response through nTreg activation expedites viral proliferation due to viral production by nTreg itself and not to reduced Natural Killer (NK) cell activity; (ii) at the same time, induction of the inflammation response through either DC activation or Th1 activation expedites viral proliferation; (iii) within the inflammatory pathway, the NK response is an effective controller of viral proliferation while DC-mediated stimulation of T-cells is a significant driver of viral proliferation; and (iv) nTreg-mediated DC deactivation plays a significant role in slowing viral proliferation by inhibiting T-cell stimulation, making this function an aide to the antiviral immune response.

Comparison of Optimal Design Methods in Inverse Problems

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher Information Matrix (FIM). A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criteria with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model [13], the standard harmonic oscillator model [13] and a popular glucose regulation model [16, 19, 29].

A Model for HCMV Infection in Immunosuppressed Patients

We propose a model for HCMV infection in healthy and immunosuppressed patients. First, we present the biological model and formulate a system of ordinary differential equations to describe the pathogenesis of primary HCMV infection in immunocompetent and immunosuppressed individuals. We then investigate how clinical data can be applied to this model. Approximate parameter values for the model are derived from data available in the literature and from mathematical and physiological considerations. Simulations with the approximated parameter values demonstrates that the model is capable of describing primary, latent, and secondary (reactivated) HCMV infection. Reactivation simulations with this model provide a window into the dynamics of HCMV infection in (D-R+) transplant situations, where latently-infected recipients (R+) receive transplant tissue from HCMV-naive donors (D-).