Esteban A. Hernandez-Vargas

Effects of Aging on Influenza Virus Infection Dynamics

ABSTRACT The consequences of influenza virus infection are generally more severe in individuals over 65 years of age (the elderly). Immunosenescence enhances the susceptibility to viral infections and renders vaccination less effective. Understanding age-related changes in the immune system is crucial in order to design prophylactic and immunomodulatory strategies to reduce morbidity and mortality in the elderly. Here, we propose different mathematical models to provide a quantitative understanding of the immune strategies in the course of influenza virus infection using experimental data from young and aged mice. Simulation results suggested a central role of CD8+ T cells for adequate viral clearance kinetics in young and aged mice. Adding the removal of infected cells by natural killer cells did not improve the model fit in either young or aged animals. We separately examined the infection-resistant state of cells promoted by the cytokines alpha/beta interferon (IFN-α/β), IFN-γ, and tumor necrosis factor alpha (TNF-α). The combination of activated CD8+ T cells with any of the cytokines provided the best fits in young and aged animals. During the first 3 days after infection, the basic reproductive number for aged mice was 1.5-fold lower than that for young mice (P < 0.05). IMPORTANCE The fits of our models to the experimental data suggest that the increased levels of IFN-α/β, IFN-γ, and TNF-α (the “inflammaging” state) promote slower viral growth in aged mice, which consequently limits the stimulation of immune cells and contributes to the reported impaired responses in the elderly. A quantitative understanding of influenza virus pathogenesis and its shift in the elderly is the key contribution of this work.

Modeling Influenza Virus Infection: A Roadmap for Influenza Research

Influenza A virus (IAV) infection represents a global threat causing seasonal outbreaks and pandemics. Additionally, secondary bacterial infections, caused mainly by Streptococcus pneumoniae, are one of the main complications and responsible for the enhanced morbidity and mortality associated with IAV infections. In spite of the significant advances in our knowledge of IAV infections, holistic comprehension of the interplay between IAV and the host immune response (IR) remains largely fragmented. During the last decade, mathematical modeling has been instrumental to explain and quantify IAV dynamics. In this paper, we review not only the state of the art of mathematical models of IAV infection but also the methodologies exploited for parameter estimation. We focus on the adaptive IR control of IAV infection and the possible mechanisms that could promote a secondary bacterial coinfection. To exemplify IAV dynamics and identifiability issues, a mathematical model to explain the interactions between adaptive IR and IAV infection is considered. Furthermore, in this paper we propose a roadmap for future influenza research. The development of a mathematical modeling framework with a secondary bacterial coinfection, immunosenescence, host genetic factors and responsiveness to vaccination will be pivotal to advance IAV infection understanding and treatment optimization.

Ebola virus infection modeling and identifiability problems

The recent outbreaks of Ebola virus (EBOV) infections have underlined the impact of the virus as a major threat for human health. Due to the high biosafety classification of EBOV (level 4), basic research is very limited. Therefore, the development of new avenues of thinking to advance quantitative comprehension of the virus and its interaction with the host cells is urgently needed to tackle this lethal disease. Mathematical modeling of the EBOV dynamics can be instrumental to interpret Ebola infection kinetics on quantitative grounds. To the best of our knowledge, a mathematical modeling approach to unravel the interaction between EBOV and the host cells is still missing. In this paper, a mathematical model based on differential equations is used to represent the basic interactions between EBOV and wild-type Vero cells in vitro. Parameter sets that represent infectivity of pathogens are estimated for EBOV infection and compared with influenza virus infection kinetics. The average infecting time of wild-type Vero cells by EBOV is slower than in influenza infection. Simulation results suggest that the slow infecting time of EBOV could be compensated by its efficient replication. This study reveals several identifiability problems and what kind of experiments are necessary to advance the quantification of EBOV infection. A first mathematical approach of EBOV dynamics and the estimation of standard parameters in viral infections kinetics is the key contribution of this work, paving the way for future modeling works on EBOV infection.

Hierarchical effects of pro-inflammatory cytokines on the post-influenza susceptibility to pneumococcal coinfection.

In the course of influenza A virus (IAV) infections, a secondary bacterial infection frequently leads to serious respiratory conditions provoking high hospitalization and death tolls. Although abundant pro-inflammatory responses have been reported as key contributing factors for these severe dual infections, the relative contributions of cytokines remain largely unclear. In the current study, mathematical modelling based on murine experimental data dissects IFN-γ as a cytokine candidate responsible for impaired bacterial clearance, thereby promoting bacterial growth and systemic dissemination during acute IAV infection. We also found a time-dependent detrimental role of IL-6 in curtailing bacterial outgrowth which was not as distinct as for IFN-γ. Our numerical simulations suggested a detrimental effect of IFN-γ alone and in synergism with IL-6 but no conclusive pathogenic effect of IL-6 and TNF-α alone. This work provides a rationale to understand the potential impact of how to manipulate temporal immune components, facilitating the formulation of hypotheses about potential therapeutic strategies to treat coinfections.

A mathematical model of T lymphocyte calcium dynamics derived from single transmembrane protein properties

Fate decision processes of T lymphocytes are crucial for health and disease. Whether a T lymphocyte is activated, divides, gets anergic, or initiates apoptosis depends on extracellular triggers and intracellular signaling. Free cytosolic calcium dynamics plays an important role in this context. The relative contributions of store-derived calcium entry and calcium entry from extracellular space to T lymphocyte activation are still a matter of debate. Here we develop a quantitative mathematical model of T lymphocyte calcium dynamics in order to establish a tool which allows to disentangle cause-effect relationships between ion fluxes and observed calcium time courses. The model is based on single transmembrane protein characteristics which have been determined in independent experiments. This reduces the number of unknown parameters in the model to a minimum and ensures the predictive power of the model. Simulation results are subsequently used for an analysis of whole cell calcium dynamics measured under various experimental conditions. The model accounts for a variety of these conditions, which supports the suitability of the modeling approach. The simulation results suggest a model in which calcium dynamics dominantly relies on the opening of channels in calcium stores while calcium entry through calcium-release activated channels (CRAC) is more associated with the maintenance of the T lymphocyte calcium levels and prevents the cell from calcium depletion. Our findings indicate that CRAC guarantees a long-term stable calcium level which is required for cell survival and sustained calcium enhancement.

Oseltamivir PK/PD Modeling and Simulation to Evaluate Treatment Strategies against Influenza-Pneumococcus Coinfection

Influenza pandemics and seasonal outbreaks have shown the potential of Influenza A virus (IAV) to enhance susceptibility to a secondary infection with the bacterial pathogen Streptococcus pneumoniae (Sp). The high morbidity and mortality rate revealed the poor efficacy of antiviral drugs and vaccines to fight IAV infections. Currently, the most effective treatment for IAV is by antiviral neuraminidase inhibitors. Among them, the most frequently stockpiled is Oseltamivir which reduces viral release and transmission. However, effectiveness of Oseltamivir is compromised by the emergence of resistant IAV strains and secondary bacterial infections. To date, little attention has been given to evaluate how Oseltamivir treatment strategies alter Influenza viral infection in presence of Sp coinfection and a resistant IAV strain emergence. In this paper we investigate the efficacy of current approved Oseltamivir treatment regimens using a computational approach. Our numerical results suggest that the curative regimen (75 mg) may yield 47% of antiviral efficacy and 9% of antibacterial efficacy. An increment in dose to 150 mg (pandemic regimen) may increase the antiviral efficacy to 49% and the antibacterial efficacy to 16%. The choice to decrease the intake frequency to once per day is not recommended due to a significant reduction in both antiviral and antibacterial efficacy. We also observe that the treatment duration of 10 days may not provide a clear improvement on the antiviral and antibacterial efficacy compared to 5 days. All together, our in silico study reveals the success and pitfalls of Oseltamivir treatment strategies within IAV-Sp coinfection and calls for testing the validity in clinical trials.

Analysis of Practical Identifiability of a Viral Infection Model.

Mathematical modelling approaches have granted a significant contribution to life sciences and beyond to understand experimental results. However, incomplete and inadequate assessments in parameter estimation practices hamper the parameter reliability, and consequently the insights that ultimately could arise from a mathematical model. To keep the diligent works in modelling biological systems from being mistrusted, potential sources of error must be acknowledged. Employing a popular mathematical model in viral infection research, existing means and practices in parameter estimation are exemplified. Numerical results show that poor experimental data is a main source that can lead to erroneous parameter estimates despite the use of innovative parameter estimation algorithms. Arbitrary choices of initial conditions as well as data asynchrony distort the parameter estimates but are often overlooked in modelling studies. This work stresses the existence of several sources of error buried in reports of modelling biological systems, voicing the need for assessing the sources of error, consolidating efforts in solving the immediate difficulties, and possibly reconsidering the use of mathematical modelling to quantify experimental data.

The 2017 plague outbreak in Madagascar: Data descriptions and epidemic modelling

From August to November 2017, Madagascar endured an outbreak of plague. A total of 2417 cases of plague were confirmed, causing a death toll of 209. Public health intervention efforts were introduced and successfully stopped the epidemic at the end of November. The plague, however, is endemic in the region and occurs annually, posing the risk of future outbreaks. To understand the plague transmission, we collected real-time data from official reports, described the outbreaks characteristics, and estimated transmission parameters using statistical and mathematical models. The pneumonic plague epidemic curve exhibited multiple peaks, coinciding with sporadic introductions of new bubonic cases. Optimal climate conditions for rat flea to flourish were observed during the epidemic. Estimate of the plague basic reproduction number during the large wave of the epidemic was high, ranging from 5 to 7 depending on model assumptions. The incubation and infection periods for bubonic and pneumonic plague were 4.3 and 3.4 days and 3.8 and 2.9 days, respectively. Parameter estimation suggested that even with a small fraction of the population exposed to infected rat fleas (1/10,000) and a small probability of transition from a bubonic case to a secondary pneumonic case (3%), the high human-to-human transmission rate can still generate a large outbreak. Controlling rodent and fleas can prevent new index cases, but managing human-to-human transmission is key to prevent large-scale outbreaks.

Modeling Kick-Kill Strategies toward HIV Cure

Although combinatorial antiretroviral therapy (cART) potently suppresses the virus, a sterile or functional cure still remains one of the greatest therapeutic challenges worldwide. Reservoirs are infected cells that can maintain HIV persistence for several years in patients with optimal cART, which is a leading obstacle to eradicate the virus. Despite the significant progress that has been made in our understanding of the diversity of cells that promote HIV persistence, many aspects that are critical to the development of effective therapeutic approaches able to purge the latent CD4+ T cell reservoir are poorly understood. Simultaneous purging strategies known as “kick-kill” have been pointed out as promising therapeutic approaches to eliminate the viral reservoir. However, long-term outcomes of purging strategies as well as the effect on the HIV reservoir are still largely fragmented. In this context, mathematical modeling can provide a rationale not only to evaluate the impact on the HIV reservoir but also to facilitate the formulation of hypotheses about potential therapeutic strategies. This review aims to discuss briefly the most recent mathematical modeling contributions, harnessing our knowledge toward the uncharted territory of HIV eradication. In addition, problems associated with current models are discussed, in particular, mathematical models consider only T cell responses but HIV control may also depend on other cell responses as well as chemokines and cytokines dynamics.

Reducing complexity: An iterative strategy for parameter determination in biological networks

Abstract The dynamics of biological networks are fundamental to a variety of processes in many areas of biology and medicine. Understanding of such networks on a systemic level is facilitated by mathematical models describing these networks. However, since mathematical models of signalling networks commonly aim to describe several highly connected biological quantities and many model parameters cannot be measured directly, quantitative dynamic models often present challenges with respect to model calibration. Here, we propose an iterative fitting routine to decompose the problem of fitting a system of coupled ordinary differential equations describing a signalling network into smaller subproblems. Parameters for each differential equation are estimated separately using a Differential Evolution algorithm while all other dynamic quantities in the model are treated as input to the system. The performance of this algorithm is evaluated on artificial networks with known structure and known model parameters and compared to a conventional optimisation procedure for the same problem. Our analysis indicates that the procedure results in a significantly higher quality of fit and more efficient reconstruction of the true parameters than the conventional algorithm.