Viral kinetic modeling: state of the art

Safety and Efficacy of Antiviral Drugs and Vaccines in Pregnant Women: Insights from Physiologically Based Pharmacokinetic Modeling and Integration of Viral Infection Dynamics

Addressing the complexities of managing viral infections during pregnancy is essential for informed medical decision-making. This comprehensive review delves into the management of key viral infections impacting pregnant women, namely Human Immunodeficiency Virus (HIV), Hepatitis B Virus/Hepatitis C Virus (HBV/HCV), Influenza, Cytomegalovirus (CMV), and SARS-CoV-2 (COVID-19). We evaluate the safety and efficacy profiles of antiviral treatments for each infection, while also exploring innovative avenues such as gene vaccines and their potential in mitigating viral threats during pregnancy. Additionally, the review examines strategies to overcome challenges, encompassing prophylactic and therapeutic vaccine research, regulatory considerations, and safety protocols. Utilizing advanced methodologies, including PBPK modeling, machine learning, artificial intelligence, and causal inference, we can amplify our comprehension and decision-making capabilities in this intricate domain. This narrative review aims to shed light on diverse approaches and ongoing advancements, this review aims to foster progress in antiviral therapy for pregnant women, improving maternal and fetal health outcomes.

A mathematical model for the within-host (re)infection dynamics of SARS-CoV-2

Interactions between SARS-CoV-2 and the immune system during infection are complex. However, understanding the within-host SARS-CoV-2 dynamics is of enormous importance for clinical and public health outcomes. Current mathematical models focus on describing the within-host SARS-CoV-2 dynamics during the acute infection phase. Thereby they ignore important long-term post-acute infection effects. We present a mathematical model, which not only describes the SARS-CoV-2 infection dynamics during the acute infection phase, but extends current approaches by also recapitulating clinically observed long-term post-acute infection effects, such as the recovery of the number of susceptible epithelial cells to an initial pre-infection homeostatic level, a permanent and full clearance of the infection within the individual, immune waning, and the formation of long-term immune capacity levels after infection. Finally, we used our model and its description of the long-term post-acute infection dynamics to explore reinfection scenarios differentiating between distinct variant-specific properties of the reinfecting virus. Together, the model's ability to describe not only the acute but also the long-term post-acute infection dynamics provides a more realistic description of key outcomes and allows for its application in clinical and public health scenarios.

The reproduction number and its probability distribution for stochastic viral dynamics

We consider stochastic models of individual infected cells. The reproduction number, R, is understood as a random variable representing the number of new cells infected by one initial infected cell in an otherwise susceptible (target cell) population. Variability in R results partly from heterogeneity in the viral burst size (the number of viral progeny generated from an infected cell during its lifetime), which depends on the distribution of cellular lifetimes and on the mechanism of virion release. We analyse viral dynamics models with an eclipse phase: the period of time after a cell is infected but before it is capable of releasing virions. The duration of the eclipse, or the subsequent infectious, phase is non-exponential, but composed of stages. We derive the probability distribution of the reproduction number for these viral dynamics models, and show it is a negative binomial distribution in the case of constant viral release from infectious cells, and under the assumption of an excess of target cells. In a deterministic model, the ultimate in-host establishment or extinction of the viral infection depends entirely on whether the mean reproduction number is greater than, or less than, one, respectively. Here, the probability of extinction is determined by the probability distribution of R, not simply its mean value. In particular, we show that in some cases the probability of infection is not an increasing function of the mean reproduction number.

Modelling the impact of JNJ-1802, a first-in-class dengue inhibitor blocking the NS3-NS4B interaction, on in-vitro DENV-2 dynamics

Dengue virus (DENV) is a public health challenge across the tropics and subtropics. Currently, there is no licensed prophylactic or antiviral treatment for dengue. The novel DENV inhibitor JNJ-1802 can significantly reduce viral load in mice and non-human primates. Here, using a mechanistic viral kinetic model calibrated against viral RNA data from experimental in-vitro infection studies, we assess the in-vitro inhibitory effect of JNJ-1802 by characterising infection dynamics of two DENV-2 strains in the absence and presence of different JNJ-1802 concentrations. Viral RNA suppression to below the limit of detection was achieved at concentrations of >1.6 nM, with a median concentration exhibiting 50% of maximal inhibitory effect (IC50) of 1.23x10-02 nM and 1.28x10-02 nM for the DENV-2/RL and DENV-2/16681 strains, respectively. This work provides important insight into the in-vitro inhibitory effect of JNJ-1802 and presents a first step towards a modelling framework to support characterization of viral kinetics and drug effect across different host systems.

What explains the poor contraction of the viral load during paediatric HIV infection?

An acute HIV infection in young children differs markedly from that in adults: Children have higher viral loads (VL), and a poor contraction to a setpoint VL that is not much lower than the peak VL. As a result, children progress faster towards AIDS in the absence of treatment. We used a classical ordinary differential equation model for viral infection dynamics to study why children have a lower viral contraction ratio than adults. We performed parameter sweeps to identify factors explaining the observed difference between children and adults. We grouped parameters associated with the host, the infection, or the immune response. Based on paediatric data available from datasets within the EPIICAL project (https://www.epiical.org/), we refuted that viral replication rates differ between young children and adults, and therefore these cannot be responsible for the low VL contraction ratios seen in children. The major differences in lowering VL contraction ratio resulted from sweeping the parameters linked to the immune response. Thus, we postulate that an "ineffective" (late and/or weak) immune response is the most parsimonious explanation for the higher setpoint VL in young children, and hence the reason for their fast disease progression.

A Novel Mathematical Model That Predicts the Protection Time of SARS-CoV-2 Antibodies

Infectious diseases such as SARS-CoV-2 pose a considerable threat to public health. Constructing a reliable mathematical model helps us quantitatively explain the kinetic characteristics of antibody-virus interactions. A novel and robust model is developed to integrate antibody dynamics with virus dynamics based on a comprehensive understanding of immunology principles. This model explicitly formulizes the pernicious effect of the antibody, together with a positive feedback stimulation of the virus-antibody complex on the antibody regeneration. Besides providing quantitative insights into antibody and virus dynamics, it demonstrates good adaptivity in recapturing the virus-antibody interaction. It is proposed that the environmental antigenic substances help maintain the memory cell level and the corresponding neutralizing antibodies secreted by those memory cells. A broader application is also visualized in predicting the antibody protection time caused by a natural infection. Suitable binding antibodies and the presence of massive environmental antigenic substances would prolong the protection time against breakthrough infection. The model also displays excellent fitness and provides good explanations for antibody selection, antibody interference, and self-reinfection. It helps elucidate how our immune system efficiently develops neutralizing antibodies with good binding kinetics. It provides a reasonable explanation for the lower SARS-CoV-2 mortality in the population that was vaccinated with other vaccines. It is inferred that the best strategy for prolonging the vaccine protection time is not repeated inoculation but a directed induction of fast-binding antibodies. Eventually, this model will inform the future construction of an optimal mathematical model and help us fight against those infectious diseases.

Global dynamics of IAV/SARS-CoV-2 coinfection model with eclipse phase and antibody immunity

Coronavirus disease 2019 (COVID-19) and influenza are two respiratory infectious diseases of high importance widely studied around the world. COVID-19 is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), while influenza is caused by one of the influenza viruses, A, B, C, and D. Influenza A virus (IAV) can infect a wide range of species. Studies have reported several cases of respiratory virus coinfection in hospitalized patients. IAV mimics the SARS-CoV-2 with respect to the seasonal occurrence, transmission routes, clinical manifestations and related immune responses. The present paper aimed to develop and investigate a mathematical model to study the within-host dynamics of IAV/SARS-CoV-2 coinfection with the eclipse (or latent) phase. The eclipse phase is the period of time that elapses between the viral entry into the target cell and the release of virions produced by that newly infected cell. The role of the immune system in controlling and clearing the coinfection is modeled. The model simulates the interaction between nine compartments, uninfected epithelial cells, latent/active SARS-CoV-2-infected cells, latent/active IAV-infected cells, free SARS-CoV-2 particles, free IAV particles, SARS-CoV-2-specific antibodies and IAV-specific antibodies. The regrowth and death of the uninfected epithelial cells are considered. We study the basic qualitative properties of the model, calculate all equilibria, and prove the global stability of all equilibria. The global stability of equilibria is established using the Lyapunov method. The theoretical findings are demonstrated via numerical simulations. The importance of considering the antibody immunity in the coinfection dynamics model is discussed. It is found that without modeling the antibody immunity, the case of IAV and SARS-CoV-2 coexistence will not occur. Further, we discuss the effect of IAV infection on the dynamics of SARS-CoV-2 single infection and vice versa.

Predicting Influenza A Virus Infection in the Lung from Hematological Data with Machine Learning

The tracking of pathogen burden and host responses with minimally invasive methods during respiratory infections is central for monitoring disease development and guiding treatment decisions. Utilizing a standardized murine model of respiratory influenza A virus (IAV) infection, we developed and tested different supervised machine learning models to predict viral burden and immune response markers, i.e., cytokines and leukocytes in the lung, from hematological data. We performed independently in vivo infection experiments to acquire extensive data for training and testing of the models. We show here that lung viral load, neutrophil counts, cytokines (such as gamma interferon [IFN-γ] and interleukin 6 [IL-6]), and other lung infection markers can be predicted from hematological data. Furthermore, feature analysis of the models showed that blood granulocytes and platelets play a crucial role in prediction and are highly involved in the immune response against IAV. The proposed in silico tools pave the path toward improved tracking and monitoring of influenza virus infections and possibly other respiratory infections based on minimally invasively obtained hematological parameters. IMPORTANCE During the course of respiratory infections such as influenza, we do have a very limited view of immunological indicators to objectively and quantitatively evaluate the outcome of a host. Methods for monitoring immunological markers in a host's lungs are invasive and expensive, and some of them are not feasible to perform. Using machine learning algorithms, we show for the first time that minimally invasively acquired hematological parameters can be used to infer lung viral burden, leukocytes, and cytokines following influenza virus infection in mice. The potential of the framework proposed here consists of a new qualitative vision of the disease processes in the lung compartment as a noninvasive tool.

Teaching undergraduate physical chemistry lab with kinetic analysis of COVID-19 in the United States

A physical chemistry lab for undergraduate students described in this report is about applying kinetic models to analyze the spread of COVID-19 in the United States and obtain the reproduction numbers. The susceptible-infectious-recovery (SIR) model and the SIR-vaccinated (SIRV) model are explained to the students and are used to analyze the COVID-19 spread data from U.S. Centers for Disease Control and Prevention (CDC). The basic reproduction number R 0 and the real-time reproduction number R t of COVID-19 are extracted by fitting the data with the models, which explains the spreading kinetics and provides a prediction of the spreading trend in a given state. The procedure outlined here shows the differences between the SIR model and the SIRV model. The SIRV model considers the effect of vaccination which helps explain the later stages of the ongoing pandemic. The predictive power of the models is also shown giving the students some certainty in the predictions they made for the following months.

Characterizing viral within-host diversity in fast and non-equilibrium demo-genetic dynamics

High-throughput sequencing has opened the route for a deep assessment of within-host genetic diversity that can be used, e.g., to characterize microbial communities and to infer transmission links in infectious disease outbreaks. The performance of such characterizations and inferences cannot be analytically assessed in general and are often grounded on computer-intensive evaluations. Then, being able to simulate within-host genetic diversity across time under various demo-genetic assumptions is paramount to assess the performance of the approaches of interest. In this context, we built an original model that can be simulated to investigate the temporal evolution of genotypes and their frequencies under various demo-genetic assumptions. The model describes the growth and the mutation of genotypes at the nucleotide resolution conditional on an overall within-host viral kinetics, and can be tuned to generate fast non-equilibrium demo-genetic dynamics. We ran simulations of this model and computed classic diversity indices to characterize the temporal variation of within-host genetic diversity (from high-throughput amplicon sequences) of virus populations under three demographic kinetic models of viral infection. Our results highlight how demographic (viral load) and genetic (mutation, selection, or drift) factors drive variations in within-host diversity during the course of an infection. In particular, we observed a non-monotonic relationship between pathogen population size and genetic diversity, and a reduction of the impact of mutation on diversity when a non-specific host immune response is activated. The large variation in the diversity patterns generated in our simulations suggests that the underlying model provides a flexible basis to produce very diverse demo-genetic scenarios and test, for instance, methods for the inference of transmission links during outbreaks.

Antiviral Used among Non-Severe COVID-19 Cases in Relation to Time till Viral Clearance: A Retrospective Cohort Study

(1) Background: The WHO identified COVID-19 as a fast-growing epidemic worldwide. A few antivirals have shown promising effectiveness in treating COVID-19. This study aimed to assess the correlation between antiviral drugs and the time until viral clearance of SARS-CoV-2. (2) Methods: This was a retrospective cohort study that included 1731 non-severe COVID-19 patients treated in NMC Royal Hospital, UAE. (3) Results: A total of 1446 patients received symptomatic treatment only (mean age of 35.6 ± 9.0 years). The analyzed antiviral treatment protocols were azithromycin, hydroxychloroquine, lopinavir/ritonavir, and favipiravir. The produced Kaplan–Meier plots showed no significant differences in the time until viral clearance among the compared protocols, which showed overlapping confidence intervals, which were determined by performing the log-rank and adjusted pairwise log-rank tests (p = 0.2, log-rank = 9.3). The age and gender of patients did not significantly affect the rate of viral clearance regardless of the antiviral therapy administered, even when compared to patients who received symptomatic treatment only, with the exception of hydroxychloroquine (HCQ), azithromycin, and favipiravir, which increased the odds of a faster rate of viral clearance by 46% after adjustments. (4) Conclusions: No significant differences were observed regarding the time until viral clearance among non-severe COVID-19 patients following the prescription of different antiviral drugs.

Variant‐specific SARS‐CoV‐2 within‐host kinetics

Since early 2021, SARS‐CoV‐2 variants of concern (VOCs) have been causing epidemic rebounds in many countries. Their properties are well characterized at the epidemiological level but the potential underlying within‐host determinants remain poorly understood. We analyze a longitudinal cohort of 6944 individuals with 14 304 cycle threshold (Ct) values of reverse‐transcription quantitative polymerase chain reaction (RT‐qPCR) VOC screening tests performed in the general population and hospitals in France between February 6 and August 21, 2021. To convert Ct values into numbers of virus copies, we performed an additional analysis using droplet digital PCR (ddPCR). We find that the number of viral genome copies reaches a higher peak value and has a slower decay rate in infections caused by Alpha variant compared to that caused by historical lineages. Following the evidence that viral genome copies in upper respiratory tract swabs are informative on contagiousness, we show that the kinetics of the Alpha variant translate into significantly higher transmission potentials, especially in older populations. Finally, comparing infections caused by the Alpha and Delta variants, we find no significant difference in the peak viral copy number. These results highlight that some of the differences between variants may be detected in virus load variations.

Effectiveness of Antiviral Therapy in Highly-Transmissible Variants of SARS-CoV-2: A Modeling and Simulation Study

As of October 2021, neither established agents (e.g., hydroxychloroquine) nor experimental drugs have lived up to their initial promise as antiviral treatment against SARS-CoV-2 infection. While vaccines are being globally deployed, variants of concern (VOCs) are emerging with the potential for vaccine escape. VOCs are characterized by a higher within-host transmissibility, and this may alter their susceptibility to antiviral treatment. Here we describe a model to understand the effect of changes in within-host reproduction number R₀, as proxy for transmissibility, of VOCs on the effectiveness of antiviral therapy with molnupiravir through modeling and simulation. Molnupiravir (EIDD-2801 or MK 4482) is an orally bioavailable antiviral drug inhibiting viral replication through lethal mutagenesis, ultimately leading to viral extinction. We simulated 800 mg molnupiravir treatment every 12 h for 5 days, with treatment initiated at different time points before and after infection. Modeled viral mutations range from 1.25 to 2-fold greater transmissibility than wild type, but also include putative co-adapted variants with lower transmissibility (0.75-fold). Antiviral efficacy was correlated with R₀, making highly transmissible VOCs more sensitive to antiviral therapy. Total viral load was reduced by up to 70% in highly transmissible variants compared to 30% in wild type if treatment was started in the first 1–3 days post inoculation. Less transmissible variants appear less susceptible. Our findings suggest there may be a role for pre- or post-exposure prophylactic antiviral treatment in areas with presence of highly transmissible SARS-CoV-2 variants. Furthermore, clinical trials with borderline efficacious results should consider identifying VOCs and examine their impact in post-hoc analysis.

Towards a Mathematical Model for the Viral Progression in the Pharynx

In this work, a comprehensive model for the viral progression in the pharynx has been developed. This one-dimension model considers both Fickian diffusion and convective flow coupled with chemical reactions, such as virus population growth, infected and uninfected cell accumulation as well as virus clearance. The effect of a sterilizing agent such as an alcoholic solution on the viral progression in the pharynx was taken into account and a parametric analysis for the effect of kinetic rate parameters on virus propagation was made. Moreover, different conditions caused by further medical treatment, such as a decrease in virus yield per infected cell, were examined. It is shown that the infection fails to establish by decreasing the virus yield per infected cell. It is believed that this work could be used to further investigate the medical treatment of viral progression in the pharynx.

Remote Learning of COVID-19 Kinetic Analysis in a Physical Chemistry Laboratory Class

The COVID-19 pandemic has affected many in-person laboratory courses across the world. The viral spreading model is complicated but parameters, such as its reproduction number, R _t, can be estimated with the susceptible, infectious, or recovered model. COVID-19 data for many states and countries are widely available online. This provides an opportunity for the students to analyze its spreading kinetics remotely. Here, we reported a laboratory set up online during the third week of the spring semester of 2021 to minimize social contacts. Due to the wide interest in developing online physical chemistry and analytical laboratories during the pandemic, we would like to share this laboratory design. The method, technique, procedure, and grading are described in this report. The student participants were able to apply the kinetic techniques learned in physical chemistry to successfully analyze an ongoing real-world problem through a remote learning environment and prepare this report.

Multiscale model of hepatitis C virus dynamics in plasma and liver following combination therapy

This work explores the application of a physiologically structured population (PSP) framework in modeling hepatitis C virus (HCV) kinetics. To do so, a model was developed for the viral RNA load in plasma and liver as observed in 15 patients treated with a combination therapy of pegylated interferon, ribavirin, and telaprevir. By including both intracellular and extracellular processes of the HCV lifecycle, the model provided a description of the treatment effect on the intracellular HCV lifecycle. Combining PSP models with a nonlinear mixed effects approach in a single model permits a natural inclusion of the direct‐acting antiviral effect on intracellular processes, which can then be integrated with the viral kinetics within the host while accounting for the interindividual variability between patients. This should allow an exploration of the treatment effect within the entire chronic HCV‐infected population.

Modeling of SARS-CoV-2 Treatment Effects for Informed Drug Repurposing

Several repurposed drugs are currently under investigation in the fight against coronavirus disease 2019 (COVID-19). Candidates are often selected solely by their effective concentrations in vitro, an approach that has largely not lived up to expectations in COVID-19. Cell lines used in in vitro experiments are not necessarily representative of lung tissue. Yet, even if the proposed mode of action is indeed true, viral dynamics in vivo, host response, and concentration-time profiles must also be considered. Here we address the latter issue and describe a model of human SARS-CoV-2 viral kinetics with acquired immune response to investigate the dynamic impact of timing and dosing regimens of hydroxychloroquine, lopinavir/ritonavir, ivermectin, artemisinin, and nitazoxanide. We observed greatest benefits when treatments were given immediately at the time of diagnosis. Even interventions with minor antiviral effect may reduce host exposure if timed correctly. Ivermectin seems to be at least partially effective: given on positivity, peak viral load dropped by 0.3-0.6 log units and exposure by 8.8-22.3%. The other drugs had little to no appreciable effect. Given how well previous clinical trial results for hydroxychloroquine and lopinavir/ritonavir are explained by the models presented here, similar strategies should be considered in future drug candidate prioritization efforts.

Biophysical analysis of SARS-CoV-2 transmission and theranostic development via N protein computational characterization

Recently, SARS-CoV-2 has been identified as the causative factor of viral infection called COVID-19 that belongs to the zoonotic beta coronavirus family known to cause respiratory disorders or viral pneumonia, followed by an extensive attack on organs that express angiotensin-converting enzyme II (ACE2). Human transmission of this virus occurs via respiratory droplets from symptomatic and asymptomatic patients, which are released into the environment after sneezing or coughing. These droplets are capable of staying in the air as aerosols or surfaces and can be transmitted to persons through inhalation or contact with contaminated surfaces. Thus, there is an urgent need for advanced theranostic solutions to control the spread of COVID-19 infection. The development of such fit-for-purpose technologies hinges on a proper understanding of the transmission, incubation, and structural characteristics of the virus in the external environment and within the host. Hence, this article describes the development of an intrinsic model to describe the incubation characteristics of the virus under varying environmental factors. It also discusses on the evaluation of SARS-CoV-2 structural nucleocapsid protein properties via computational approaches to generate high-affinity binding probes for effective diagnosis and targeted treatment applications by specific targeting of viruses. In addition, this article provides useful insights on the transmission behavior of the virus and creates new opportunities for theranostics development.

Model-informed drug repurposing: A pharmacometric approach to novel pathogen preparedness, response and retrospection

During a pandemic caused by a novel pathogen (NP), drug repurposing offers the potential of a rapid treatment response via a repurposed drug (RD) while more targeted treatments are developed. Five steps of model‐informed drug repurposing (MIDR) are discussed: (i) utilize RD product label and in vitro NP data to determine initial proof of potential, (ii) optimize potential posology using clinical pharmacokinetics (PK) considering both efficacy and safety, (iii) link events in the viral life cycle to RD PK, (iv) link RD PK to clinical and virologic outcomes, and optimize clinical trial design, and (v) assess RD treatment effects from trials using model‐based meta‐analysis. Activities which fall under these five steps are categorized into three stages: what can be accomplished prior to an NP emergence (preparatory stage), during the NP pandemic (responsive stage) and once the crisis has subsided (retrospective stage). MIDR allows for extraction of a greater amount of information from emerging data and integration of disparate data into actionable insight.

Cooperative nature of viral replication

The ability of viruses to infect their hosts depends on rapid dissemination following transmission. The notion that viral particles function as independent propagules has been challenged by recent observations suggesting that viral aggregates show enhanced infectivity and faster spread. However, these observations remain poorly understood. Here, we show that viral replication is a cooperative process, such that entry of multiple viral genome copies into the same cell disproportionately increases short-term viral progeny production. This cooperativity arises from the positive feedback established between replication templates and virus-encoded products involved in replication and should be a general feature of viruses. We develop a simple model that captures this effect, verify that cooperativity also emerges in more complex models for specific human viruses, validate our predictions experimentally using different mammalian viruses, and discuss the implications of cooperative replication for viral fitness.

Mathematical modeling of hepatitis C RNA replication, exosome secretion and virus release

Hepatitis C virus (HCV) causes acute hepatitis C and can lead to life-threatening complications if it becomes chronic. The HCV genome is a single plus strand of RNA. Its intracellular replication is a spatiotemporally coordinated process of RNA translation upon cell infection, RNA synthesis within a replication compartment, and virus particle production. While HCV is mainly transmitted via mature infectious virus particles, it has also been suggested that HCV-infected cells can secrete HCV RNA carrying exosomes that can infect cells in a receptor independent manner. In order to gain insight into these two routes of transmission, we developed a series of intracellular HCV replication models that include HCV RNA secretion and/or virus assembly and release. Fitting our models to in vitro data, in which cells were infected with HCV, suggests that initially most secreted HCV RNA derives from intracellular cytosolic plus-strand RNA, but subsequently secreted HCV RNA derives equally from the cytoplasm and the replication compartments. Furthermore, our model fits to the data suggest that the rate of virus assembly and release is limited by host cell resources. Including the effects of direct acting antivirals in our models, we found that in spite of decreasing intracellular HCV RNA and extracellular virus concentration, low level HCV RNA secretion may continue as long as intracellular RNA is available. This may possibly explain the presence of detectable levels of plasma HCV RNA at the end of treatment even in patients that ultimately attain a sustained virologic response.

Approximately 70 million people are chronically infected with hepatitis C virus (HCV), which if left untreated may lead to cirrhosis and liver cancer. However, modern drug therapy is highly effective and hepatitis C is the first chronic virus infection that can be cured with short-term therapy in almost all infected individuals. The within-host transmission of HCV occurs mainly via infectious virus particles, but experimental studies suggest that there may be additional receptor-independent cell-to-cell transmission by exosomes that carry the HCV genome. In order to understand the intracellular HCV lifecycle and HCV RNA spread, we developed a series of mathematical models that take both exosomal secretion and viral secretion into account. By fitting these models to in vitro data, we found that secretion of both HCV RNA as well as virus probably occurs and that the rate of virus assembly is likely limited by cellular co-factors on which the virus strongly depends for its own replication. Furthermore, our modeling predicted that the parameters governing the processes in the viral lifecycle that are targeted by direct acting antivirals are the most sensitive to perturbations, which may help explain their ability to cure this infection.

Modelling infectious viral diseases in swine populations: a state of the art

Mathematical modelling is nowadays a pivotal tool for infectious diseases studies, completing regular biological investigations. The rapid growth of computer technology allowed for development of computational tools to address biological issues that could not be unravelled in the past. The global understanding of viral disease dynamics requires to account for all interactions at all levels, from within-host to between-herd, to have all the keys for development of control measures. A literature review was performed to disentangle modelling frameworks according to their major objectives and methodologies. One hundred and seventeen articles published between 1994 and 2020 were found to meet our inclusion criteria, which were defined to target papers representative of studies dealing with models of viral infection dynamics in pigs. A first descriptive analysis, using bibliometric indexes, permitted to identify keywords strongly related to the study scopes. Modelling studies were focused on particular infectious agents, with a shared objective: to better understand the viral dynamics for appropriate control measure adaptation. In a second step, selected papers were analysed to disentangle the modelling structures according to the objectives of the studies. The system representation was highly dependent on the nature of the pathogens. Enzootic viruses, such as swine influenza or porcine reproductive and respiratory syndrome, were generally investigated at the herd scale to analyse the impact of husbandry practices and prophylactic measures on infection dynamics. Epizootic agents (classical swine fever, foot-and-mouth disease or African swine fever viruses) were mostly studied using spatio-temporal simulation tools, to investigate the efficiency of surveillance and control protocols, which are predetermined for regulated diseases. A huge effort was made on model parameterization through the development of specific studies and methodologies insuring the robustness of parameter values to feed simulation tools. Integrative modelling frameworks, from within-host to spatio-temporal models, is clearly on the way. This would allow to capture the complexity of individual biological variabilities and to assess their consequences on the whole system at the population level. This would offer the opportunity to test and evaluate in silico the efficiency of possible control measures targeting specific epidemiological units, from hosts to herds, either individually or through their contact networks. Such decision support tools represent a strength for stakeholders to help mitigating infectious diseases dynamics and limiting economic consequences.

An approximate solution of the interferon-dependent viral kinetics model of influenza

The analysis of viral kinetics models is mostly achieved by numerical methods. We present an approach via a Magnus expansion that allows us to give an approximate solution to the interferon-dependent viral infection model of influenza which is compared with numerical results. The time of peak viral load is calculated from the approximation and stays within 10% in the studied range of interferon (IFN) efficacy ϵ ∈ [0, 1000]. We utilize our solution to interpret the effect of varying IFN efficacy, suggesting a competition between virions and interferon that can cause an additional peak in the usually exponential increase in the viral load.

A theoretical framework for transitioning from patient-level to population-scale epidemiological dynamics: influenza A as a case study

Multi-scale epidemic forecasting models have been used to inform population-scale predictions with within-host models and/or infection data collected in longitudinal cohort studies. However, most multi-scale models are complex and require significant modelling expertise to run. We formulate an alternative multi-scale modelling framework using a compartmental model with multiple infected stages. In the large-compartment limit, our easy-to-use framework generates identical results compared to previous more complicated approaches. We apply our framework to the case study of influenza A in humans. By using a viral dynamics model to generate synthetic patient-level data, we explore the effects of limited and inaccurate patient data on the accuracy of population-scale forecasts. If infection data are collected daily, we find that a cohort of at least 40 patients is required for a mean population-scale forecasting error below 10%. Forecasting errors may be reduced by including more patients in future cohort studies or by increasing the frequency of observations for each patient. Our work, therefore, provides not only an accessible epidemiological modelling framework but also an insight into the data required for accurate forecasting using multi-scale models.

Towards a multi-level and a multi-disciplinary approach to DNA oncovirus virulence

One out of 10 cancers is estimated to arise from infections by a handful of oncogenic viruses. These infectious cancers constitute an opportunity for primary prevention through immunization against the viral infection, for early screening through molecular detection of the infectious agent, and potentially for specific treatments, by targeting the virus as a marker of cancer cells. Accomplishing these objectives will require a detailed understanding of the natural history of infections, the mechanisms by which the viruses contribute to disease, the mutual adaptation of viruses and hosts, and the possible viral evolution in the absence and in the presence of the public health interventions conceived to target them. This issue showcases the current developments in experimental tissue-like and animal systems, mathematical models and evolutionary approaches to understand DNA oncoviruses. Our global aim is to provide proximate explanations to the present-day interface and interactions between virus and host, as well as ultimate explanations about the adaptive value of these interactions and about the evolutionary pathways that have led to the current malignant phenotype of oncoviral infections. This article is part of the theme issue 'Silent cancer agents: multi-disciplinary modelling of human DNA oncoviruses'.

Mathematical modelling identifies the role of adaptive immunity as a key controller of respiratory syncytial virus in cotton rats

Respiratory syncytial virus (RSV) is a common virus that can have varying effects ranging from mild cold-like symptoms to mortality depending on the age and immune status of the individual. We combined mathematical modelling using ordinary differential equations (ODEs) with measurement of RSV infection kinetics in primary well-differentiated human bronchial epithelial cultures in vitro and in immunocompetent and immunosuppressed cotton rats to glean mechanistic details that underlie RSV infection kinetics in the lung. Quantitative analysis of viral titre kinetics in our mathematical model showed that the elimination of infected cells by the adaptive immune response generates unique RSV titre kinetic features including a faster timescale of viral titre clearance than viral production, and a monotonic decrease in the peak RSV titre with decreasing inoculum dose. Parameter estimation in the ODE model using a nonlinear mixed effects approach revealed a very low rate (average single-cell lifetime > 10 days) of cell lysis by RSV before the adaptive immune response is initiated. Our model predicted negligible changes in the RSV titre kinetics at early times post-infection (less than 5 dpi) but a slower decay in RSV titre in immunosuppressed cotton rats compared to that in non-suppressed cotton rats at later times (greater than 5 dpi) in silico. These predictions were in excellent agreement with the experimental results. Our combined approach quantified the importance of the adaptive immune response in suppressing RSV infection in cotton rats, which could be useful in testing RSV vaccine candidates.

Antiviral interferon response at single-cell resolution

Experimental studies of the innate immune response of mammalian cells to viruses reveal pervasive heterogeneity at the level of single cells. Interferons are induced only in a fraction of virus-infected cells; subsequently a fraction of cells exposed to interferons upregulate interferon-stimulated genes. Nevertheless, quantitative experiments and linked mathematical models show that the interferon response can be effective in curbing viral spread through two distinct mechanisms. First, paracrine interferon signals from scattered source cells can protect many uninfected cells, and the self-amplification of interferon production might serve to calibrate response amplitude to strength of viral infection. Second, models of the tug-of-war between viral replication and the innate interferon response imply a pivotal role of interferon action on already infected cells in curbing viral spread, through effectively lowering virus replication rate. This finding is in line with the observation that several pathogenic viruses selectively abrogate interferon action on infected cells. Thus, interferons may delay viral spread in acute infections by acting as sentinels, warning uninfected cells of imminent danger, or as negative feedback regulators of virus replication in infected cells. The timing of the interferon response relative to the onset of viral replication is critical for its effectiveness in curbing viral spread.

Natural history, dynamics, and ecology of human papillomaviruses in genital infections of young women: protocol of the PAPCLEAR cohort study

INTRODUCTION

Human papillomaviruses (HPVs) are responsible for one-third of all cancers caused by infections. Most HPV studies focus on chronic infections and cancers, and we know little about the early stages of the infection. Our main objective is to better understand the course and natural history of cervical HPV infections in healthy, unvaccinated and vaccinated, young women, by characterising the dynamics of various infection-related populations (virus, epithelial cells, vaginal microbiota and immune effectors). Another objective is to analyse HPV diversity within hosts, and in the study population, in relation to co-factors (lifestyle characteristics, vaccination status, vaginal microbiota, human genetics).

METHODS AND ANALYSIS

The PAPCLEAR study is a single center longitudinal study following 150 women, aged 18-25 years, for up to 2 years. Visits occur every 2 or 4 months (depending on HPV status) during which several variables are measured, such as behaviours (via questionnaires), vaginal pH, HPV presence and viral load (via qPCR), local concentrations of cytokines (via MesoScale Discovery technology) and immune cells (via flow cytometry). Additional analyses are outsourced, such as titration of circulating anti-HPV antibodies, vaginal microbiota sequencing (16S and ITS1 loci) and human genotyping. To increase the statistical power of the epidemiological arm of the study, an additional 150 women are screened cross-sectionally. Finally, to maximise the resolution of the time series, participants are asked to perform weekly self-samples at home. Statistical analyses will involve classical tools in epidemiology, genomics and virus kinetics, and will be performed or coordinated by the Centre National de la Recherche Scientifique (CNRS) in Montpellier.

ETHICS AND DISSEMINATION

This study has been approved by the Comité de Protection des Personnes Sud Méditerranée I (reference number 2016-A00712-49); by the Comité Consultatif sur le Traitement de l'Information en matière de Recherche dans le domaine de la Santé (reference number 16.504); by the Commission Nationale Informatique et Libertés (reference number MMS/ABD/AR1612278, decision number DR-2016-488) and by the Agence Nationale de Sécurité du Médicament et des Produits de Santé (reference 20160072000007). Results will be published in preprint servers, peer-reviewed journals and disseminated through conferences.

TRIAL REGISTRATION NUMBER

NCT02946346; Pre-results.

Applications of mechanistic modelling to clinical and experimental immunology: an emerging technology to accelerate immunotherapeutic discovery and development

The application of in-silico modelling is beginning to emerge as a key methodology to advance our understanding of mechanisms of disease pathophysiology and related drug action, and in the design of experimental medicine and clinical studies. From this perspective, we will present a non-technical discussion of a small number of recent and historical applications of mathematical, statistical and computational modelling to clinical and experimental immunology. We focus specifically upon mechanistic questions relating to human viral infection, tumour growth and metastasis and T cell activation. These exemplar applications highlight the potential of this approach to impact upon human immunology informed by ever-expanding experimental, clinical and 'omics' data. Despite the capacity of mechanistic modelling to accelerate therapeutic discovery and development and to de-risk clinical trial design, it is not utilized widely across the field. We outline ongoing challenges facing the integration of mechanistic modelling with experimental and clinical immunology, and suggest how these may be overcome. Advances in key technologies, including multi-scale modelling, machine learning and the wealth of 'omics' data sets, coupled with advancements in computational capacity, are providing the basis for mechanistic modelling to impact on immunotherapeutic discovery and development during the next decade.

Modeling of fusion inhibitor treatment of RSV in African green monkeys

Respiratory syncytial virus (RSV) is a respiratory infection that can cause serious illness, particularly in infants. In this study, we test four different model implementations for the effect of a fusion inhibitor, including one model that combines different drug effects, by fitting the models to data from a study of TMC353121 in African green monkeys. We use mathematical modeling to estimate the drug efficacy parameters, ε_max, the maximum efficacy of the drug, and EC₅₀, the drug concentration needed to achieve half the maximum effect. We find that if TMC353121 is having multiple effects on viral kinetics, more detailed data, using different treatment delays, is needed to detect this effect.

Mathematical Analysis of Viral Replication Dynamics and Antiviral Treatment Strategies: From Basic Models to Age-Based Multi-Scale Modeling

Viral infectious diseases are a global health concern, as is evident by recent outbreaks of the middle east respiratory syndrome, Ebola virus disease, and re-emerging zika, dengue, and chikungunya fevers. Viral epidemics are a socio-economic burden that causes short- and long-term costs for disease diagnosis and treatment as well as a loss in productivity by absenteeism. These outbreaks and their socio-economic costs underline the necessity for a precise analysis of virus-host interactions, which would help to understand disease mechanisms and to develop therapeutic interventions. The combination of quantitative measurements and dynamic mathematical modeling has increased our understanding of the within-host infection dynamics and has led to important insights into viral pathogenesis, transmission, and disease progression. Furthermore, virus-host models helped to identify drug targets, to predict the treatment duration to achieve cure, and to reduce treatment costs. In this article, we review important achievements made by mathematical modeling of viral kinetics on the extracellular, intracellular, and multi-scale level for Human Immunodeficiency Virus, Hepatitis C Virus, Influenza A Virus, Ebola Virus, Dengue Virus, and Zika Virus. Herein, we focus on basic mathematical models on the population scale (so-called target cell-limited models), detailed models regarding the most important steps in the viral life cycle, and the combination of both. For this purpose, we review how mathematical modeling of viral dynamics helped to understand the virus-host interactions and disease progression or clearance. Additionally, we review different types and effects of therapeutic strategies and how mathematical modeling has been used to predict new treatment regimens.

Accounting for Space—Quantification of Cell-To-Cell Transmission Kinetics Using Virus Dynamics Models

Mathematical models based on ordinary differential equations (ODE) that describe the population dynamics of viruses and infected cells have been an essential tool to characterize and quantify viral infection dynamics. Although an important aspect of viral infection is the dynamics of viral spread, which includes transmission by cell-free virions and direct cell-to-cell transmission, models used so far ignored cell-to-cell transmission completely, or accounted for this process by simple mass-action kinetics between infected and uninfected cells. In this study, we show that the simple mass-action approach falls short when describing viral spread in a spatially-defined environment. Using simulated data, we present a model extension that allows correct quantification of cell-to-cell transmission dynamics within a monolayer of cells. By considering the decreasing proportion of cells that can contribute to cell-to-cell spread with progressing infection, our extension accounts for the transmission dynamics on a single cell level while still remaining applicable to standard population-based experimental measurements. While the ability to infer the proportion of cells infected by either of the transmission modes depends on the viral diffusion rate, the improved estimates obtained using our novel approach emphasize the need to correctly account for spatial aspects when analyzing viral spread.

A New Age-Structured Multiscale Model of the Hepatitis C Virus Life-Cycle During Infection and Therapy With Direct-Acting Antiviral Agents

The dynamics of hepatitis C virus (HCV) RNA during translation and replication within infected cells were added to a previous age-structured multiscale mathematical model of HCV infection and treatment. The model allows the study of the dynamics of HCV RNA inside infected cells as well as the release of virus from infected cells and the dynamics of subsequent new cell infections. The model was used to fit in vitro data and estimate parameters characterizing HCV replication. This is the first model to our knowledge to consider both positive and negative strands of HCV RNA with an age-structured multiscale modeling approach. Using this model we also studied the effects of direct-acting antiviral agents (DAAs) in blocking HCV RNA intracellular replication and the release of new virions and fit the model to in vivo data obtained from HCV-infected subjects under therapy.

Incomplete inhibition of HIV infection results in more HIV infected lymph node cells by reducing cell death

HIV has been reported to be cytotoxic in vitro and in lymph node infection models. Using a computational approach, we found that partial inhibition of transmissions of multiple virions per cell could lead to increased numbers of live infected cells. If the number of viral DNA copies remains above one after inhibition, then eliminating the surplus viral copies reduces cell death. Using a cell line, we observed increased numbers of live infected cells when infection was partially inhibited with the antiretroviral efavirenz or neutralizing antibody. We then used efavirenz at concentrations reported in lymph nodes to inhibit lymph node infection by partially resistant HIV mutants. We observed more live infected lymph node cells, but with fewer HIV DNA copies per cell, relative to no drug. Hence, counterintuitively, limited attenuation of HIV transmission per cell may increase live infected cell numbers in environments where the force of infection is high.

The HIVvirus infects cells of the immune system. Once inside, it hijacks the cellular molecular machineries to make more copies of itself, which are then transmitted to new host cells. HIV eventually kills most cells it infects, either in the steps leading to the infection of the cell, or after the cell is already producing virus. HIV can spread between cells in two ways, known as cell-free or cell-to-cell. In the first, individual viruses are released from infected cells and move randomly through the body in the hope of finding new cells to infect. In the second, infected cells interact directly with uninfected cells. The second method is often much more successful at infecting new cells since they are exposed to multiple virus particles.

HIV infections can be controlled by using combinations of antiretroviral drugs, such as efavirenz, to prevent the virus from making more of itself. With a high enough dose, the drugs can in theory completely stop HIV infections, unless the virus becomes resistant to treatment. However, some patients continue to use these drugs even after the virus they are infected with develops resistance. It is not clear what effect taking ineffective, or partially effective, drugs has on how HIV progresses.

Using efavirenz, Jackson, Hunter et al. partially limited the spread of HIV between human cells grown in the laboratory. The experiments mirrored the situation where a partially resistant HIV strain spreads through the body. The results show that the success of cell-free infection is reduced as drug dose increases. Yet paradoxically, in cell-to-cell infection, the presence of drug caused more cells to become infected. This can be explained by the fact that, in cell-to-cell spread, each cell is exposed to multiple copies of the virus. The drug dose reduced the number of viral copies per cell without stopping the virus from infecting completely. The reduced number of viral copies per cell made it more likely that infected cells would survive the infection long enough to produce virus particles themselves.

Viruses that can kill cells, such as HIV, must balance the need to make more of themselves against the speed that they kill their host cell to maximize the number of infected cells. If transmission between cells is too effective and too many virus particles are delivered to the new cell, the virus may not manage to infect new hosts before killing the old ones. These findings highlight this delicate balance. They also indicate a potential issue in using drugs to treat partially resistant virus strains. Without care, these treatments could increase the number of infected cells in the body, potentially worsening the effects of living with HIV.

Kinetics of Double-Stranded DNA Viremia After Allogeneic Hematopoietic Cell Transplantation

Background

Improved understanding of double-stranded DNA (dsDNA) virus kinetics after hematopoietic cell transplantation (HCT) would facilitate development of therapeutic strategies.

Methods

We tested weekly plasma samples from 404 patients through day 100 after allogeneic HCT for cytomegalovirus (CMV), human herpesvirus (HHV) 6A and 6B, BK polyomavirus (BKV), adenovirus (AdV), and Epstein-Barr virus (EBV) using quantitative polymerase chain reaction. Episodes lasting ≤1 week were defined as blips and >1 week as persistent. We described virus-specific kinetics, analyzed the association of virus area under the curve (AUC) with overall mortality, and identified risk factors for persistent episodes.

Results

We identified 428 episodes of CMV, 292 of BKV, 224 of HHV-6B, 46 of AdV, and 53 of EBV. CMV and BKV had the highest proportions of persistent episodes (68% and 80%, respectively). Detection and kinetics varied by virus. HHV-6B episodes reached maximum levels fastest and had the shortest intervals between detection and end-organ disease. End-organ disease occurred within 14 days of viremia in 68% of cases, generally during persistent episodes. For all viruses, higher viral load AUC increased risk for overall mortality through day 365, persistent episodes had higher viral load than blips, and higher first positive viral load significantly increased risk for persistent episodes. First viral load >2 log10 copies/mL (range, 2.04-3.06 per virus) had high specificity for persistent episodes.

Conclusions

Persistent high viral load dsDNA viremia episodes after allogeneic HCT predict mortality. Virus-specific kinetics can guide timing and thresholds for early intervention in studies of novel agents.

Integrated pharmacokinetic/viral dynamic model for daclatasvir/asunaprevir in treatment of patients with genotype 1 chronic hepatitis C

In order to develop an integrated pharmacokinetic/viral dynamic (PK/VD) model to predict long-term virological response rates to daclatasvir (DCV) and asunaprevir (ASV) combination therapy in patients infected with genotype 1 (GT1) chronic hepatitis C virus (HCV), a systematic publication search was conducted for DCV and ASV administered alone and/or in combination in healthy subjects or patients with GT1 HCV infection. On the basis of a constructed meta-database, an integrated PK/VD model was developed, which adequately described both DCV and ASV PK profiles and viral load time curves. The IC₅₀ values of DCV and ASV were estimated to be 0.041 and 2.45 μg/L, respectively, in GT1A patients. A sigmoid E_max function was applied to describe the antiviral effects of DCV and ASV, depending on the drug concentrations in the effect compartment. An empirical exponential function revealed that IC₅₀ changing over time described drug resistance in HCV GT1A patients during DCV or ASV monotherapy. Finally, the PK/VD model was evaluated externally by comparing the expected and observed virological response rates during and post-treatment with DCV and ASV combination therapy in HCV GT1B patients. Both the rates were in general agreement. Our PK/VD model provides a useful platform for the characterization of pharmacokinetic/pharmacodynamic relationships and the prediction of long-term virological response rates to aid future development of direct acting antiviral drugs.

Parameter Estimation in Mathematical Models of Viral Infections Using R

In recent years, mathematical modeling approaches have played a central role in understanding and quantifying mechanisms in different viral infectious diseases. In this approach, biology-based hypotheses are expressed via mathematical relations and then tested based on empirical data. The simulation results can be used to either identify underlying mechanisms and provide predictions of infection outcomes or to evaluate the efficacy of a treatment.Conducting parameter estimation for mathematical models is not an easy task. Here we detail an approach to conduct parameter estimation and to evaluate the results using the free software R. The method is applicable to influenza virus dynamics at different complexity levels, widening experimentalists' capabilities in understanding their data. The parameter estimation approach presented here can be also applied to other viral infections or biological applications.

A Robust and Efficient Numerical Method for RNA-Mediated Viral Dynamics

The multiscale model of hepatitis C virus (HCV) dynamics, which includes intracellular viral RNA (vRNA) replication, has been formulated in recent years in order to provide a new conceptual framework for understanding the mechanism of action of a variety of agents for the treatment of HCV. We present a robust and efficient numerical method that belongs to the family of adaptive stepsize methods and is implicit, a Rosenbrock type method that is highly suited to solve this problem. We provide a Graphical User Interface that applies this method and is useful for simulating viral dynamics during treatment with anti-HCV agents that act against HCV on the molecular level.

Fighting Cancer with Mathematics and Viruses

After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex antitumor effects, such as innate and adaptive immune responses and the destruction of tumor vasculature. With the availability of different vector platforms and the potential of both genetic engineering and combination regimens to enhance particular aspects of safety and efficacy, the identification of optimal treatments for patient subpopulations or even individual patients becomes a top priority. Mathematical modeling can provide support in this arena by making use of experimental and clinical data to generate hypotheses about the mechanisms underlying complex biology and, ultimately, predict optimal treatment protocols. Increasingly complex models can be applied to account for therapeutically relevant parameters such as components of the immune system. In this review, we describe current developments in oncolytic virotherapy and mathematical modeling to discuss the benefit of integrating different modeling approaches into biological and clinical experimentation. Conclusively, we propose a mutual combination of these research fields to increase the value of the preclinical development and the therapeutic efficacy of the resulting treatments.

Zika plasma viral dynamics in nonhuman primates provides insights into early infection and antiviral strategies

The recent outbreak of Zika virus (ZIKV) has been associated with fetal abnormalities and neurological complications, prompting global concern. Here we present a mathematical analysis of the within-host dynamics of plasma ZIKV burden in a nonhuman primate model, allowing for characterization of the growth and clearance of ZIKV within individual macaques. We estimate that the eclipse phase for ZIKV, the time between cell infection and viral production, is most likely short (∼4 h), the median within-host basic reproductive number R₀ is 10.7, the rate of viral production is rapid (>25,000 virions d^-1), and the lifetime of an infected cell while producing virus is ∼5 h. We also estimate that the minimum number of virions produced by an infected cell over its lifetime is ∼5,500. We assess the potential effect of an antiviral treatment that blocks viral replication, showing that the median time to undetectable plasma viral load (VL) can be reduced from ∼5 d to ∼3 d with a drug concentration ∼15 times the drug's EC₅₀ when treatment is given prophylactically starting at the time of infection. In the case of favipiravir, a polymerase inhibitor with activity against ZIKV, we predict a dose of 150 mg/kg given twice a day initiated at the time of infection can reduce the peak median VL by ∼3 logs and shorten the time to undetectable median VL by ∼2 d, whereas treatment given 2 d postinfection is mostly ineffective in accelerating plasma VL loss in macaques.

In-host modeling

Understanding the mechanisms governing host-pathogen kinetics is important and can guide human interventions. In-host mathematical models, together with biological data, have been used in this endeavor. In this review, we present basic models used to describe acute and chronic pathogenic infections. We highlight the power of model predictions, the role of drug therapy, and advantage of considering the dynamics of immune responses. We also present the limitations of these models due in part to the trade-off between the complexity of the model and their predictive power, and the challenges a modeler faces in determining the appropriate formulation for a given problem.

Spatiotemporal Dynamics of Virus Infection Spreading in Tissues

Virus spreading in tissues is determined by virus transport, virus multiplication in host cells and the virus-induced immune response. Cytotoxic T cells remove infected cells with a rate determined by the infection level. The intensity of the immune response has a bell-shaped dependence on the concentration of virus, i.e., it increases at low and decays at high infection levels. A combination of these effects and a time delay in the immune response determine the development of virus infection in tissues like spleen or lymph nodes. The mathematical model described in this work consists of reaction-diffusion equations with a delay. It shows that the different regimes of infection spreading like the establishment of a low level infection, a high level infection or a transition between both are determined by the initial virus load and by the intensity of the immune response. The dynamics of the model solutions include simple and composed waves, and periodic and aperiodic oscillations. The results of analytical and numerical studies of the model provide a systematic basis for a quantitative understanding and interpretation of the determinants of the infection process in target organs and tissues from the image-derived data as well as of the spatiotemporal mechanisms of viral disease pathogenesis, and have direct implications for a biopsy-based medical testing of the chronic infection processes caused by viruses, e.g. HIV, HCV and HBV.

Relapse prediction in Graves´ disease: Towards mathematical modeling of clinical, immune and genetic markers

PROBLEM

Graves' disease (GD) is an important and prevalent thyroid autoimmune disorder. Standard therapy for GD consists of antithyroid drugs (ATD) with treatment periods of around 12 months but relapse is frequent. Since predictors for relapse are difficult to identify the individual decision making for optimal treatment is often arbitrary.

METHODS

After reviewing the literature on this topic we summarize important factors involved in GD and with respect to their potential for relapse prediction from markers before and after treatment. This information was used to design a mathematical model integrating thyroid hormone parameters, thyroid size, antibody titers and a complex algorithm encompassing genetic predisposition, environmental exposures and current immune activity in order to arrive at a prognostic index for relapse risk after treatment.

CONCLUSION

In the search for a tool to analyze and predict relapse in GD mathematical modeling is a promising approach. In analogy to mathematical modeling approaches in other diseases such as viral infections, we developed a differential equation model on the basis of published clinical trials in patients with GD. Although our model needs further evaluation to be applicable in a clinical context, it provides a perspective for an important contribution to a final statistical prediction model.

Mathematical Models for Immunology: Current State of the Art and Future Research Directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

Treatment of chronic hepatitis D with the entry inhibitor myrcludex B: First results of a phase Ib/IIa study

BACKGROUND & AIMS

The therapeutic option for patients with chronic hepatitis delta virus infection (CHD) is limited to interferon alpha with rare curative outcome. Myrcludex B is a first-in-class entry inhibitor inactivating the hepatitis B virus (HBV) and hepatitis D virus (HDV) receptor sodium taurocholate co-transporting polypeptide. We report the interim results of a pilot trial on chronically infected HDV patients treated with myrcludex B, or pegylated interferon alpha (PegIFNα-2a) or their combination.

METHODS

Twenty-four patients with CHD infection were equally randomized (1:1:1) to receive myrcludex B, or PegIFNα-2a or their combination. Patients were evaluated for virological and biochemical response and tolerability of the study drugs at weeks 12 and 24.

RESULTS

Myrcludex B was well tolerated and no serious adverse event occurred. Although hepatitis B surface antigen levels remained unchanged, HDV RNA significantly declined at week 24 in all cohorts. HDV RNA became negative in two patients each in the Myrcludex B and PegIFNα-2a cohorts, and in five patients of the Myrcludex B+PegIFNα-2a cohort. ALT decreased significantly in the Myrcludex B cohort (six of eight patients), and HBV DNA was significantly reduced at week 24 in the Myrcludex B+PegIFNα-2a cohort. Virus kinetic modeling suggested a strong synergistic effect of myrcludex B and PegIFNα-2a on both HDV and HBV.

CONCLUSIONS

Myrcludex B showed a strong effect on HDV RNA serum levels and induced ALT normalization under monotherapy. Synergistic antiviral effects on HDV RNA and HBV DNA in the Myr-IFN cohort indicated a benefit of the combination of entry inhibition with PegIFNα-2a to treat CHD patients.

LAY SUMMARY

Myrcludex B is a new drug to treat hepatitis B and D infection. After 24weeks of treatment with myrcludex B and/or pegylated interferon α-2a, HDV R NA, a relevant marker for hepatitis D infection, decreased in all patients with chronic hepatitis B and D. Two of eight patients which received either myrcludex B or pegylated interferon α-2a, became negative for HDV RNA, and five of seven patients who received both drugs at the same time became negative. The drug was well tolerated.

Modeling Viral Spread

The way in which a viral infection spreads within a host is a complex process that is not well understood. Different viruses, such as human immunodeficiency virus type 1 and hepatitis C virus, have evolved different strategies, including direct cell-to-cell transmission and cell-free transmission, to spread within a host. To what extent these two modes of transmission are exploited in vivo is still unknown. Mathematical modeling has been an essential tool to get a better systematic and quantitative understanding of viral processes that are difficult to discern through strictly experimental approaches. In this review, we discuss recent attempts that combine experimental data and mathematical modeling in order to determine and quantify viral transmission modes. We also discuss the current challenges for a systems-level understanding of viral spread, and we highlight the promises and challenges that novel experimental techniques and data will bring to the field.

Ebola Virus Infection: Review of the Pharmacokinetic and Pharmacodynamic Properties of Drugs Considered for Testing in Human Efficacy Trials

The 2014-2015 outbreak of Ebola virus disease is the largest epidemic to date in terms of the number of cases, deaths, and affected areas. In October 2015, no antiviral agents had proven antiviral efficacy in patients. However, in September 2014, the World Health Organization inventoried and has since regularly updated a list of potential drug candidates with demonstrated antiviral efficacy in in vitro or animal models. This includes agents belonging to various therapeutic classes, namely direct antiviral agents (favipiravir and BCX4430), a combination of antibodies (ZMapp), type I interferons, RNA interference-based drugs (TKM-Ebola and AVI-7537), and anticoagulant drugs (rNAPc2). Here, we review the pharmacokinetic and pharmacodynamic information presently available for these drugs, using data obtained in healthy volunteers for pharmacokinetics and data obtained in human clinical trials or animal models for pharmacodynamics. Future studies evaluating these drugs in clinical trials are critical to confirm their efficacy in humans, propose appropriate doses, and evaluate the possibility of treatment combinations.