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

Incorporating Intracellular Processes in Virus Dynamics Models

In-host models have been essential for understanding the dynamics of virus infection inside an infected individual. When used together with biological data, they provide insight into viral life cycle, intracellular and cellular virus-host interactions, and the role, efficacy, and mode of action of therapeutics. In this review, we present the standard model of virus dynamics and highlight situations where added model complexity accounting for intracellular processes is needed. We present several examples from acute and chronic viral infections where such inclusion in explicit and implicit manner has led to improvement in parameter estimates, unification of conclusions, guidance for targeted therapeutics, and crossover among model systems. We also discuss trade-offs between model realism and predictive power and highlight the need of increased data collection at finer scale of resolution to better validate complex models.

How robust are estimates of key parameters in standard viral dynamic models?

Mathematical models of viral infection have been developed, fitted to data, and provide insight into disease pathogenesis for multiple agents that cause chronic infection, including HIV, hepatitis C, and B virus. However, for agents that cause acute infections or during the acute stage of agents that cause chronic infections, viral load data are often collected after symptoms develop, usually around or after the peak viral load. Consequently, we frequently lack data in the initial phase of viral growth, i.e., when pre-symptomatic transmission events occur. Missing data may make estimating the time of infection, the infectious period, and parameters in viral dynamic models, such as the cell infection rate, difficult. However, having extra information, such as the average time to peak viral load, may improve the robustness of the estimation. Here, we evaluated the robustness of estimates of key model parameters when viral load data prior to the viral load peak is missing, when we know the values of some parameters and/or the time from infection to peak viral load. Although estimates of the time of infection are sensitive to the quality and amount of available data, particularly pre-peak, other parameters important in understanding disease pathogenesis, such as the loss rate of infected cells, are less sensitive. Viral infectivity and the viral production rate are key parameters affecting the robustness of data fits. Fixing their values to literature values can help estimate the remaining model parameters when pre-peak data is missing or limited. We find a lack of data in the pre-peak growth phase underestimates the time to peak viral load by several days, leading to a shorter predicted growth phase. On the other hand, knowing the time of infection (e.g., from epidemiological data) and fixing it results in good estimates of dynamical parameters even in the absence of early data. While we provide ways to approximate model parameters in the absence of early viral load data, our results also suggest that these data, when available, are needed to estimate model parameters more precisely.

Mathematical Modeling of Virus-Mediated Syncytia Formation: Past Successes and Future Directions

Many viruses have the ability to cause cells to fuse into large multi-nucleated cells, known as syncytia. While the existence of syncytia has long been known and its importance in helping spread viral infection within a host has been understood, few mathematical models have incorporated syncytia formation or examined its role in viral dynamics. This review examines mathematical models that have incorporated virus-mediated cell fusion and the insights they have provided on how syncytia can change the time course of an infection. While the modeling efforts are limited, they show promise in helping us understand the consequences of syncytia formation if future modeling efforts can be coupled with appropriate experimental efforts to help validate the models.

Trajectories of COVID-19: A longitudinal analysis of many nations and subnational regions

The COVID-19 pandemic is the first to be rapidly and sequentially measured by nation-wide PCR community testing for the presence of the viral RNA at a global scale. We take advantage of the novel "natural experiment" where diverse nations and major subnational regions implemented various policies including social distancing and vaccination at different times with different levels of stringency and adherence. Initially, case numbers expand exponentially with doubling times of ~1-2 weeks. In the nations where interventions were not implemented or perhaps lees effectual, case numbers increased exponentially but then stabilized around 102-to-103 new infections (per km2 built-up area per day). Dynamics under effective interventions were perturbed and infections decayed to low levels. They rebounded concomitantly with the lifting of social distancing policies or pharmaceutical efficacy decline, converging on a stable equilibrium setpoint. Here we deploy a mathematical model which captures this V-shape behavior, incorporating a direct measure of intervention efficacy. Importantly, it allows the derivation of a maximal estimate for the basic reproductive number Ro (mean 1.6-1.8). We were able to test this approach by comparing the approximated "herd immunity" to the vaccination coverage observed that corresponded to rapid declines in community infections during 2021. The estimates reported here agree with the observed phenomena. Moreover, the decay (0.4-0.5) and rebound rates (0.2-0.3) were similar throughout the pandemic and among all the nations and regions studied. Finally, a longitudinal analysis comparing multiple national and regional results provides insights on the underlying epidemiology of SARS-CoV-2 and intervention efficacy, as well as evidence for the existence of an endemic steady state of COVID-19.

Monkeypox: a review of epidemiological modelling studies and how modelling has led to mechanistic insight

Human monkeypox (mpox) virus is a viral zoonosis that belongs to the Orthopoxvirus genus of the Poxviridae family, which presents with similar symptoms as those seen in human smallpox patients. Mpox is an increasing concern globally, with over 80,000 cases in non-endemic countries as of December 2022. In this review, we provide a brief history and ecology of mpox, its basic virology, and the key differences in mpox viral fitness traits before and after 2022. We summarize and critique current knowledge from epidemiological mathematical models, within-host models, and between-host transmission models using the One Health approach, where we distinguish between models that focus on immunity from vaccination, geography, climatic variables, as well as animal models. We report various epidemiological parameters, such as the reproduction number, R0, in a condensed format to facilitate comparison between studies. We focus on how mathematical modelling studies have led to novel mechanistic insight into mpox transmission and pathogenesis. As mpox is predicted to lead to further infection peaks in many historically non-endemic countries, mathematical modelling studies of mpox can provide rapid actionable insights into viral dynamics to guide public health measures and mitigation strategies.

A mathematical model and numerical simulation for SARS-CoV-2 dynamics

Since its outbreak the corona virus-19 disease has been particularly aggressive for the lower respiratory tract, and lungs in particular. The dynamics of the abnormal immune response leading to lung damage with fatal outcomes is not yet fully understood. We present a mathematical model describing the dynamics of corona virus disease-19 starting from virus seeding inside the human respiratory tract, taking into account its interaction with the components of the innate immune system as classically and alternatively activated macrophages, interleukin-6 and -10. The numerical simulations have been performed for two different parameter values related to the pro-inflammatory interleukin, searching for a correlation among components dynamics during the early stage of infection, in particular pro- and anti-inflammatory polarizations of the immune response. We found that in the initial stage of infection the immune machinery is unable to stop or weaken the virus progression. Also an abnormal anti-inflammatory interleukin response is predicted, induced by the disease progression and clinically associated to tissue damages. The numerical results well reproduce experimental results found in literature.

Computational framework to understand the clinical stages of COVID-19 and visualization of time course for various treatment strategies

Coronavirus disease 2019 is known to be regulated by multiple factors such as delayed immune response, impaired T cell activation, and elevated levels of proinflammatory cytokines. Clinical management of the disease remains challenging due to interplay of various factors as drug candidates may elicit different responses depending on the staging of the disease. In this context, we propose a computational framework which provides insights into the interaction between viral infection and immune response in lung epithelial cells, with an aim of predicting optimal treatment strategies based on infection severity. First, we formulate the model for visualizing the nonlinear dynamics during the disease progression considering the role of T cells, macrophages and proinflammatory cytokines. Here, we show that the model is capable of emulating the dynamic and static data trends of viral load, T cell, macrophage levels, interleukin (IL)-6 and TNF-α levels. Second, we demonstrate the ability of the framework to capture the dynamics corresponding to mild, moderate, severe, and critical condition. Our result shows that, at late phase (>15 days), severity of disease is directly proportional to pro-inflammatory cytokine IL6 and tumor necrosis factor (TNF)-α levels and inversely proportional to the number of T cells. Finally, the simulation framework was used to assess the effect of drug administration time as well as efficacy of single or multiple drugs on patients. The major contribution of the proposed framework is to utilize the infection progression model for clinical management and administration of drugs inhibiting virus replication and cytokine levels as well as immunosuppressant drugs at various stages of the disease.

Effect of cellular regeneration and viral transmission mode on viral spread

Illness negatively affects all aspects of life and one major cause of illness is viral infections. Some viral infections can last for weeks; others, like influenza (the flu), can resolve quickly. During infections, uninfected cells can replicate in order to replenish the cells that have died due to the virus. Many viral models, especially those for short-lived infections like influenza, tend to ignore cellular regeneration since many think that uncomplicated influenza resolves much faster than cells regenerate. This research accounts for cellular regeneration, using an agent-based framework, and varies the regeneration rate in order to understand how cell regeneration affects viral infection dynamics under assumptions of different modes of transmission. We find that although the general trends in peak viral load, time of viral peak, and chronic viral load as regeneration rate changes are the same for cell-free or cell-to-cell transmission, the changes are more extreme for cell-to-cell transmission due to limited access of infected cells to newly generated cells.

Modulating Immune Response in Viral Infection for Quantitative Forecasts of Drug Efficacy

The antiretroviral drug, the total level of viral production, and the effectiveness of immune responses are the main topics of this review because they are all dynamically interrelated. Immunological and viral processes interact in extremely complex and non-linear ways. For reliable analysis and quantitative forecasts that may be used to follow the immune system and create a disease profile for each patient, mathematical models are helpful in characterizing these non-linear interactions. To increase our ability to treat patients and identify individual differences in disease development, immune response profiling might be useful. Identifying which patients are moving from mild to severe disease would be more beneficial using immune system parameters. Prioritize treatments based on their inability to control the immune response and prevent T cell exhaustion. To increase treatment efficacy and spur additional research in this field, this review intends to provide examples of the effects of modelling immune response in viral infections, as well as the impact of pharmaceuticals on immune response.

Advances in RT-LAMP for COVID-19 testing and diagnosis

INTRODUCTION

The SARS-CoV-2 pandemic, and the subsequent limitations on standard diagnostics, has vastly expanded the user base of Reverse Transcription Loop-mediated isothermal Amplification (RT-LAMP) in fundamental research and development. RT-LAMP has also penetrated commercial markets, with emergency use authorizations for clinical diagnosis.

AREAS COVERED

This review discusses the role of RT-LAMP within the context of other technologies like RT-qPCR and rapid antigen tests, progress in sample preparation strategies to enable simplified workflow for RT-LAMP directly from clinical specimens, new challenges with primer and assay design for the evolving pandemic, prominent detection modalities including colorimetric and CRISPR-mediated methods, and translational research and commercial development of RT-LAMP for clinical applications.

EXPERT OPINION

RT-LAMP occupies a middle ground between RT-qPCR and rapid antigen tests. The simplicity approaches that of rapid antigen tests, making it suitable for point-of-care use, but the sensitivity nears that of RT-qPCR. RT-LAMP still lags RT-qPCR in fundamental understanding of the mechanism, and the interplay between sample preparation and assay performance. Industry is now beginning to address issues around scalability and usability, which could finally enable LAMP and RT-LAMP to find future widespread application as a diagnostic for other conditions, including other pathogens with pandemic potential.

Clinical efficacy of Jingyin granules, a Chinese patent medicine, in treating patients infected with coronavirus disease 2019

BACKGROUND

Jingyin granules (JY), one patented Chinese herbal formula, have been advised for treating coronavirus disease 2019 (COVID-19) in China. As of now, the safety and effectiveness of JY in treating COVID-19 patients were still to be evaluated.

PURPOSE

To investigate the safety and clinical effectiveness of JY in treating mild COVID-19 patients.

STUDY DESIGN

We carried out a prospective cohort study, as the highly infectious COVID-19 omicron variant ranged in Shanghai (ClinicalTrial.gov registration number: ChiCTR2200058692).

METHODS

Participants infected with COVID-19, who were diagnosed as mild cases, were assigned to receive either JY (JY group) or traditional Chinese medicine placebo (placebo group) orally for 7 days. The primary clinical indicators were the RNA negative conversion rate (NCR) and the incidence of severe cases. The secondary clinical indicators were the negative conversion time (NCT), inpatient length of stay (ILOS), and the disappearance rates of clinical symptoms.

RESULTS

Nine hundred participants were recruited in this clinical trial study, and 830 patients met the eligibility criteria. Seven hundred and ninety-one patients, accomplished the following-up assessment, including 423 cases of JY group and 368 cases of placebo group. NCR in JY group at 7-day posttreatment was considerably greater compared with placebo group (89.8% [380/423] vs 82.6% [304/368], P = 0.003). None of the patients with mild COVID-19 developed into severe cases. The median NCT of SARS-CoV-2 and ILOS in JY group were lesser than that in placebo group (4.0 [3.0,6.0]vs 5.0 [4.0,7.0] days, P < 0.001; 6.0 [4.0, 8.0] vs 7.0 [5.0, 9.0] days, P < 0.001). In both groups, the obvious improvement in clinical symptoms was observed, but the difference was not significant. In the subgroup of age ≤ 60 years, JY promoted SARS-CoV-2 RNA negative conversion (HR=1.242; 95% CI: 1.069-1.444, P < 0.001). No patients in both groups were reported as the case of serious adverse event.

CONCLUSION

JY maybe the potential medicine for treating mild COVID-19 patients, which had beneficial effects on increasing NCR, and shortening NCT and ILOS.

A drug-disease model for predicting survival in an Ebola outbreak

REGN-EB3 (Inmazeb) is a cocktail of three human monoclonal antibodies approved for treatment of Ebola infection. This paper describes development of a mathematical model linking REGN-EB3's inhibition of Ebola virus to survival in a non-human primate (NHP) model, and translational scaling to predict survival in humans. Pharmacokinetic/pharmacodynamic data from single- and multiple-dose REGN-EB3 studies in infected rhesus macaques were incorporated. Using discrete indirect response models, the antiviral mechanism of action was used as a forcing function to drive the reversal of key Ebola disease hallmarks over time, for example, liver and kidney damage (elevated alanine [ALT] and aspartate aminotransferases [AST], blood urea nitrogen [BUN], and creatinine), and hemorrhage (decreased platelet count). A composite disease characteristic function was introduced to describe disease severity and integrated with the ordinary differential equations estimating the time course of clinical biomarkers. Model simulation results appropriately represented the concentration-dependence of the magnitude and time course of Ebola infection (viral and pathophysiological), including time course of viral load, ALT and AST elevations, platelet count, creatinine, and BUN. The model estimated the observed survival rate in rhesus macaques and the dose of REGN-EB3 required for saturation of the pharmacodynamic effects of viral inhibition, reversal of Ebola pathophysiology, and survival. The model also predicted survival in clinical trials with appropriate scaling to humans. This mathematical investigation demonstrates that drug-disease modeling can be an important translational tool to integrate preclinical data from an NHP model recapitulating disease progression to guide future translation of preclinical data to clinical study design.

Triphenylphosphine gold(I) derivatives promote antiviral effects against the Chikungunya virus

Herein a systematic series of four [AuLL']n+ n = 0, +1 complexes, where L = 1,3-bis(mesityl)imidazole-2-ylidene (IMes), or triphenylphosphine (PPh3), and L' = chloride, or 4-dimethylaminopyridine (DMAP), had their in vitro antiviral activity assessed against Chikungunya virus (CHIKV). The PPh3 derivatives inhibited viral replication by 99%, whereas the IMes derivatives about 50%. The lipophilicity of the PPh3 derivatives is higher than the IMes-bearing compounds, which can be related to their more prominent antiviral activities. The dissociation of DMAP is faster than chloride in solution for both IMes and PPh3 derivatives; however, it does not significantly affect their in vitro activities, showing a higher dependence on the nature of L rather than L' towards their antiviral effects. All complexes bind to N-acetyl-L-cysteine, with the Ph3P-bearing complexes coordinating at a faster rate to this amino acid. The binding constants to bovine serum albumin (BSA) are in the order of 104, slightly higher for the DMAP complexes in both PPh3 and IMes derivatives. Mechanistic investigations of the PPh3 complexes showed a ubiquitous protective effect of the compounds in the pre-treatment, early stages, and post-entry assays. The most significant inhibition was observed in post-entry activity, in which the complexes blocked viral replication in 99%, followed by up to 95% inhibition of the early stages of infection. Pre-treatment assays showed a 92% and 80% replication decrease for the chloride and DMAP derivatives, respectively. dsRNA binding assays showed a significant interaction of the compounds with dsRNA, an essential biomolecule to viral replication.

Mathematical modeling of plus-strand RNA virus replication to identify broad-spectrum antiviral treatment strategies

Plus-strand RNA viruses are the largest group of viruses. Many are human pathogens that inflict a socio-economic burden. Interestingly, plus-strand RNA viruses share remarkable similarities in their replication. A hallmark of plus-strand RNA viruses is the remodeling of intracellular membranes to establish replication organelles (so-called "replication factories"), which provide a protected environment for the replicase complex, consisting of the viral genome and proteins necessary for viral RNA synthesis. In the current study, we investigate pan-viral similarities and virus-specific differences in the life cycle of this highly relevant group of viruses. We first measured the kinetics of viral RNA, viral protein, and infectious virus particle production of hepatitis C virus (HCV), dengue virus (DENV), and coxsackievirus B3 (CVB3) in the immuno-compromised Huh7 cell line and thus without perturbations by an intrinsic immune response. Based on these measurements, we developed a detailed mathematical model of the replication of HCV, DENV, and CVB3 and show that only small virus-specific changes in the model were necessary to describe the in vitro dynamics of the different viruses. Our model correctly predicted virus-specific mechanisms such as host cell translation shut off and different kinetics of replication organelles. Further, our model suggests that the ability to suppress or shut down host cell mRNA translation may be a key factor for in vitro replication efficiency which may determine acute self-limited or chronic infection. We further analyzed potential broad-spectrum antiviral treatment options in silico and found that targeting viral RNA translation, especially polyprotein cleavage, and viral RNA synthesis may be the most promising drug targets for all plus-strand RNA viruses. Moreover, we found that targeting only the formation of replicase complexes did not stop the viral replication in vitro early in infection, while inhibiting intracellular trafficking processes may even lead to amplified viral growth.

Author summary

Plus-strand RNA viruses comprise a large group of related and medically relevant viruses. The current global pandemic of COVID-19 caused by the SARS-coronavirus-2 as well as the constant spread of diseases such as dengue and chikungunya fever show the necessity of a comprehensive and precise analysis of plus-strand RNA virus infections. Plus-strand RNA viruses share similarities in their life cycle. To understand their within-host replication strategies, we developed a mathematical model that studies pan-viral similarities and virus-specific differences of three plus-strand RNA viruses, namely hepatitis C, dengue, and coxsackievirus. By fitting our model to in vitro data, we found that only small virus-specific variations in the model were required to describe the dynamics of all three viruses. Furthermore, our model predicted that ribosomes involved in viral RNA translation seem to be a key player in plus-strand RNA replication efficiency, which may determine acute or chronic infection outcome. Furthermore, our in-silico drug treatment analysis suggests that targeting viral proteases involved in polyprotein cleavage, in combination with viral RNA replication, may represent promising drug targets with broad-spectrum antiviral activity.

Inhibition of drug-metabolizing enzymes by Jingyin granules: implications of herb-drug interactions in antiviral therapy

Jingyin granules, a marketed antiviral herbal medicine, have been recommended for treating H1N1 influenza A virus infection and Coronavirus disease 2019 (COVID-19) in China. To fight viral diseases in a more efficient way, Jingyin granules are frequently co-administered in clinical settings with a variety of therapeutic agents, including antiviral drugs, anti-inflammatory drugs, and other Western medicines. However, it is unclear whether Jingyin granules modulate the pharmacokinetics of Western drugs or trigger clinically significant herb-drug interactions. This study aims to assess the inhibitory potency of the herbal extract of Jingyin granules (HEJG) against human drug-metabolizing enzymes and to clarify whether HEJG can modulate the pharmacokinetic profiles of Western drug(s) in vivo. The results clearly demonstrated that HEJG dose-dependently inhibited human CES1A, CES2A, CYPs1A, 2A6, 2C8, 2C9, 2D6, and 2E1; this herbal medicine also time- and NADPH-dependently inhibited human CYP2C19 and CYP3A. In vivo tests showed that HEJG significantly increased the plasma exposure of lopinavir (a CYP3A-substrate drug) by 2.43-fold and strongly prolonged its half-life by 1.91-fold when HEJG (3 g/kg) was co-administered with lopinavir to rats. Further investigation revealed licochalcone A, licochalcone B, licochalcone C and echinatin in Radix Glycyrrhizae, as well as quercetin and kaempferol in Folium Llicis Purpureae, to be time-dependent CYP3A inhibitors. Collectively, our findings reveal that HEJG modulates the pharmacokinetics of CYP substrate-drug(s) by inactivating CYP3A, providing key information for both clinicians and patients to use herb-drug combinations for antiviral therapy in a scientific and reasonable way.

Multiscale Model of Antiviral Timing, Potency, and Heterogeneity Effects on an Epithelial Tissue Patch Infected by SARS-CoV-2

We extend our established agent-based multiscale computational model of infection of lung tissue by SARS-CoV-2 to include pharmacokinetic and pharmacodynamic models of remdesivir. We model remdesivir treatment for COVID-19; however, our methods are general to other viral infections and antiviral therapies. We investigate the effects of drug potency, drug dosing frequency, treatment initiation delay, antiviral half-life, and variability in cellular uptake and metabolism of remdesivir and its active metabolite on treatment outcomes in a simulated patch of infected epithelial tissue. Non-spatial deterministic population models which treat all cells of a given class as identical can clarify how treatment dosage and timing influence treatment efficacy. However, they do not reveal how cell-to-cell variability affects treatment outcomes. Our simulations suggest that for a given treatment regime, including cell-to-cell variation in drug uptake, permeability and metabolism increase the likelihood of uncontrolled infection as the cells with the lowest internal levels of antiviral act as super-spreaders within the tissue. The model predicts substantial variability in infection outcomes between similar tissue patches for different treatment options. In models with cellular metabolic variability, antiviral doses have to be increased significantly (>50% depending on simulation parameters) to achieve the same treatment results as with the homogeneous cellular metabolism.

Comparison of Chicken Immune Responses to Immunization with Vaccine La Sota or ZG1999HDS Strain of Newcastle Disease Virus

Newcastle disease (ND) is a highly contagious avian disease. Global control of ND is mainly based on vaccination of poultry; however, reported outbreaks of ND in vaccinated flocks indicate a constant need to re-evaluate the existing vaccines and a development of the new ones. In this study, 4-week-old male chickens of the layer commercial hybrid were immunized oculonasally with a commercial NDV live La Sota vaccine (LS group), a suspension of lyophilized NDV strain ZG1999HDS (ZG group), or saline (Control (K) group). Antibody response was determined by haemagglutination inhibition (HI) assay. Cell-mediated immunity (CMI) was characterized by immunophenotyping of leukocyte's and T-lymphocyte's subpopulations (flow cytometry). Applied NDV strains did not cause any adverse reaction in treated chickens. Both strains induced the significantly higher HI antibody response in comparison to the control group, and overall antibody titer was higher in ZG group than in LS group. CMI, manifested as a higher proliferation of B- and T-helper cells, yielded better results in the ZG groups than in the LS group. Based on the obtained results, we conclude that the strain ZG1999HDS is immunogenic and is a suitable candidate for further research and development of poultry vaccines.

Mathematical modeling of viral infection dynamics and immune response in SARS-CoV-2: A computational framework for testing drug efficacy

SARS-CoV-2 has emerged to cause the outbreak of COVID-19, which has expanded into a worldwide human pandemic. Although detailed experimental data on animal experiments would provide insight into drug efficacy, the scientists involved in these experiments would be exposed to severe risks. In this context, we propose a computational framework for studying infection dynamics that can be used to capture the growth rate of viral replication and lung epithelial cell in presence of SARS-CoV-2. Specifically, we formulate the model consisting of a system of non-linear ODEs that can be used for visualizing the infection dynamics in a cell population considering the role of T cells and Macrophages. The major contribution of the proposed simulation method is to utilize the infection progression model in testing the efficacy of the drugs having various mechanisms and analyzing the effect of time of drug administration on virus clearance.Clinical Relevance-The proposed computational framework incorporates viral infection dynamics and role of immune response in Covid-19 that can be used to test the impact of drug efficacy and time of drug administration on infection mitigation.

Life cycle process dependencies of positive-sense RNA viruses suggest strategies for inhibiting productive cellular infection

Life cycle processes of positive-strand (+)RNA viruses are broadly conserved across families, yet they employ different strategies to grow in the cell. Using a generalized dynamical model for intracellular (+)RNA virus growth, we decipher these life cycle determinants and their dependencies for several viruses and parse the effects of viral mutations, drugs and host cell permissivity. We show that poliovirus employs rapid replication and virus assembly, whereas the Japanese encephalitis virus leverages its higher rate of translation and efficient cellular reorganization compared to the hepatitis C virus. Stochastic simulations demonstrate infection extinction if all seeding (inoculating) viral RNA degrade before establishing robust replication critical for infection. The probability of this productive cellular infection, 'cellular infectivity', is affected by virus-host processes and defined by early life cycle events and viral seeding. An increase in cytoplasmic RNA degradation and delay in vesicular compartment formation reduces infectivity, more so when combined. Synergy among these parameters in limiting (+)RNA virus infection as predicted by our model suggests new avenues for inhibiting infections by targeting the early life cycle bottlenecks.

Within Host Dynamics of SARS-CoV-2 in Humans: Modeling Immune Responses and Antiviral Treatments

In December 2019, a newly discovered SARS-CoV-2 virus was emerged from China and propagated worldwide as a pandemic, resulting in about 3–5% mortality. Mathematical models can provide useful scientific insights about transmission patterns and targets for drug development. In this study, we propose a within-host mathematical model of SARS-CoV-2 infection considering innate and adaptive immune responses. We analyze the equilibrium points of the proposed model and obtain an expression of the basic reproduction number. We then numerically show the existence of a transcritical bifurcation. The proposed model is calibrated to real viral load data of two COVID-19 patients. Using the estimated parameters, we perform global sensitivity analysis with respect to the peak of viral load. Finally, we study the efficacy of antiviral drugs and vaccination on the dynamics of SARS-CoV-2 infection. Results suggest that blocking the virus production from infected cells can be an effective target for antiviral drug development. Finally, it is found that vaccination is more effective intervention as compared to the antiviral treatments.

Dengue virus is sensitive to inhibition prior to productive replication

Uncovering vulnerable steps in the life cycle of viruses supports the rational design of antiviral treatments. However, information on viral replication dynamics obtained from traditional bulk assays with host cell populations is inherently limited as the data represent averages over a multitude of unsynchronized replication cycles. Here, we use time-lapse imaging of virus replication in thousands of single cells, combined with computational inference, to identify rate-limiting steps for dengue virus (DENV), a widespread human pathogen. Comparing wild-type DENV with a vaccine candidate mutant, we show that the viral spread in the mutant is greatly attenuated by delayed onset of productive replication, whereas wild-type and mutant virus have identical replication rates. Single-cell analysis done after applying the broad-spectrum antiviral drug, ribavirin, at clinically relevant concentrations revealed the same mechanism of attenuating viral spread. We conclude that the initial steps of infection, rather than the rate of established replication, are quantitatively limiting DENV spread.

Physiologically Based Pharmacokinetic/Pharmacodynamic Model for the Treatment of Dengue Infections Applied to the Broad Spectrum Antiviral Soraphen A

While a drug treatment is unavailable, the global incidence of Dengue virus (DENV) infections and its associated severe manifestations continues to rise. We report the construction of the first physiologically based pharmacokinetic/pharmacodynamic (PBPK/PD) model that predicts viremia levels in relevant target organs based on preclinical data with the broad spectrum antiviral soraphen A (SorA), an inhibitor of the host cell target acetyl-CoA-carboxylase. SorA was highly effective against DENV in vitro (EC₅₀ = 4.7 nM) and showed in vivo efficacy by inducing a significant reduction of viral load in the spleen and liver of IFNAR^-/- mice infected with DENV-2. PBPK/PD predictions for SorA matched well with the experimental infection data. Transfer to a human PBPK/PD model for DENV to mimic a clinical scenario predicted a reduction in viremia by more than one log₁₀ unit for an intravenous infusion regimen of SorA. The PBPK/PD model is applicable to any DENV drug lead and, thus, represents a valuable tool to accelerate and facilitate DENV drug discovery and development.

Molecular Communications in Viral Infections Research: Modeling, Experimental Data, and Future Directions

Hundreds of millions of people worldwide are affected by viral infections each year, and yet, several of them neither have vaccines nor effective treatment during and post-infection. This challenge has been highlighted by the COVID-19 pandemic, showing how viruses can quickly spread and impact society as a whole. Novel interdisciplinary techniques must emerge to provide forward-looking strategies to combat viral infections, as well as possible future pandemics. In the past decade, an interdisciplinary area involving bioengineering, nanotechnology and information and communication technology (ICT) has been developed, known as Molecular Communications. This new emerging area uses elements of classical communication systems to molecular signalling and communication found inside and outside biological systems, characterizing the signalling processes between cells and viruses. In this paper, we provide an extensive and detailed discussion on how molecular communications can be integrated into the viral infectious diseases research, and how possible treatment and vaccines can be developed considering molecules as information carriers. We provide a literature review on molecular communications models for viral infection (intra-body and extra-body), a deep analysis on their effects on immune response, how experimental can be used by the molecular communications community, as well as open issues and future directions.

Nanotechnology-based antiviral therapeutics

The host immune system is highly compromised in case of viral infections and relapses are very common. The capacity of the virus to destroy the host cell by liberating its own DNA or RNA and replicating inside the host cell poses challenges in the development of antiviral therapeutics. In recent years, many new technologies have been explored for diagnosis, prevention, and treatment of viral infections. Nanotechnology has emerged as one of the most promising technologies on account of its ability to deal with viral diseases in an effective manner, addressing the limitations of traditional antiviral medicines. It has not only helped us to overcome problems related to solubility and toxicity of drugs, but also imparted unique properties to drugs, which in turn has increased their potency and selectivity toward viral cells against the host cells. The initial part of the paper focuses on some important proteins of influenza, Ebola, HIV, herpes, Zika, dengue, and corona virus and those of the host cells important for their entry and replication into the host cells. This is followed by different types of nanomaterials which have served as delivery vehicles for the antiviral drugs. It includes various lipid-based, polymer-based, lipid-polymer hybrid-based, carbon-based, inorganic metal-based, surface-modified, and stimuli-sensitive nanomaterials and their application in antiviral therapeutics. The authors also highlight newer promising treatment approaches like nanotraps, nanorobots, nanobubbles, nanofibers, nanodiamonds, nanovaccines, and mathematical modeling for the future. The paper has been updated with the recent developments in nanotechnology-based approaches in view of the ongoing pandemic of COVID-19.Graphical abstract.

Dynamic causal modelling of immune heterogeneity

An interesting inference drawn by some COVID-19 epidemiological models is that there exists a proportion of the population who are not susceptible to infection-even at the start of the current pandemic. This paper introduces a model of the immune response to a virus. This is based upon the same sort of mean-field dynamics as used in epidemiology. However, in place of the location, clinical status, and other attributes of people in an epidemiological model, we consider the state of a virus, B and T-lymphocytes, and the antibodies they generate. Our aim is to formalise some key hypotheses as to the mechanism of resistance. We present a series of simple simulations illustrating changes to the dynamics of the immune response under these hypotheses. These include attenuated viral cell entry, pre-existing cross-reactive humoral (antibody-mediated) immunity, and enhanced T-cell dependent immunity. Finally, we illustrate the potential application of this sort of model by illustrating variational inversion (using simulated data) of this model to illustrate its use in testing hypotheses. In principle, this furnishes a fast and efficient immunological assay-based on sequential serology-that provides a (1) quantitative measure of latent immunological responses and (2) a Bayes optimal classification of the different kinds of immunological response (c.f., glucose tolerance tests used to test for insulin resistance). This may be especially useful in assessing SARS-CoV-2 vaccines.

Innate Immunity Plays a Key Role in Controlling Viral Load in COVID-19: Mechanistic Insights from a Whole-Body Infection Dynamics Model

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a pathogen of immense public health concern. Efforts to control the disease have only proven mildly successful, and the disease will likely continue to cause excessive fatalities until effective preventative measures (such as a vaccine) are developed. To develop disease management strategies, a better understanding of SARS-CoV-2 pathogenesis and population susceptibility to infection are needed. To this end, mathematical modeling can provide a robust in silico tool to understand COVID-19 pathophysiology and the in vivo dynamics of SARS-CoV-2. Guided by ACE2-tropism (ACE2 receptor dependency for infection) of the virus and by incorporating cellular-scale viral dynamics and innate and adaptive immune responses, we have developed a multiscale mechanistic model for simulating the time-dependent evolution of viral load distribution in susceptible organs of the body (respiratory tract, gut, liver, spleen, heart, kidneys, and brain). Following parameter quantification with in vivo and clinical data, we used the model to simulate viral load progression in a virtual patient with varying degrees of compromised immune status. Further, we ranked model parameters through sensitivity analysis for their significance in governing clearance of viral load to understand the effects of physiological factors and underlying conditions on viral load dynamics. Antiviral drug therapy, interferon therapy, and their combination were simulated to study the effects on viral load kinetics of SARS-CoV-2. The model revealed the dominant role of innate immunity (specifically interferons and resident macrophages) in controlling viral load, and the importance of timing when initiating therapy after infection.

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.

Innate immunity plays a key role in controlling viral load in COVID-19: mechanistic insights from a whole-body infection dynamics model

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a pathogen of immense public health concern. Efforts to control the disease have only proven mildly successful, and the disease will likely continue to cause excessive fatalities until effective preventative measures (such as a vaccine) are developed. To develop disease management strategies, a better understanding of SARS-CoV-2 pathogenesis and population susceptibility to infection are needed. To this end, physiologically-relevant mathematical modeling can provide a robust in silico tool to understand COVID-19 pathophysiology and the in vivo dynamics of SARS-CoV-2. Guided by ACE2-tropism (ACE2 receptor dependency for infection) of the virus, and by incorporating cellular-scale viral dynamics and innate and adaptive immune responses, we have developed a multiscale mechanistic model for simulating the time-dependent evolution of viral load distribution in susceptible organs of the body (respiratory tract, gut, liver, spleen, heart, kidneys, and brain). Following calibration with in vivo and clinical data, we used the model to simulate viral load progression in a virtual patient with varying degrees of compromised immune status. Further, we conducted global sensitivity analysis of model parameters and ranked them for their significance in governing clearance of viral load to understand the effects of physiological factors and underlying conditions on viral load dynamics. Antiviral drug therapy, interferon therapy, and their combination was simulated to study the effects on viral load kinetics of SARS-CoV-2. The model revealed the dominant role of innate immunity (specifically interferons and resident macrophages) in controlling viral load, and the importance of timing when initiating therapy following infection.

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.

Quantification of Ebola virus replication kinetics in vitro

Mathematical modelling has successfully been used to provide quantitative descriptions of many viral infections, but for the Ebola virus, which requires biosafety level 4 facilities for experimentation, modelling can play a crucial role. Ebola virus modelling efforts have primarily focused on in vivo virus kinetics, e.g., in animal models, to aid the development of antivirals and vaccines. But, thus far, these studies have not yielded a detailed specification of the infection cycle, which could provide a foundational description of the virus kinetics and thus a deeper understanding of their clinical manifestation. Here, we obtain a diverse experimental data set of the Ebola virus infection in vitro, and then make use of Bayesian inference methods to fully identify parameters in a mathematical model of the infection. Our results provide insights into the distribution of time an infected cell spends in the eclipse phase (the period between infection and the start of virus production), as well as the rate at which infectious virions lose infectivity. We suggest how these results can be used in future models to describe co-infection with defective interfering particles, which are an emerging alternative therapeutic.

Modeling HIV multiple infection

Multiple infection of target cells by human immunodeficiency virus (HIV) may lead to viral escape from host immune responses and drug resistance to antiretroviral therapy, bringing more challenges to the control of infection. The mechanisms underlying HIV multiple infection and their relative contributions are not fully understood. In this paper, we develop and analyze a mathematical model that includes sequential cell-free virus infection (i.e.one virus is transmitted each time in a sequential infection of target cells by virus) and cell-to-cell transmission (i.e.multiple viral genomes are transmitted simultaneously from infected to uninfected cells). By comparing model prediction with the distribution data of proviral genomes in HIV-infected spleen cells, we find that multiple infection can be well explained when the two modes of viral transmission are both included. Numerical simulation using the parameter estimates from data fitting shows that the majority of T cell infections are attributed to cell-to-cell transmission and this transmission mode also accounts for more than half of cell's multiple infections. These results suggest that cell-to-cell transmission plays a critical role in forming HIV multiple infection and thus has important implications for HIV evolution and pathogenesis.

Mathematical modeling of interaction between innate and adaptive immune responses in COVID-19 and implications for viral pathogenesis

We have applied mathematical modeling to investigate the infections of the ongoing coronavirus disease-2019 (COVID-19) pandemic caused by SARS-CoV-2 virus. We first validated our model using the well-studied influenza viruses and then compared the pathogenesis processes between the two viruses. The interaction between host innate and adaptive immune responses was found to be a potential cause for the higher severity and mortality in COVID-19 patients. Specifically, the timing mismatch between the two immune responses has a major impact on disease progression. The adaptive immune response of the COVID-19 patients is more likely to come before the peak of viral load, while the opposite is true for influenza patients. This difference in timing causes delayed depletion of vulnerable epithelial cells in the lungs in COVID-19 patients while enhancing viral clearance in influenza patients. Stronger adaptive immunity in COVID-19 patients can potentially lead to longer recovery time and more severe secondary complications. Based on our analysis, delaying the onset of adaptive immune responses during the early phase of infections may be a potential treatment option for high-risk COVID-19 patients. Suppressing the adaptive immune response temporarily and avoiding its interference with the innate immune response may allow the innate immunity to more efficiently clear the virus.

Chemical kinetics of the development of coronaviral infection in the human body: Critical conditions, toxicity mechanisms, "thermoheliox", and "thermovaccination"

Kinetic modeling of the behavior of complex chemical and biochemical systems is an effective approach to study of the mechanisms of the process. A kinetic model of coronaviral infection development with a description of the dynamic behavior of the main variables, including the concentration of viral particles, affected cells, and pathogenic microflora, is proposed. Changes in the concentration of hydrogen ions in the lungs and the pH -dependence of carbonic anhydrase activity (a key breathing enzyme) are critical. A significant result is the demonstration of an acute bifurcation transition that determines life or system collapse. This transition is connected with exponential growth of concentrations of the process participants and with functioning of the key enzyme carbonic anhydrase in development of toxic effects. Physical and chemical interpretations of the therapeutic effects of the body temperature rise and the potential therapeutic effect of “thermoheliox” (respiration with a thermolized mixture of helium and oxygen) are given. The phenomenon of “thermovaccination” is predicted, which involves stimulation of the immune response by “thermoheliox”.

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The proposed kinetic model describes the dynamics of coronaviral infection development.

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Acidification and pH dependence of key enzymes is discussed as a basis of viral toxicity.

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An acute bifurcation transition of the system to collapse is demonstrated.

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The theory and experimental facts of “thermoheliox” therapy are discussed.

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“Thermovaccination” by “thermoheliox” is predicted.

Mechanistic modeling explains the dsRNA length-dependent activation of the RIG-I mediated immune response

In cell-intrinsic antiviral immunity, cytoplasmic receptors such as retinoic acid-inducible gene I (RIG-I) detect viral double-stranded RNA (dsRNA) and trigger a signaling cascade activating the interferon (IFN) system. This leads to the transcription of hundreds of interferon-stimulated genes (ISGs) with a wide range of antiviral effects. This recognition of dsRNA not only has to be very specific to discriminate foreign from self but also highly sensitive to detect even very low numbers of pathogenic dsRNA molecules. Previous work indicated an influence of the dsRNA length on the binding behavior of RIG-I and its potential to elicit antiviral signaling. However, the molecular mechanisms behind the binding process are still under debate. We compare two hypothesized RIG-I binding mechanisms by translating them into mathematical models and analyzing their potential to describe published experimental data. The models consider the length of the dsRNA as well as known RIG-I binding motifs and describe RIG-I pathway activation after stimulation with dsRNA. We show that internal RIG-I binding sites in addition to cooperative RIG-I oligomerization are essential to describe the experimentally observed RIG-I binding behavior and immune response activation for different dsRNA lengths and concentrations. The combination of RIG-I binding to internal sites on the dsRNA and cooperative oligomerization compensates for a lack of high-affinity binding motifs and triggers a strong antiviral response for long dsRNAs. Model analysis reveals dsRNA length-dependency as a potential mechanism to discriminate between different types of dsRNAs: It allows for sensitive detection of small numbers of long dsRNAs, a typical by-product of viral replication, while ensuring tolerance against non-harming small dsRNAs.

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.

A Coupled Mathematical Model of the Intracellular Replication of Dengue Virus and the Host Cell Immune Response to Infection

Dengue virus (DV) is a positive-strand RNA virus of the Flavivirus genus. It is one of the most prevalent mosquito-borne viruses, infecting globally 390 million individuals per year. The clinical spectrum of DV infection ranges from an asymptomatic course to severe complications such as dengue hemorrhagic fever (DHF) and dengue shock syndrome (DSS), the latter because of severe plasma leakage. Given that the outcome of infection is likely determined by the kinetics of viral replication and the antiviral host cell immune response (HIR) it is of importance to understand the interaction between these two parameters. In this study, we use mathematical modeling to characterize and understand the complex interplay between intracellular DV replication and the host cells' defense mechanisms. We first measured viral RNA, viral protein, and virus particle production in Huh7 cells, which exhibit a notoriously weak intrinsic antiviral response. Based on these measurements, we developed a detailed intracellular DV replication model. We then measured replication in IFN competent A549 cells and used this data to couple the replication model with a model describing IFN activation and production of IFN stimulated genes (ISGs), as well as their interplay with DV replication. By comparing the cell line specific DV replication, we found that host factors involved in replication complex formation and virus particle production are crucial for replication efficiency. Regarding possible modes of action of the HIR, our model fits suggest that the HIR mainly affects DV RNA translation initiation, cytosolic DV RNA degradation, and naïve cell infection. We further analyzed the potential of direct acting antiviral drugs targeting different processes of the DV lifecycle in silico and found that targeting RNA synthesis and virus assembly and release are the most promising anti-DV drug targets.

Trends in mathematical modeling of host-pathogen interactions

Pathogenic microorganisms entail enormous problems for humans, livestock, and crop plants. A better understanding of the different infection strategies of the pathogens enables us to derive optimal treatments to mitigate infectious diseases or develop vaccinations preventing the occurrence of infections altogether. In this review, we highlight the current trends in mathematical modeling approaches and related methods used for understanding host-pathogen interactions. Since these interactions can be described on vastly different temporal and spatial scales as well as abstraction levels, a variety of computational and mathematical approaches are presented. Particular emphasis is placed on dynamic optimization, game theory, and spatial modeling, as they are attracting more and more interest in systems biology. Furthermore, these approaches are often combined to illuminate the complexities of the interactions between pathogens and their host. We also discuss the phenomena of molecular mimicry and crypsis as well as the interplay between defense and counter defense. As a conclusion, we provide an overview of method characteristics to assist non-experts in their decision for modeling approaches and interdisciplinary understanding.

Structure and Hierarchy of Influenza Virus Models Revealed by Reaction Network Analysis

Influenza A virus is recognized today as one of the most challenging viruses that threatens both human and animal health worldwide. Understanding the control mechanisms of influenza infection and dynamics is crucial and could result in effective future treatment strategies. Many kinetic models based on differential equations have been developed in recent decades to capture viral dynamics within a host. These models differ in their complexity in terms of number of species elements and number of reactions. Here, we present a new approach to understanding the overall structure of twelve influenza A virus infection models and their relationship to each other. To this end, we apply chemical organization theory to obtain a hierarchical decomposition of the models into chemical organizations. The decomposition is based on the model structure (reaction rules) but is independent of kinetic details such as rate constants. We found different types of model structures ranging from two to eight organizations. Furthermore, the model's organizations imply a partial order among models entailing a hierarchy of model, revealing a high model diversity with respect to their long-term behavior. Our methods and results can be helpful in model development and model integration, also beyond the influenza area.

Research Models and Tools for the Identification of Antivirals and Therapeutics against Zika Virus Infection

Zika virus recently re-emerged and caused global outbreaks mainly in Central Africa, Southeast Asia, the Pacific Islands and in Central and South America. Even though there is a declining trend, the virus continues to spread throughout different geographical regions of the world. Since its re-emergence in 2015, massive advances have been made regarding our understanding of clinical manifestations, epidemiology, genetic diversity, genomic structure and potential therapeutic intervention strategies. Nevertheless, treatment remains a challenge as there is no licensed effective therapy available. This review focuses on the recent advances regarding research models, as well as available experimental tools that can be used for the identification and characterization of potential antiviral targets and therapeutic intervention strategies.