In-host Mathematical Modelling of COVID-19 in Humans

Allometric comparison of viral dynamics in the nasal cavity-nasopharyngeal mucus layer of human and rhesus monkey by CFD-HCD approach

BACKGROUND AND OBJECTIVE

Viral respiratory infections stand as a considerable global health concern, presenting significant risks to the health of both humans and animals. This study aims to conduct a preliminary analysis of the time series of viral load in the nasal cavity-nasopharynx (NC-NP) of the human and rhesus macaque (RM).

METHODS

Taking into account the random uniform distribution of virus-laden droplets with a diameter of 10 μm in the mucus layer, this study applies the computational fluid dynamics-host cell dynamics (CFD-HCD) method to 3D-shell NC-NP models of human and RM, analyzing the impact of initial distribution of droplets on the viral dynamics of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), estimating parameters in the HCD model based on experimental data, integrating them into simulations to predict the time series of viral load and cell counts, and being visualized. The reproductive number (R0) are calculated to determine the occurrence of infection. The study also considers cross-parameter combinations and cross-experimental datasets to explore potential correlations between the human and RM.

RESULTS

The research findings indicate that the uniform distribution of virus-laden droplets throughout the whole NC-NP models of human and RM is reasonable for simulating and predicting viral dynamics. The visualization results offer dynamic insights into virus infection over a period of 20 days. Studies involving parameter and dataset exchanges between the two species underscore certain similarities in predicting virus infections between the human and RM.

CONCLUSIONS

This study lays the groundwork for further exploration into the parallels and distinctions in respiratory virus dynamics between humans and RMs, thus aiding in making more informed decisions in research and experimentation.

Vaccine and antiviral drug promise for preventing post-acute sequelae of COVID-19, and their combination for its treatment

Introduction

Most healthy individuals recover from acute SARS-CoV-2 infection, whereas a remarkable number continues to suffer from unexplained symptoms, known as Long COVID or post-acute COVID-19 syndrome (PACS). It is therefore imperative that methods for preventing and treating the onset of PASC be investigated with the utmost urgency.

Methods

A mathematical model of the immune response to vaccination and viral infection with SARS-CoV-2, incorporating immune memory cells, was developed.

Results and discussion

Similar to our previous model, persistent infection was observed by the residual virus in the host, implying the possibility of chronic inflammation and delayed recovery from tissue injury. Pre-infectious vaccination and antiviral medication administered during onset can reduce the acute viral load; however, they show no beneficial effects in preventing persistent infection. Therefore, the impact of these treatments on the PASC, which has been clinically observed, is mainly attributed to their role in preventing severe tissue damage caused by acute viral infections. For PASC patients with persistent infection, vaccination was observed to cause an immediate rapid increase in viral load, followed by a temporary decrease over approximately one year. The former was effectively suppressed by the coadministration of antiviral medications, indicating that this combination is a promising treatment for PASC.

Development of a SARS-CoV-2 viral dynamic model for patients with COVID-19 based on the amount of viral RNA and viral titer

The target-cell limited model, which is one of the mathematical modeling approaches providing a quantitative understanding of viral dynamics, has been applied to describe viral RNA profiles of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in previous studies. However, these models have been developed mainly using patient data from the early phase of the pandemic. Furthermore, no reports focused on the profiles of the viral titer. In this study, the dynamics of both viral RNA and viral titer were characterized using data reflecting the current clinical situation in which the Omicron variant has become epidemic and vaccines for SARS-CoV-2 have become available. Consecutive data for 5212 viral RNA levels and 5216 viral titers were obtained from 720 patients with coronavirus disease 2019 (COVID-19) in a phase II/III study for ensitrelvir. Our model assumed that productively infected cells would produce only infectious viruses, which could be transformed into non-infectious viruses, and has been used to describe the dynamics of both viral RNA levels and viral titer. The time from infection to symptom onset (tinf) of unvaccinated patients was estimated to be 3.0 days, which was shorter than that of the vaccinated patients. The immune-related parameter as a power function for the vaccinated patients was 1.1 times stronger than that for the unvaccinated patients. Our model allows the prediction of the viral dynamics in patients with COVID-19 from the time of infection to symptom onset. Vaccination status was identified as a factor influencing tinf and the immune function.

Local and global stability of an HCV viral dynamics model with two routes of infection and adaptive immunity

The aim of this article is to formulate and study a mathematical model describing hepatitis C virus (HCV) infection dynamics. The model includes two essential modes of infection transmission, namely, virus-to-cell and cell-to-cell. The effect of therapy and adaptive immunity are incorporated in the suggested model. The adaptive immunity is represented by its two categories, namely, the humoral and cellular immune responses. Our article begins by establishing some mathematical results through proving the model's well-posedness in terms of existence, positivity and boundedness of solutions. We present all the steady states of the problem that depend on specific reproduction numbers. It moves then to the theoretical investigation of the local and global stability analysis of the free disease equilibrium and the four disease equilibria. The local and global stability analysis of the HCV mathematical model are established via the Routh-Hurwitz criteria and Lyapunov-LaSalle invariance principle, respectively. Finally, our article presents some numerical simulations to validate the analytical study of the global stability. Numerical simulations have shown the effect of the drug therapies on the system's dynamical behavior.

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.

In silico identification of viral loads in cough-generated droplets - Seamless integrated analysis of CFPD-HCD-EWF

BACKGROUND AND OBJECTIVE

Respiratory diseases caused by respiratory viruses have significantly threatened public health worldwide. This study presents a comprehensive approach to predict viral dynamics and the generation of stripped droplets within the mucus layer of the respiratory tract during coughing using a larynx-trachea-bifurcation (LTB) model.

METHODS

This study integrates computational fluid-particle dynamics (CFPD), host-cell dynamics (HCD), and the Eulerian wall film (EWF) model to propose a potential means for seamless integrated analysis. The verified CFPD-HCD coupling model based on a 3D-shell model was used to characterize the severe acute respiratory syndrome, coronavirus 2 (SARS-CoV-2) dynamics in the LTB mucus layer, whereas the EWF model was employed to account for the interfacial fluid to explore the generation mechanism and trace the origin site of droplets exhaled during a coughing event of an infected host.

RESULTS

The results obtained using CFPD delineated the preferential deposition sites for droplets in the laryngeal and tracheal regions. Thus, the analysis of the HCD model showed that the viral load increased rapidly in the laryngeal region during the peak of infection, whereas there was a growth delay in the tracheal region (up to day 8 after infection). After two weeks of infection, the high viral load gradually migrated towards the glottic region. Interestingly, the EWF model demonstrated a high concentration of exhaled droplets originating from the larynx. The coupling technique indicated a concurrent high viral load in the mucus layer and site of origin of the exhaled droplets.

CONCLUSIONS

This interdisciplinary research underscores the seamless analysis from initial exposure to virus-laden droplets, the dynamics of viral infection in the LTB mucus layer, and the re-emission from the coughing activities of an infected host. Our efforts aimed to address the complex challenges at the intersection of viral dynamics and respiratory health, which can contribute to a more detailed understanding and targeted prevention of respiratory diseases.

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.

Modeling the emergence of viral resistance for SARS-CoV-2 during treatment with an anti-spike monoclonal antibody

To mitigate the loss of lives during the COVID-19 pandemic, emergency use authorization was given to several anti-SARS-CoV-2 monoclonal antibody (mAb) therapies for the treatment of mild-to-moderate COVID-19 in patients with a high risk of progressing to severe disease. Monoclonal antibodies used to treat SARS-CoV-2 target the spike protein of the virus and block its ability to enter and infect target cells. Monoclonal antibody therapy can thus accelerate the decline in viral load and lower hospitalization rates among high-risk patients with variants susceptible to mAb therapy. However, viral resistance has been observed, in some cases leading to a transient viral rebound that can be as large as 3-4 orders of magnitude. As mAbs represent a proven treatment choice for SARS-CoV-2 and other viral infections, evaluation of treatment-emergent mAb resistance can help uncover underlying pathobiology of SARS-CoV-2 infection and may also help in the development of the next generation of mAb therapies. Although resistance can be expected, the large rebounds observed are much more difficult to explain. We hypothesize replenishment of target cells is necessary to generate the high transient viral rebound. Thus, we formulated two models with different mechanisms for target cell replenishment (homeostatic proliferation and return from an innate immune response antiviral state) and fit them to data from persons with SARS-CoV-2 treated with a mAb. We showed that both models can explain the emergence of resistant virus associated with high transient viral rebounds. We found that variations in the target cell supply rate and adaptive immunity parameters have a strong impact on the magnitude or observability of the viral rebound associated with the emergence of resistant virus. Both variations in target cell supply rate and adaptive immunity parameters may explain why only some individuals develop observable transient resistant viral rebound. Our study highlights the conditions that can lead to resistance and subsequent viral rebound in mAb treatments during acute infection.

Mathematical model explains differences in Omicron and Delta SARS-CoV-2 dynamics in Caco-2 and Calu-3 cells

Within-host infection dynamics of Omicron dramatically differs from previous variants of SARS-CoV-2. However, little is still known about which parameters of virus-cell interplay contribute to the observed attenuated replication and pathogenicity of Omicron. Mathematical models, often expressed as systems of differential equations, are frequently employed to study the infection dynamics of various viruses. Adopting such models for results of in vitro experiments can be beneficial in a number of aspects, such as model simplification (e.g., the absence of adaptive immune response and innate immunity cells), better measurement accuracy, and the possibility to measure additional data types in comparison with in vivo case. In this study, we consider a refinement of our previously developed and validated model based on a system of integro-differential equations. We fit the model to the experimental data of Omicron and Delta infections in Caco-2 (human intestinal epithelium model) and Calu-3 (lung epithelium model) cell lines. The data include known information on initial conditions, infectious virus titers, and intracellular viral RNA measurements at several time points post-infection. The model accurately explains the experimental data for both variants in both cell lines using only three variant- and cell-line-specific parameters. Namely, the cell entry rate is significantly lower for Omicron, and Omicron triggers a stronger cytokine production rate (i.e., innate immune response) in infected cells, ultimately making uninfected cells resistant to the virus. Notably, differences in only a single parameter (e.g., cell entry rate) are insufficient to obtain a reliable model fit for the experimental data.

Confinement tonicity on epidemic spreading

Emerging and re-emerging pathogens are latent threats in our society with the risk of killing millions of people worldwide, without forgetting the severe economic and educational backlogs. From COVID-19, we learned that self isolation and quarantine restrictions (confinement) were the main way of protection till availability of vaccines. However, abrupt lifting of social confinement would result in new waves of new infection cases and high death tolls. Here, inspired by how an extracellular solution can make water move into or out of a cell through osmosis, we define confinement tonicity. This can serve as a standalone measurement for the net direction and magnitude of flows between the confined and deconfined susceptible compartments. Numerical results offer insights on the effects of easing quarantine restrictions.

Virus-mediated cell fusion of SARS-CoV-2 variants

SARS-CoV-2 has the ability to form large multi-nucleated cells known as syncytia. Little is known about how syncytia affect the dynamics of the infection or severity of the disease. In this manuscript, we extend a mathematical model of cell-cell fusion assays to estimate both the syncytia formation rate and the average duration of the fusion phase for five strains of SARS-CoV-2. We find that the original Wuhan strain has the slowest rate of syncytia formation (6.4×10-4/h), but takes only 4.0 h to complete the fusion process, while the Alpha strain has the fastest rate of syncytia formation (0.36 /h), but takes 7.6 h to complete the fusion process. The Beta strain also has a fairly fast syncytia formation rate (9.7×10-2/h), and takes the longest to complete fusion (8.4 h). The D614G strain has a fairly slow syncytia formation rate (2.8×10-3/h), but completes fusion in 4.0 h. Finally, the Delta strain is in the middle with a syncytia formation rate of 3.2×10-2/h and a fusing time of 6.1 h. We note that for these SARS-CoV-2 strains, there appears to be a tradeoff between the ease of forming syncytia and the speed at which they complete the fusion process.

Within-host delay differential model for SARS-CoV-2 kinetics with saturated antiviral responses

The present study discussed a model to describe the SARS-CoV-2 viral kinetics in the presence of saturated antiviral responses. A discrete-time delay was introduced due to the time required for uninfected epithelial cells to activate a suitable antiviral response by generating immune cytokines and chemokines. We examined the system's stability at each equilibrium point. A threshold value was obtained for which the system switched from stability to instability via a Hopf bifurcation. The length of the time delay has been computed, for which the system has preserved its stability. Numerical results show that the system was stable for the faster antiviral responses of epithelial cells to the virus concentration, i.e., quick antiviral responses stabilized patients' bodies by neutralizing the virus. However, if the antiviral response of epithelial cells to the virus increased, the system became unstable, and the virus occupied the whole body, which caused patients' deaths.

SARS-CoV-2 viral dynamic modeling to inform model selection and timing and efficacy of antiviral therapy

Mathematical models of viral dynamics have been reported to describe adequately the dynamic changes of severe acute respiratory syndrome-coronavirus 2 viral load within an individual host. In this study, eight published viral dynamic models were assessed, and model selection was performed. Viral load data were collected from a community surveillance study, including 2155 measurements from 162 patients (124 household and 38 non-household contacts). An extended version of the target-cell limited model that includes an eclipse phase and an immune response component that enhances viral clearance described best the data. In general, the parameter estimates showed good precision (relative standard error <10), apart from the death rate of infected cells. The parameter estimates were used to simulate the outcomes of a clinical trial of the antiviral tixagevimab-cilgavimab, a monoclonal antibody combination which blocks infection of the target cells by neutralizing the virus. The simulated outcome of the effectiveness of the antiviral therapy in controlling viral replication was in a good agreement with the clinical trial data. Early treatment with high antiviral efficacy is important for desired therapeutic outcome.

Aging, Inflammation, and Comorbidity in Cancers-A General In Silico Study Exemplified by Myeloproliferative Malignancies

(1) Background: We consider dormant, pre-cancerous states prevented from developing into cancer by the immune system. Inflammatory morbidity may compromise the immune system and cause the pre-cancer to escape into an actual cancerous development. The immune deficiency described is general, but the results may vary across specific cancers due to different variances (2) Methods: We formulate a general conceptual model to perform rigorous in silico consequence analysis. Relevant existing data for myeloproliferative malignancies from the literature are used to calibrate the in silico computations. (3) Results and conclusions: The hypothesis suggests a common physiological origin for many clinical and epidemiological observations in relation to cancers in general. Examples are the observed age-dependent prevalence for hematopoietic cancers, a general mechanism-based explanation for why the risk of cancer increases with age, and how somatic mutations in general, and specifically seen in screenings of citizens, sometimes are non-increased or even decrease when followed over time. The conceptual model is used to characterize different groups of citizens and patients, describing different treatment responses and development scenarios.

Choice of spatial discretisation influences the progression of viral infection within multicellular tissues

There has been an increasing recognition of the utility of models of the spatial dynamics of viral spread within tissues. Multicellular models, where cells are represented as discrete regions of space coupled to a virus density surface, are a popular approach to capture these dynamics. Conventionally, such models are simulated by discretising the viral surface and depending on the rate of viral diffusion and other considerations, a finer or coarser discretisation may be used. The impact that this choice may have on the behaviour of the system has not been studied. Here we demonstrate that under realistic parameter regimes - where viral diffusion is small enough to support the formation of familiar ring-shaped infection plaques - the choice of spatial discretisation of the viral surface can qualitatively change key model outcomes including the time scale of infection. Importantly, we show that the choice between implementing viral spread as a cell-scale process, or as a high-resolution converged PDE can generate distinct model outcomes, which raises important conceptual questions about the strength of assumptions underpinning the spatial structure of the model. We investigate the mechanisms driving these discretisation artefacts, the impacts they may have on model predictions, and provide guidance on the design and implementation of spatial and especially multicellular models of viral dynamics. We obtain our results using the simplest TIV construct for the viral dynamics, and therefore anticipate that the important effects we describe will also influence model predictions in more complex models of virus-cell-immune system interactions. This analysis will aid in the construction of models for robust and biologically realistic modelling and inference.

Modeling the emergence of viral resistance for SARS-CoV-2 during treatment with an anti-spike monoclonal antibody

The COVID-19 pandemic has led to over 760 million cases and 6.9 million deaths worldwide. To mitigate the loss of lives, emergency use authorization was given to several anti-SARS-CoV-2 monoclonal antibody (mAb) therapies for the treatment of mild-to-moderate COVID-19 in patients with a high risk of progressing to severe disease. Monoclonal antibodies used to treat SARS-CoV-2 target the spike protein of the virus and block its ability to enter and infect target cells. Monoclonal antibody therapy can thus accelerate the decline in viral load and lower hospitalization rates among high-risk patients with susceptible variants. However, viral resistance has been observed, in some cases leading to a transient viral rebound that can be as large as 3-4 orders of magnitude. As mAbs represent a proven treatment choice for SARS-CoV-2 and other viral infections, evaluation of treatment-emergent mAb resistance can help uncover underlying pathobiology of SARS-CoV-2 infection and may also help in the development of the next generation of mAb therapies. Although resistance can be expected, the large rebounds observed are much more difficult to explain. We hypothesize replenishment of target cells is necessary to generate the high transient viral rebound. Thus, we formulated two models with different mechanisms for target cell replenishment (homeostatic proliferation and return from an innate immune response anti-viral state) and fit them to data from persons with SARS-CoV-2 treated with a mAb. We showed that both models can explain the emergence of resistant virus associated with high transient viral rebounds. We found that variations in the target cell supply rate and adaptive immunity parameters have a strong impact on the magnitude or observability of the viral rebound associated with the emergence of resistant virus. Both variations in target cell supply rate and adaptive immunity parameters may explain why only some individuals develop observable transient resistant viral rebound. Our study highlights the conditions that can lead to resistance and subsequent viral rebound in mAb treatments during acute infection.

An explanation for SARS-CoV-2 rebound after Paxlovid treatment

In a fraction of SARS-CoV-2 infected individuals treated with the oral antiviral Paxlovid, the virus rebounds following treatment. The mechanism driving rebound is not understood. Here, we show that viral dynamic models based on the hypothesis that Paxlovid treatment near the time of symptom onset halts the depletion of target cells, but may not fully eliminate the virus, which can lead to viral rebound. We also show that the occurrence of viral rebound is sensitive to model parameters, and the time treatment is initiated, which may explain why only a fraction of individuals develop viral rebound. Finally, the models are used to test the therapeutic effects of two alternative treatment schemes. These findings also provide a possible explanation for rebounds following other antiviral treatments for SARS-CoV-2.

Visual prediction and parameter optimization of viral dynamics in the mucus milieu of the upper airway based on CFPD-HCD analysis

BACKGROUND AND OBJECTIVE

Respiratory diseases caused by viruses are a major human health problem. To better control the infection and understand the pathogenesis of these diseases, this paper studied SARS-CoV-2, a novel coronavirus outbreak, as an example.

METHODS

Based on coupled computational fluid and particle dynamics (CFPD) and host-cell dynamics (HCD) analyses, we studied the viral dynamics in the mucus layer of the human nasal cavity-nasopharynx. To reproduce the effect of mucociliary movement on the diffusive and convective transport of viruses in the mucus layer, a 3D-shell model was constructed using CT data of the upper respiratory tract (URT) of volunteers. Considering the mucus environment, the HCD model was established by coupling the target cell-limited model with the convection-diffusion term. Parameter optimization of the HCD model is the key problem in the simulation. Therefore, this study focused on the parameter optimization of the viral dynamics model, divided the geometric model into multiple compartments, and used Monolix to perform the nonlinear mixed effects (NLME) of pharmacometrics to discuss the influence of factors such as the number of mucus layers, number of compartments, diffusion rate, and mucus flow velocity on the prediction results.

RESULTS

The findings showed that sufficient experimental data can be used to estimate the corresponding parameters of the HCD model. The optimized convection-diffusion case with a two-layer multi-compartment low-velocity model could accurately predict the viral dynamics.

CONCLUSIONS

Its visualization process could explain the symptoms of the disease in the nose and contribute to the prevention and targeted treatment of respiratory diseases.

Within-host modeling to measure dynamics of antibody responses after natural infection or vaccination: A systematic review

BACKGROUND

Within-host models describe the dynamics of immune cells when encountering a pathogen, and how these dynamics can lead to an individual-specific immune response. This systematic review aims to summarize which within-host methodology has been used to study and quantify antibody kinetics after infection or vaccination. In particular, we focus on data-driven and theory-driven mechanistic models.

MATERIALS

PubMed and Web of Science databases were used to identify eligible papers published until May 2022. Eligible publications included those studying mathematical models that measure antibody kinetics as the primary outcome (ranging from phenomenological to mechanistic models).

RESULTS

We identified 78 eligible publications, of which 8 relied on an Ordinary Differential Equations (ODEs)-based modelling approach to describe antibody kinetics after vaccination, and 12 studies used such models in the context of humoral immunity induced by natural infection. Mechanistic modeling studies were summarized in terms of type of study, sample size, measurements collected, antibody half-life, compartments and parameters included, inferential or analytical method, and model selection.

CONCLUSIONS

Despite the importance of investigating antibody kinetics and underlying mechanisms of (waning of) the humoral immunity, few publications explicitly account for this in a mathematical model. In particular, most research focuses on phenomenological rather than mechanistic models. The limited information on the age groups or other risk factors that might impact antibody kinetics, as well as a lack of experimental or observational data remain important concerns regarding the interpretation of mathematical modeling results. We reviewed the similarities between the kinetics following vaccination and infection, emphasising that it may be worth translating some features from one setting to another. However, we also stress that some biological mechanisms need to be distinguished. We found that data-driven mechanistic models tend to be more simplistic, and theory-driven approaches lack representative data to validate model results.

Topological data analysis of antibody dynamics of severe and non-severe patients with COVID-19

The COVID-19 pandemic is a significant public health threat with unanswered questions regarding the immune system's role in the disease's severity level. Here, based on antibody kinetic data of severe and non-severe COVID-19 patients, topological data analysis (TDA) highlights that severity is not binary. However, there are differences in the shape of antibody responses that further classify COVID-19 patients into non-severe, severe, and intermediate cases of severity. Based on the results of TDA, different mathematical models were developed to represent the dynamics between the different severity groups. The best model was the one with the lowest average value of the Akaike Information Criterion for all groups of patients. Our results suggest that different immune mechanisms drive differences between the severity groups. Further inclusion of different longitudinal data sets will be central for a holistic way of tackling COVID-19.

Determination of significant immunological timescales from mRNA-LNP-based vaccines in humans

A compartment model for an in-host liquid nanoparticle delivered mRNA vaccine is presented. Through non-dimensionalisation, five timescales are identified that dictate the lifetime of the vaccine in-host: decay of interferon gamma, antibody priming, autocatalytic growth, antibody peak and decay, and interleukin cessation. Through asymptotic analysis we are able to obtain semi-analytical solutions in each of the time regimes which allows us to predict maximal concentrations and better understand parameter dependence in the model. We compare our model to 22 data sets for the BNT162b2 and mRNA-1273 mRNA vaccines demonstrating good agreement. Using our analysis, we estimate the values for each of the five timescales in each data set and predict maximal concentrations of plasma B-cells, antibody, and interleukin. Through our comparison, we do not observe any discernible differences between vaccine candidates and sex. However, we do identify an age dependence, specifically that vaccine activation takes longer and that peak antibody occurs sooner in patients aged 55 and greater.

Stability of a delayed SARS-CoV-2 reactivation model with logistic growth and adaptive immune response

This paper develops and analyzes a SARS-CoV-2 dynamics model with logistic growth of healthy epithelial cells, CTL immune and humoral (antibody) immune responses. The model is incorporated with four mixed (distributed/discrete) time delays, delay in the formation of latent infected epithelial cells, delay in the formation of active infected epithelial cells, delay in the activation of latent infected epithelial cells, and maturation delay of new SARS-CoV-2 particles. We establish that the model's solutions are non-negative and ultimately bounded. We deduce that the model has five steady states and their existence and stability are perfectly determined by four threshold parameters. We study the global stability of the model's steady states using Lyapunov method. The analytical results are enhanced by numerical simulations. The impact of intracellular time delays on the dynamical behavior of the SARS-CoV-2 is addressed. We noted that increasing the time delay period can suppress the viral replication and control the infection. This could be helpful to create new drugs that extend the delay time period.

Simplified within-host and Dose-response Models of SARS-CoV-2

Understanding the mechanistic dynamics of transmission is key to designing more targeted and effective interventions to limit the spread of infectious diseases. A well-described within-host model allows explicit simulation of how infectiousness changes over time at an individual level. This can then be coupled with dose-response models to investigate the impact of timing on transmission. We collected and compared a range of within-host models used in previous studies and identified a minimally-complex model that provides suitable within-host dynamics while keeping a reduced number of parameters to allow inference and limit unidentifiability issues. Furthermore, non-dimensionalised models were developed to further overcome the uncertainty in estimates of the size of the susceptible cell population, a common problem in many of these approaches. We will discuss these models, and their fit to data from the human challenge study (see Killingley et al. (2022)) for SARS-CoV-2 and the model selection results, which has been performed using ABC-SMC. The parameter posteriors have then used to simulate viral-load based infectiousness profiles via a range of dose-response models, which illustrate the large variability of the periods of infection window observed for COVID-19.

The race to understand immunopathology in COVID-19: Perspectives on the impact of quantitative approaches to understand within-host interactions

The COVID-19 pandemic has revealed the need for the increased integration of modelling and data analysis to public health, experimental, and clinical studies. Throughout the first two years of the pandemic, there has been a concerted effort to improve our understanding of the within-host immune response to the SARS-CoV-2 virus to provide better predictions of COVID-19 severity, treatment and vaccine development questions, and insights into viral evolution and the impacts of variants on immunopathology. Here we provide perspectives on what has been accomplished using quantitative methods, including predictive modelling, population genetics, machine learning, and dimensionality reduction techniques, in the first 26 months of the COVID-19 pandemic approaches, and where we go from here to improve our responses to this and future pandemics.

Mechanistic modeling of viral particle production

Viral systems such as wild-type viruses, viral vectors, and virus-like particles are essential components of modern biotechnology and medicine. Despite their importance, the commercial-scale production of viral systems remains highly inefficient for multiple reasons. Computational strategies are a promising avenue for improving process development, optimization, and control, but require a mathematical description of the system. This article reviews mechanistic modeling strategies for the production of viral particles, both at the cellular and bioreactor scales. In many cases, techniques and models from adjacent fields such as epidemiology and wild-type viral infection kinetics can be adapted to construct a suitable process model. These process models can then be employed for various purposes such as in-silico testing of novel process operating strategies and/or advanced process control.

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.

Development of a novel mathematical model that explains SARS-CoV-2 infection dynamics in Caco-2 cells

Mathematical modeling is widely used to study within-host viral dynamics. However, to the best of our knowledge, for the case of SARS-CoV-2 such analyses were mainly conducted with the use of viral load data and for the wild type (WT) variant of the virus. In addition, only few studies analyzed models for in vitro data, which are less noisy and more reproducible. In this work we collected multiple data types for SARS-CoV-2-infected Caco-2 cell lines, including infectious virus titers, measurements of intracellular viral RNA, cell viability data and percentage of infected cells for the WT and Delta variants. We showed that standard models cannot explain some key observations given the absence of cytopathic effect in human cell lines. We propose a novel mathematical model for in vitro SARS-CoV-2 dynamics, which included explicit modeling of intracellular events such as exhaustion of cellular resources required for virus production. The model also explicitly considers innate immune response. The proposed model accurately explained experimental data. Attenuated replication of the Delta variant in Caco-2 cells could be explained by our model on the basis of just two parameters: decreased cell entry rate and increased cytokine production rate.

A mathematical model of the within-host kinetics of SARS-CoV-2 neutralizing antibodies following COVID-19 vaccination

Compelling evidence continues to build to support the idea that SARS-CoV-2 Neutralizing Antibody (NAb) levels in an individual can serve as an important indicator of the strength of protective immunity against infection. It is not well understood why NAb levels in some individuals remain high over time, while in others levels decline rapidly. In this work, we present a two-state mathematical model of within-host NAb dynamics in response to vaccination. By fitting only four host-specific parameters, the model is able to capture individual-specific NAb levels over time as measured by the AditxtScore™ for NAbs. The model can serve as a foundation for predicting NAb levels in the long-term, understanding connections between NAb levels, protective immunity, and breakthrough infections, and potentially guiding decisions about whether and when a booster vaccination may be warranted.

Machine Learning and COVID-19: Lessons from SARS-CoV-2

Currently, methods in machine learning have opened a significant number of applications to construct classifiers with capacities to recognize, identify, and interpret patterns hidden in massive amounts of data. This technology has been used to solve a variety of social and health issues against coronavirus disease 2019 (COVID-19). In this chapter, we present some supervised and unsupervised machine learning techniques that have contributed in three aspects to supplying information to health authorities and diminishing the deadly effects of the current worldwide outbreak on the population. First is the identification and construction of powerful classifiers capable of predicting severe, moderate, or asymptomatic responses in COVID-19 patients starting from clinical or high-throughput technologies. Second is the identification of groups of patients with similar physiological responses to improve the triage classification and inform treatments. The final aspect is the combination of machine learning methods and schemes from systems biology to link associative studies with mechanistic frameworks. This chapter aims to discuss some practical applications in the use of machine learning techniques to handle data coming from social behavior and high-throughput technologies, associated with COVID-19 evolution.

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.

Impulsive Neural Control to Schedule Antivirals and Immunomodulators for COVID-19

New SARS-CoV-2 variants escaping the effect of vaccines are an eminent threat. The use of antivirals to inhibit the viral replication cycle or immunomodulators to regulate host immune responses can help to tackle the viral infection at the host level. To evaluate the potential use of these therapies, we propose the application of an inverse optimal neural controller to a mathematical model that represents SARS-CoV-2 dynamics in the host. Antiviral effects and immune responses are considered as the control actions. The variability between infected hosts can be large, thus, the host infection dynamics are identified based on a Recurrent High-Order Neural Network (RHONN) trained with the Extended Kalman Filter (EKF). The performance of the control strategies is tested by employing a Monte Carlo analysis. Simulation results present different scenarios where potential antivirals and immunomodulators could reduce the viral load.

Clinical effects of 2-DG drug restraining SARS-CoV-2 infection: A fractional order optimal control study

Fractional calculus is very convenient tool in modeling of an emergent infectious disease system comprising previous disease states, memory of disease patterns, profile of genetic variation etc. Significant complex behaviors of a disease system could be calibrated in a proficient manner through fractional order derivatives making the disease system more realistic than integer order model. In this study, a fractional order differential equation model is developed in micro level to gain perceptions regarding the effects of host immunological memory in dynamics of SARS-CoV-2 infection. Additionally, the possible optimal control of the infection with the help of an antiviral drug, viz. 2-DG, has been exemplified here. The fractional order optimal control would enable to employ the proper administration of the drug minimizing its systematic cost which will assist the health policy makers in generating better therapeutic measures against SARS-CoV-2 infection. Numerical simulations have advantages to visualize the dynamical effects of the immunological memory and optimal control inputs in the epidemic system.

Comparative assessment of viral dynamic models for SARS-CoV-2 for pharmacodynamic assessment in early treatment trials

Pharmacometric analyses of time series viral load data may detect drug effects with greater power than approaches using single time points. Because SARS-CoV-2 viral load rapidly rises and then falls, viral dynamic models have been used. We compared different modelling approaches when analysing Phase II-type viral dynamic data. Using two SARS-CoV-2 datasets of viral load starting within 7 days of symptoms, we fitted the slope-intercept exponential decay (SI), reduced target cell limited (rTCL), target cell limited (TCL) and TCL with eclipse phase (TCLE) models using nlmixr. Model performance was assessed via Bayesian information criterion (BIC), visual predictive checks (VPCs), goodness-of-fit plots, and parameter precision. The most complex (TCLE) model had the highest BIC for both datasets. The estimated viral decline rate was similar for all models except the TCL model for dataset A with a higher rate (median [range] day^-1 : dataset A; 0.63 [0.56-1.84]; dataset B: 0.81 [0.74-0.85]). Our findings suggest simple models should be considered during pharmacodynamic model development.

Global Dynamics of SARS-CoV-2 Infection with Antibody Response and the Impact of Impulsive Drug Therapy

Mathematical modeling is crucial to investigating tthe ongoing coronavirus disease 2019 (COVID-19) pandemic. The primary target area of the SARS-CoV-2 virus is epithelial cells in the human lower respiratory tract. During this viral infection, infected cells can activate innate and adaptive immune responses to viral infection. Immune response in COVID-19 infection can lead to longer recovery time and more severe secondary complications. We formulate a micro-level mathematical model by incorporating a saturation term for SARS-CoV-2-infected epithelial cell loss reliant on infected cell levels. Forward and backward bifurcation between disease-free and endemic equilibrium points have been analyzed. Global stability of both disease-free and endemic equilibrium is provided. We have seen that the disease-free equilibrium is globally stable for R0<1, and endemic equilibrium exists and is globally stable for R0>1. Impulsive application of drug dosing has been applied for the treatment of COVID-19 patients. Additionally, the dynamics of the impulsive system are discussed when a patient takes drug holidays. Numerical simulations support the analytical findings and the dynamical regimes in the systems.

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.

Estimation of virus-mediated cell fusion rate of SARS-CoV-2

Several viruses have the ability to form large multinucleated cells known as syncytia. Many properties of syncytia and the role they play in the evolution of a viral infection are not well understood. One basic question that has not yet been answered is how quickly syncytia form. We use a novel mathematical model of cell-cell fusion assays and apply it to experimental data from SARS-CoV-2 fusion assays to provide the first estimates of virus-mediated cell fusion rate. We find that for SARS-CoV2, the fusion rate is in the range of 6 × 10-4-12×10-4/h. We also use our model to compare fusion rates when the protease TMPRSS2 is overexpressed (2-4 times larger fusion rate), when the protease furin is removed (one third the original fusion rate), and when the spike protein is altered (1/10th the original fusion rate). The use of mathematical models allows us to provide additional quantitative information about syncytia formation.

Identifiability of parameters in mathematical models of SARS-CoV-2 infections in humans

Determining accurate estimates for the characteristics of the severe acute respiratory syndrome coronavirus 2 in the upper and lower respiratory tracts, by fitting mathematical models to data, is made difficult by the lack of measurements early in the infection. To determine the sensitivity of the parameter estimates to the noise in the data, we developed a novel two-patch within-host mathematical model that considered the infection of both respiratory tracts and assumed that the viral load in the lower respiratory tract decays in a density dependent manner and investigated its ability to match population level data. We proposed several approaches that can improve practical identifiability of parameters, including an optimal experimental approach, and found that availability of viral data early in the infection is of essence for improving the accuracy of the estimates. Our findings can be useful for designing interventions.

Immune response to SARS-CoV-2 in severe disease and long COVID-19

COVID-19 is mild to moderate in otherwise healthy individuals but may nonetheless cause life-threatening disease and/or a wide range of persistent symptoms. The general determinant of disease severity is age mainly because the immune response declines in aging patients. Here, we developed a mathematical model of the immune response to SARS-CoV-2 and revealed that typical age-related risk factors such as only a several 10% decrease in innate immune cell activity and inhibition of type-I interferon signaling by autoantibodies drastically increased the viral load. It was reported that the numbers of certain dendritic cell subsets remained less than half those in healthy donors even seven months after infection. Hence, the inflammatory response was ongoing. Our model predicted the persistent DC reduction and showed that certain patients with severe and even mild symptoms could not effectively eliminate the virus and could potentially develop long COVID.

A Multiscale Model of COVID-19 Dynamics

COVID-19, caused by the infection of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has been a global pandemic and created unprecedented public health challenges throughout the world. Despite significant progresses in understanding the disease pathogenesis and progression, the epidemiological triad of pathogen, host, and environment remains unclear. In this paper, we develop a multiscale model to study the coupled within-host and between-host dynamics of COVID-19. The model includes multiple transmission routes (both human-to-human and environment-to-human) and connects multiple scales (both the population and individual levels). A detailed analysis on the local and global dynamics of the fast system, slow system and full system shows that rich dynamics, including both forward and backward bifurcations, emerge with the coupling of viral infection and epidemiological models. Model fitting to both virological and epidemiological data facilitates the evaluation of the influence of a few infection characteristics and antiviral treatment on the spread of the disease. Our work underlines the potential role that the environment can play in the transmission of COVID-19. Antiviral treatment of infected individuals can delay but cannot prevent the emergence of disease outbreaks. These results highlight the implementation of comprehensive intervention measures such as social distancing and wearing masks that aim to stop airborne transmission, combined with surface disinfection and hand hygiene that can prevent environmental transmission. The model also provides a multiscale modeling framework to study other infectious diseases when the environment can serve as a reservoir of pathogens.

Modeling within-host and aerosol dynamics of SARS-CoV-2: The relationship with infectiousness

The relationship between transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and the amount of virus present in the proximity of a susceptible host is not understood. Here, we developed a within-host and aerosol mathematical model and used it to determine the relationship between viral kinetics in the upper respiratory track, viral kinetics in the aerosols, and new transmissions in golden hamsters challenged with SARS-CoV-2. We determined that infectious virus shedding early in infection correlates with transmission events, shedding of infectious virus diminishes late in the infection, and high viral RNA levels late in the infection are a poor indicator of transmission. We further showed that viral infectiousness increases in a density dependent manner with viral RNA and that their relative ratio is time-dependent. Such information is useful for designing interventions.

Quantifying the relationship between SARS-CoV-2 dynamics in upper respiratory tract and in aerosols is key to understanding SARS-CoV-2 transmission and evaluating intervention strategies. Of particular interest is the link between the viral RNA measured by PCR and a subject’s infectiousness. Here, we developed a mechanistic model of viral transmission in golden hamsters and used data in upper respiratory tract and aerosols to evaluate key within-host and environment based viral parameters. The significance of our research is in identifying the timing and duration of viral shedding, how long it stays infectious, and the link between infectious virus and total viral RNA. Such knowledge enhances our understanding of the SARS-CoV-2 transmission window.

Within-host dynamics of SARS-CoV-2 infection: A systematic review and meta-analysis

Within-host model specified by viral dynamic parameters is a mainstream tool to understand SARS-CoV-2 replication cycle in infected patients. The parameter uncertainty further affects the output of the model, such as the efficacy of potential antiviral drugs. However, gathering empirical data on these parameters is challenging. Here, we aim to conduct a systematic review of viral dynamic parameters used in within-host models by calibrating the model to the viral load data measured from upper respiratory specimens. We searched the PubMed, Embase and Web of Science databases (between 1 December 2019 and 10 February 2022) for within-host modelling studies. We identified seven independent within-host models from the above nine studies, including Type I interferon, innate response, humoral immune response or cell-mediated immune response. From these models, we extracted and analyse seven widely used viral dynamic parameters including the viral load at the point of infection or symptom onset, the rate of viral particles infecting susceptible cells, the rate of infected cells releasing virus, the rate of virus particles cleared, the rate of infected cells cleared and the rate of cells in the eclipse phase can become productively infected. We identified seven independent within-host models from nine eligible studies. The viral load at symptom onset is 4.78 (95% CI:2.93, 6.62) log(copies/ml), and the viral load at the point of infection is -1.00 (95% CI:-1.94, -0.05) log(copies/ml). The rate of viral particles infecting susceptible cells and the rate of infected cells cleared have the pooled estimates as -6.96 (95% CI:-7.66, -6.25) log([copies/ml]^-1 day^-1 ) and 0.92 (95% CI:-0.09, 1.93) day^-1 , respectively. We found that the rate of infected cells cleared was associated with the reported model in the meta-analysis by including the model type as a categorical variable (p < .01). Joint viral dynamic parameters estimates when parameterizing within-host models have been published for SARS-CoV-2. The reviewed viral dynamic parameters can be used in the same within-host model to understand SARS-CoV-2 replication cycle in infected patients and assess the impact of pharmaceutical interventions.

Dynamical Behavior of a Fractional Order Model for Within-Host SARS-CoV-2

The prime objective of the current study is to propose a novel mathematical framework under the fractional-order derivative, which describes the complex within-host behavior of SARS-CoV-2 by taking into account the effects of memory and carrier. To do this, we formulate a mathematical model of SARS-CoV-2 under the Caputo fractional-order derivative. We derived the conditions for the existence of equilibria of the model and computed the basic reproduction number R0. We used mathematical analysis to establish the proposed model’s local and global stability results. Some numerical resolutions of our theoretical results are presented. The main result of this study is that as the fractional derivative order increases, the approach of the solution to the equilibrium points becomes faster. It is also observed that the value of R0 increases as the value of β and πv increases.

Modeling recapitulates the heterogeneous outcomes of SARS-CoV-2 infection and quantifies the differences in the innate immune and CD8 T-cell responses between patients experiencing mild and severe symptoms

SARS-CoV-2 infection results in highly heterogeneous outcomes, from cure without symptoms to acute respiratory distress and death. Empirical evidence points to the prominent roles of innate immune and CD8 T-cell responses in determining the outcomes. However, how these immune arms act in concert to elicit the outcomes remains unclear. Here, we developed a mathematical model of within-host SARS-CoV-2 infection that incorporates the essential features of the innate immune and CD8 T-cell responses. Remarkably, by varying the strengths and timings of the two immune arms, the model recapitulated the entire spectrum of outcomes realized. Furthermore, model predictions offered plausible explanations of several confounding clinical observations, including the occurrence of multiple peaks in viral load, viral recrudescence after symptom loss, and prolonged viral positivity. We applied the model to analyze published datasets of longitudinal viral load measurements from patients exhibiting diverse outcomes. The model provided excellent fits to the data. The best-fit parameter estimates indicated a nearly 80-fold stronger innate immune response and an over 200-fold more sensitive CD8 T-cell response in patients with mild compared to severe infection. These estimates provide quantitative insights into the likely origins of the dramatic inter-patient variability in the outcomes of SARS-CoV-2 infection. The insights have implications for interventions aimed at preventing severe disease and for understanding the differences between viral variants.

Global Stability of a Humoral Immunity COVID-19 Model with Logistic Growth and Delays

The mathematical modeling and analysis of within-host or between-host coronavirus disease 2019 (COVID-19) dynamics are considered robust tools to support scientific research. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the cause of COVID-19. This paper proposes and investigates a within-host COVID-19 dynamics model with latent infection, the logistic growth of healthy epithelial cells and the humoral (antibody) immune response. Time delays can affect the dynamics of SARS-CoV-2 infection predicted by mathematical models. Therefore, we incorporate four time delays into the model: (i) delay in the formation of latent infected epithelial cells, (ii) delay in the formation of active infected epithelial cells, (iii) delay in the activation of latent infected epithelial cells, and (iv) maturation delay of new SARS-CoV-2 particles. We establish that the model’s solutions are non-negative and ultimately bounded. This confirms that the concentrations of the virus and cells should not become negative or unbounded. We deduce that the model has three steady states and their existence and stability are perfectly determined by two threshold parameters. We use Lyapunov functionals to confirm the global stability of the model’s steady states. The analytical results are enhanced by numerical simulations. The effect of time delays on the SARS-CoV-2 dynamics is investigated. We observe that increasing time delay values can have the same impact as drug therapies in suppressing viral progression. This offers some insight useful to develop a new class of treatment that causes an increase in the delay periods and then may control SARS-CoV-2 replication.

A multicompartment mathematical model based on host immunity for dissecting COVID-19 heterogeneity

The determinants underlying the heterogeneity of coronavirus disease 2019 (COVID-19) remain to be elucidated. To systemically analyze the immunopathogenesis of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection, we built a multicompartment mathematical model based on immunological principles and typical COVID-19-related characteristics. This model integrated the trafficking of immune cells and cytokines among the secondary lymphoid organs, peripheral blood and lungs. Our results suggested that early-stage lymphopenia was related to lymphocyte chemotaxis, while prolonged lymphopenia in critically ill patients was associated with myeloid-derived suppressor cells. Furthermore, our model predicted that insufficient SARS-CoV-2-specific naïve T/B cell pools and ineffective activation of antigen-presenting cells (APCs) would cause delayed immunity activation, resulting in elevated viral load, low immunoglobulin level, etc. Overall, we provided a comprehensive view of the dynamics of host immunity after SARS-CoV-2 infection that enabled us to understand COVID-19 heterogeneity from systemic perspective.

In Silico Evaluation of Paxlovid's Pharmacometrics for SARS-CoV-2: A Multiscale Approach

Paxlovid is a promising, orally bioavailable novel drug for SARS-CoV-2 with excellent safety profiles. Our main goal here is to explore the pharmacometric features of this new antiviral. To provide a detailed assessment of Paxlovid, we propose a hybrid multiscale mathematical approach. We demonstrate that the results of the present in silico evaluation match the clinical expectations remarkably well: on the one hand, our computations successfully replicate the outcome of an actual in vitro experiment; on the other hand, we verify both the sufficiency and the necessity of Paxlovid's two main components (nirmatrelvir and ritonavir) for a simplified in vivo case. Moreover, in the simulated context of our computational framework, we visualize the importance of early interventions and identify the time window where a unit-length delay causes the highest level of tissue damage. Finally, the results' sensitivity to the diffusion coefficient of the virus is explored in detail.