Characterization of SARS-CoV-2 dynamics in the host

Understanding antibody magnitude and durability following vaccination against SARS-CoV-2

Vaccination against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) results in transient antibody response against the spike protein. The individual immune status at the time of vaccination influences the response. Using mathematical models of antibody decay, we determined the dynamics of serum immunoglobulin G (IgG) and serum immunoglobulin A (IgA) over time. Data fitting to longitudinal IgG and IgA titers was used to quantify differences in antibody magnitude and antibody duration among infection-naïve and infection-positive vaccinees. We found that prior infections result in more durable serum IgG and serum IgA responses, with prior symptomatic infections resulting in the most durable serum IgG response and prior asymptomatic infections resulting in the most durable serum IgA response. These findings can guide vaccine boosting schedules.

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.

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.

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.

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.

Minimizing the epidemic final size while containing the infected peak prevalence in SIR systems

Mathematical models are critical to understand the spread of pathogens in a population and evaluate the effectiveness of non-pharmaceutical interventions (NPIs). A plethora of optimal strategies has been recently developed to minimize either the infected peak prevalence ( I P P ) or the epidemic final size ( E F S ). While most of them optimize a simple cost function along a fixed finite-time horizon, no consensus has been reached about how to simultaneously handle the I P P and the E F S , while minimizing the intervention's side effects. In this work, based on a new characterization of the dynamical behaviour of SIR-type models under control actions (including the stability of equilibrium sets in terms of herd immunity), we study how to minimize the E F S while keeping the I P P controlled at any time. A procedure is proposed to tailor NPIs by separating transient from stationary control objectives: the potential benefits of the strategy are illustrated by a detailed analysis and simulation results related to the COVID-19 pandemic.

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.

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

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

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.

The dominant strain of SARS-CoV-2 is a mosaicism

COVID-19 is seriously threatening human health all over the world. A comprehensive understanding of the genetic mechanisms driving the rapid evolution of its pathogen (SARS-CoV-2) is the key to controlling this pandemic. In this study, by comparing the entire genome sequences of SARS-CoV-2 isolates from Asia, Europe and America, and analyzing their phylogenetic histories, we found a lineage derived from a recombination event that likely occurred before March 2020. More importantly, the recombinant offspring has become the dominant strain responsible for more than one-third of the global cases in the pandemic. These results indicated that the recombination might have played a key role in the pandemic of the virus.

Differential evolution and particle swarm optimization against COVID-19

COVID-19 disease, which highly affected global life in 2020, led to a rapid scientific response. Versatile optimization methods found their application in scientific studies related to COVID-19 pandemic. Differential Evolution (DE) and Particle Swarm Optimization (PSO) are two metaheuristics that for over two decades have been widely researched and used in various fields of science. In this paper a survey of DE and PSO applications for problems related with COVID-19 pandemic that were rapidly published in 2020 is presented from two different points of view: 1. practitioners seeking the appropriate method to solve particular problem, 2. experts in metaheuristics that are interested in methodological details, inter comparisons between different methods, and the ways for improvement. The effectiveness and popularity of DE and PSO is analyzed in the context of other metaheuristics used against COVID-19. It is found that in COVID-19 related studies: 1. DE and PSO are most frequently used for calibration of epidemiological models and image-based classification of patients or symptoms, but applications are versatile, even interconnecting the pandemic and humanities; 2. reporting on DE or PSO methodological details is often scarce, and the choices made are not necessarily appropriate for the particular algorithm or problem; 3. mainly the basic variants of DE and PSO that were proposed in the late XX century are applied, and research performed in recent two decades is rather ignored; 4. the number of citations and the availability of codes in various programming languages seems to be the main factors for choosing metaheuristics that are finally used.

Data-driven methods for present and future pandemics: Monitoring, modelling and managing

This survey analyses the role of data-driven methodologies for pandemic modelling and control. We provide a roadmap from the access to epidemiological data sources to the control of epidemic phenomena. We review the available methodologies and discuss the challenges in the development of data-driven strategies to combat the spreading of infectious diseases. Our aim is to bring together several different disciplines required to provide a holistic approach to epidemic analysis, such as data science, epidemiology, and systems-and-control theory. A 3M-analysis is presented, whose three pillars are: Monitoring, Modelling and Managing. The focus is on the potential of data-driven schemes to address three different challenges raised by a pandemic: (i) monitoring the epidemic evolution and assessing the effectiveness of the adopted countermeasures; (ii) modelling and forecasting the spread of the epidemic; (iii) making timely decisions to manage, mitigate and suppress the contagion. For each step of this roadmap, we review consolidated theoretical approaches (including data-driven methodologies that have been shown to be successful in other contexts) and discuss their application to past or present epidemics, such as Covid-19, as well as their potential application to future epidemics.

Current and prospective computational approaches and challenges for developing COVID-19 vaccines

SARS-CoV-2, which causes COVID-19, was first identified in humans in late 2019 and is a coronavirus which is zoonotic in origin. As it spread around the world there has been an unprecedented effort in developing effective vaccines. Computational methods can be used to speed up the long and costly process of vaccine development. Antigen selection, epitope prediction, and toxicity and allergenicity prediction are areas in which computational tools have already been applied as part of reverse vaccinology for SARS-CoV-2 vaccine development. However, there is potential for computational methods to assist further. We review approaches which have been used and highlight additional bioinformatic approaches and PK modelling as in silico methods which may be useful for SARS-CoV-2 vaccine design but remain currently unexplored. As more novel viruses with pandemic potential are expected to arise in future, these techniques are not limited to application to SARS-CoV-2 but also useful to rapidly respond to novel emerging viruses.

Corticosteroid therapy for 2019-nCoV-infected patients: A case series of eight mechanically ventilated patients

High-dose short-term corticosteroid therapy is effective and produces favorable clinical outcome in patients with severe 2019-nCoV infection who are candidates for mechanical ventilation with close monitor/ing for the adverse effect of corticosteroids.

Dynamical characterization of antiviral effects in COVID-19

Mathematical models describing SARS-CoV-2 dynamics and the corresponding immune responses in patients with COVID-19 can be critical to evaluate possible clinical outcomes of antiviral treatments. In this work, based on the concept of virus spreadability in the host, antiviral effectiveness thresholds are determined to establish whether or not a treatment will be able to clear the infection. In addition, the virus dynamic in the host - including the time-to-peak and the final monotonically decreasing behavior - is characterized as a function of the time to treatment initiation. Simulation results, based on nine patient data, show the potential clinical benefits of a treatment classification according to patient critical parameters. This study is aimed at paving the way for the different antivirals being developed to tackle SARS-CoV-2.

Universal features of epidemic models under social distancing guidelines

Social distancing as a form of nonpharmaceutical intervention has been enacted in many countries as a form of mitigating the spread of COVID-19. There has been a large interest in mathematical modeling to aid in the prediction of both the total infected population and virus-related deaths, as well as to aid government agencies in decision making. As the virus continues to spread, there are both economic and sociological incentives to minimize time spent with strict distancing mandates enforced, and/or to adopt periodically relaxed distancing protocols, which allow for scheduled economic activity. The main objective of this study is to reduce the disease burden in a population, here measured as the peak of the infected population, while simultaneously minimizing the length of time the population is socially distanced, utilizing both a single period of social distancing as well as periodic relaxation. We derive a linear relationship among the optimal start time and duration of a single interval of social distancing from an approximation of the classic epidemic SIR model. Furthermore, we see a sharp phase transition region in start times for a single pulse of distancing, where the peak of the infected population changes rapidly; notably, this transition occurs well before one would intuitively expect. By numerical investigation of more sophisticated epidemiological models designed specifically to describe the COVID-19 pandemic, we see that all share remarkably similar dynamic characteristics when contact rates are subject to periodic or one-shot changes, and hence lead us to conclude that these features are universal in epidemic models. On the other hand, the nonlinearity of epidemic models leads to non-monotone behavior of the peak of infected population under periodic relaxation of social distancing policies. This observation led us to hypothesize that an additional single interval social distancing at a proper time can significantly decrease the infected peak of periodic policies, and we verified this improvement numerically. While synchronous quarantine and social distancing mandates across populations effectively minimize the spread of an epidemic over the world, relaxation decisions should not be enacted at the same time for different populations.