Within-host Virus Research Articles

Differences in virus and immune dynamics for SARS-CoV-2 Delta and Omicron infections by age and vaccination histories

Vaccination against COVID-19 was integral to controlling the pandemic that persisted with the continuous emergence of SARS-CoV-2 variants. Using a mathematical model describing SARS-CoV-2 within-host infection dynamics, we estimate differences in virus and immunity due to factors of infecting variant, age, and vaccination history (vaccination brand, number of doses and time since vaccination). We fit our model in a Bayesian framework to upper respiratory tract viral load measurements obtained from cases of Delta and Omicron infections in Singapore, of whom the majority only had one nasopharyngeal swab measurement. With this dataset, we are able to recreate similar trends in URT virus dynamics observed in past within-host modelling studies fitted to longitudinal patient data.We found that Omicron had higher R0,within values than Delta, indicating greater initial cell-to-cell spread of infection within the host. Moreover, heterogeneities in infection dynamics across patient subgroups could be recreated by fitting immunity-related parameters as vaccination history-specific, with or without age modification. Our model results are consistent with the notion of immunosenescence in SARS-CoV-2 infection in elderly individuals, and the issue of waning immunity with increased time since last vaccination. Lastly, vaccination was not found to subdue virus dynamics in Omicron infections as well as it had for Delta infections.This study provides insight into the influence of vaccine-elicited immunity on SARS-CoV-2 within-host dynamics, and the interplay between age and vaccination history. Furthermore, it demonstrates the need to disentangle host factors and changes in pathogen to discern factors influencing virus dynamics. Finally, this work demonstrates a way forward in the study of within-host virus dynamics, by use of viral load datasets including a large number of patients without repeated measurements.

Mathematical analysis of a within-host dengue virus dynamics model with adaptive immunity using Caputo fractional-order derivatives

AbstractDengue fever poses a significant global health threat, with over 50 million annual infections spanning more than 100 countries. Given the absence of a specific treatment, medical intervention primarily targets symptom alleviation. The present study utilizes a Caputo-type fractional-order derivative operator to investigate and analyze the dynamics of dengue virus spread within a host with adaptive immune responses. The developed model describes and analyzes the dynamics of immune cells, free dengue particles, infected monocytes, and susceptible monocytes in the presence of cytotoxic T-Lymphocytes. A range of analytical methods is employed to probe the fractional-order within-host model. The application of the generalized mean value theorem aids in investigating the model’s solutions, employing positivity and boundedness theory. Furthermore, the Banach fixed-point approach is utilized to establish the existence and uniqueness of solutions. Employing the normalized forward sensitivity approach, the fractional-order system’s response to various model parameters is scrutinized. The study reveals that the dynamics of the viral model are significantly influenced by the transmission rate and parameters representing adaptive immune responses. Numerical simulations underscore the critical role of transmission rates and adaptive immune responses in the model. Additionally, the study examines the impact of memory on the density of susceptible monocytes, infected monocytes, free dengue particles, and immune cells to optimize immune responses. Through simulations, the study illustrates the influence of memory on immune dynamics.

A nonlinear mathematical model for exploring the optimal cost-effective therapeutic strategies and within-host viral infections spread dynamics

This study presents a nonlinear mathematical model to capture the constant rates of three different target cells class-specific drug therapeutic measures (namely, drug therapy for blocking new infections, drug therapy for actively infected cells, and drug therapy inhibiting viral production) for the dynamics of within-host viral infections with multiple classes of target cells. The threshold quantity of the control reproduction number of the model is calculated. The global asymptotic behaviours of the model around the steady states are investigated in terms of the control reproduction number. Moreover, the model is extended to an optimal control problem by considering the three constant parameters for drug therapeutic measures as time-dependent control variables. Qualitative analysis of the proposed model is conducted using optimal control theory. Numerical solutions of the derived optimality system are sought to illustrate the efficacies of different combination strategies consisting of using at least any of the three target cells’ class-specific optimal controls in reducing the burden of within-host virus transmission and spread at a minimum cost. Cost-effectiveness analysis is further carried out to determine the least costly and most effective intervention strategy. The cost analysis reveals that the use of only target cells class-specific drug therapy control for blocking new infections is the most cost-effective control strategy.

The effect of model structure and data availability on Usutu virus dynamics at three biological scales.

Understanding the epidemiology of emerging pathogens, such as Usutu virus (USUV) infections, requires systems investigation at each scale involved in the host-virus transmission cycle, from individual bird infections, to bird-to-vector transmissions, and to USUV incidence in bird and vector populations. For new pathogens field data are sparse, and predictions can be aided by the use of laboratory-type inoculation and transmission experiments combined with dynamical mathematical modelling. In this study, we investigated the dynamics of two strains of USUV by constructing mathematical models for the within-host scale, bird-to-vector transmission scale and vector-borne epidemiological scale. We used individual within-host infectious virus data and per cent mosquito infection data to predict USUV incidence in birds and mosquitoes. We addressed the dependence of predictions on model structure, data uncertainty and experimental design. We found that uncertainty in predictions at one scale change predicted results at another scale. We proposed in silico experiments that showed that sampling every 12 hours ensures practical identifiability of the within-host scale model. At the same time, we showed that practical identifiability of the transmission scale functions can only be improved under unrealistically high sampling regimes. Instead, we proposed optimal experimental designs and suggested the types of experiments that can ensure identifiability at the transmission scale and, hence, induce robustness in predictions at the epidemiological scale.

A Model of Hepatitis B Viral Dynamics with Delays

Hepatitis B is a liver disease caused by the human hepatitis B virus (HBV). Mathematical models help further the understanding of the processes involved and help make predictions. The basic reproduction number, R0, is an index that predicts whether the disease will be chronic or not. This is the single most-important information that a mathematical model can give. Within-host virus processes involve delays. We study two within-host hepatitis B virus infection models without and with delay. One is a standard one, and the other considering additional processes and with two delays is new. We analyze the basic reproduction number and alternative threshold indices. The values of R0 and the alternative indices change depending on the model. All these indices predict whether the infection will persist or not, but they do not give the same rate of growth of the infection when it is starting. Therefore, the choice of the model is very important in establishing whether the infection is chronic or not and how fast it initially grows. We analyze these indices to see how to decrease their value. We study the effect of adding delays and how the threshold indices depend on how the delays are included. We do this by studying the local asymptotic stability of the disease-free equilibrium or by using an equivalent method. We show that, for some models, the indices do not change by introducing delays, but they change when the delays are introduced differently. Numerical simulations are presented to confirm the results. Finally, some conclusions are presented.

Mathematical modeling of the effect of immunosuppressive therapy on within-host Ebola virus disease dynamics

Mathematical modeling of the effect of immunosuppressive therapy on within-host Ebola virus disease dynamics

A fractional-order nonlinear model for a within-host chikungunya virus dynamics with adaptive immunity using Caputo derivative operator

The study of within-host dynamics of viral infection is a vital process of understanding how healthy cells in the body are affected by viral foreign bodies and how body immunity responds to such changes. This paper presents and analyses the dynamics of a within-host Chikungunya virus transmission with adaptive immune responses using a fractional-order derivative operator of the Caputo type. The formulated model describes the interaction of uninfected cells, infected cells and viral particles in the presence of Cytotoxic T-Lymphocytes and antibody immune responses. Several analytical methods are employed to analyse the fractional-order within-host model. Positivity and boundedness theory are used to investigate the properties of solutions of the model via the generalized mean value theorem approach. The existence and uniqueness of solutions are examined using the Banach fixed point method. The normalized forward sensitivity method determines how different model parameters affect the fractional-order system. It was shown that transmission rate and parameters representing adaptive immune responses played a significant role in the Chikungunya virus model’s dynamics. Further, the time-dependent optimal control fractional-order model is analysed to optimize the performance of adaptive immune responses using the optimal control theory approach made popular by Pontryagin’s maximum principle. Simulations are performed to visualize the theoretical results and show the influence of memory on the trajectories of concentrations of uninfected cells, infected cells, viral particles, Cytotoxic T-Lymphocytes and antibodies.

Direct and indirect viral associations predict coexistence in wild plant virus communities

Viruses are a vastly underestimated component of biodiversity that occur as diverse communities across hierarchical scales from the landscape level to individual hosts. The integration of community ecology with disease biology is a powerful, novel approach that can yield unprecedented insights into the abiotic and biotic drivers of pathogen community assembly. Here, we sampled wild plant populations to characterize and analyze the diversity and co-occurrence structure of within-host virus communities and their predictors. Our results show that these virus communities are characterized by diverse, non-random coinfections. Using a novel graphical network modeling framework, we demonstrate how environmental heterogeneity influences the network of virus taxa and how the virus co-occurrence patterns can be attributed to non-random, direct statistical virus-virus associations. Moreover, we show that environmental heterogeneity changed virus association networks, especially through their indirect effects. Our results highlight a previously underestimated mechanism of how environmental variability can influence disease risks by changing associations between viruses that are conditional on their environment.

Semi-infectious particles contribute substantially to influenza virus within-host dynamics when infection is dominated by spatial structure.

Influenza is an ribonucleic acid virus with a genome that comprises eight segments. Experiments show that the vast majority of virions fail to express one or more gene segments and thus cannot cause a productive infection on their own. These particles, called semi-infectious particles (SIPs), can induce virion production through complementation when multiple SIPs are present in an infected cell. Previous within-host influenza models did not explicitly consider SIPs and largely ignore the potential effects of coinfection during virus infection. Here, we constructed and analyzed two distinct models explicitly keeping track of SIPs and coinfection: one without spatial structure and the other implicitly considering spatial structure. While the model without spatial structure fails to reproduce key aspects of within-host influenza virus dynamics, we found that the model implicitly considering the spatial structure of the infection process makes predictions that are consistent with biological observations, highlighting the crucial role that spatial structure plays during an influenza infection. This model predicts two phases of viral growth prior to the viral peak: a first phase driven by fully infectious particles at the initiation of infection followed by a second phase largely driven by coinfections of fully infectious particles and SIPs. Fitting this model to two sets of data, we show that SIPs can contribute substantially to viral load during infection. Overall, the model provides a new interpretation of the in vivo exponential viral growth observed in experiments and a mechanistic explanation for why the production of large numbers of SIPs does not strongly impede viral growth. Being simple and predictive, our model framework serves as a useful tool to understand coinfection dynamics in spatially structured acute viral infections.

Mathematical modelling of within-host Chikungunya virus dynamics with adaptive immune response

Mathematical modelling of within-host Chikungunya virus dynamics with adaptive immune response

Influenza A virus undergoes compartmentalized replication in vivo dominated by stochastic bottlenecks

Transmission of influenza A viruses (IAV) between hosts is subject to numerous physical and biological barriers that impose genetic bottlenecks, constraining viral diversity and adaptation. The bottlenecks within hosts and their potential impacts on evolutionary pathways taken during infection are poorly understood. To address this, we created highly diverse IAV libraries bearing molecular barcodes on two gene segments, enabling high-resolution tracking and quantification of unique virus lineages within hosts. Here we show that IAV infection in lungs is characterized by multiple within-host bottlenecks that result in “islands” of infection in lung lobes, each with genetically distinct populations. We perform site-specific inoculation of barcoded IAV in the upper respiratory tract of ferrets and track viral diversity as infection spreads to the trachea and lungs. We detect extensive compartmentalization of discrete populations within lung lobes. Bottleneck events and localized replication stochastically sample individual viruses from the upper respiratory tract or the trachea that become the dominant genotype in a particular lobe. These populations are shaped strongly by founder effects, with limited evidence for positive selection. The segregated sites of replication highlight the jackpot-style events that contribute to within-host influenza virus evolution and may account for low rates of intrahost adaptation.

Sensitivity Analysis in an Immuno-Epidemiological Vector-Host Model.

Sensitivity Analysis (SA) is a useful tool to measure the impact of changes in model parameters on the infection dynamics, particularly to quantify the expected efficacy of disease control strategies. SA has only been applied to epidemic models at the population level, ignoring the effect of within-host virus-with-immune-system interactions on the disease spread. Connecting the scales from individual to population can help inform drug and vaccine development. Thus the value of understanding the impact of immunological parameters on epidemiological quantities. Here we consider an age-since-infection structured vector-host model, in which epidemiological parameters are formulated as functions of within-host virus and antibody densities, governed by an ODE system. We then use SA for these immuno-epidemiological models to investigate the impact of immunological parameters on population-level disease dynamics such as basic reproduction number, final size of the epidemic or the infectiousness at different phases of an outbreak. As a case study, we consider Rift Valley Fever Disease utilizing parameter estimations from prior studies. SA indicates that 1% increase in within-host pathogen growth rate can lead up to 8% increase in mathcal R_0, up to 1 % increase in steady-state infected host abundance, and up to 4% increase in infectiousness of hosts when the reproduction number mathcal R_0 is larger than one. These significant increases in population-scale disease quantities suggest that control strategies that reduce the within-host pathogen growth can be important in reducing disease prevalence.

Dynamics of a Within-Host Virus Infection Model with Multiple Pathways: Stability Switch and Global Stability

In this paper, we consider an HIV infection model with virus-to-cell infection, cell-to-cell transmission, intracellular delay and mitosis of uninfected cells. The basic reproduction number is calculated by using the method of the next generation matrix. By comparison arguments, it is proved that when the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. When the basic reproduction number is greater than unity, the existence of Hopf bifurcation and stability switch at the chronic-infection equilibrium of the model with or without intracellular delay is established. Further, by constructing Lyapunov functionals, sufficient conditions are obtained for the global asymptotic stability of the chronic-infection equilibrium when the cell-to-cell transmission is negligible. Numerical simulations are carried out to illustrate the main theoretical results. The normal form is calculated to determine the bifurcation direction and stability, as well as amplitude and period of bifurcating periodic solutions when the intracellular delay is absent.

Distinct patterns of within-host virus populations between two subgroups of human respiratory syncytial virus

Human respiratory syncytial virus (RSV) is a major cause of lower respiratory tract infection in young children globally, but little is known about within-host RSV diversity. Here, we characterised within-host RSV populations using deep-sequencing data from 319 nasopharyngeal swabs collected during 2017–2020. RSV-B had lower consensus diversity than RSV-A at the population level, while exhibiting greater within-host diversity. Two RSV-B consensus sequences had an amino acid alteration (K68N) in the fusion (F) protein, which has been associated with reduced susceptibility to nirsevimab (MEDI8897), a novel RSV monoclonal antibody under development. In addition, several minor variants were identified in the antigenic sites of the F protein, one of which may confer resistance to palivizumab, the only licensed RSV monoclonal antibody. The differences in within-host virus populations emphasise the importance of monitoring for vaccine efficacy and may help to explain the different prevalences of monoclonal antibody-escape mutants between the two subgroups.

Mathematical analysis and optimal control for Chikungunya virus with two routes of infection with nonlinear incidence rate

Chikungunya fever, caused by Chikungunya virus (CHIKV) and transmitted to humans by infected Aedes mosquitoes, has posed a global threat in several countries. In this paper, we investigated a modified within-host Chikungunya virus (CHIKV) infection model with antibodies where two routes of infection are considered. In a first step, the basic reproduction number [Formula: see text] was calculated and the local and global stability analysis of the steady states is carried out using the local linearization and the Lyapunov method. It is proven that the CHIKV-free steady-state [Formula: see text] is globally asymptotically stable when [Formula: see text], and the infected steady-state [Formula: see text] is globally asymptotically stable when [Formula: see text]. In a second step, we applied an optimal strategy in order to optimize the infected compartment and to maximize the uninfected one. For this, we formulated a nonlinear optimal control problem. Existence of the optimal solution was discussed and characterized using some adjoint variables. Thus, an algorithm based on competitive Gauss–Seidel-like implicit difference method was applied in order to resolve the optimality system. The theoretical results are confirmed by some numerical simulations.

Within-host evolutionary dynamics of seasonal and pandemic human influenza A viruses in young children.

The evolution of influenza viruses is fundamentally shaped by within-host processes. However, the within-host evolutionary dynamics of influenza viruses remain incompletely understood, in part because most studies have focused on infections in healthy adults based on single timepoint data. Here, we analyzed the within-host evolution of 82 longitudinally sampled individuals, mostly young children, infected with A/H1N1pdm09 or A/H3N2 viruses between 2007 and 2009. For A/H1N1pdm09 infections during the 2009 pandemic, nonsynonymous minority variants were more prevalent than synonymous ones. For A/H3N2 viruses in young children, early infection was dominated by purifying selection. As these infections progressed, nonsynonymous variants typically increased in frequency even when within-host virus titers decreased. Unlike the short-lived infections of adults where de novo within-host variants are rare, longer infections in young children allow for the maintenance of virus diversity via mutation-selection balance creating potentially important opportunities for within-host virus evolution.

A diffusive virus model with a fixed intracellular delay and combined drug treatments.

The method of administration of an effective drug treatment to eradicate viruses within a host is an important issue in studying viral dynamics. Overuse of a drug can lead to deleterious side effects, and overestimating the efficacy of a drug can result in failure to treat infection. In this study, we proposed a reaction-diffusion within-host virus model which incorporated information regarding spatial heterogeneity, drug treatment, and the intracellular delay to produce productively infected cells and viruses. We also calculated the basic reproduction number [Formula: see text] under the assumptions of spatial heterogeneity. We have shown that the infection-free periodic solution is globally asymptotically stable when [Formula: see text], whereas when [Formula: see text] there is an infected periodic solution and the infection is uniformly persistent. By conducting numerical simulations, we also revealed the effects of various parameters on the value of [Formula: see text]. First, we showed that the dependence of [Formula: see text] on the intracellular delay could be monotone or non-monotone, depending on the death rate of infected cells in the immature stage. Second, we found that the mobility of infected cells or virions could facilitate the virus clearance. Third, we found that the spatial fragmentation of the virus environment enhanced viral infection. Finally, we showed that the combination of spatial heterogeneity and different sets of diffusion rates resulted in complicated viral dynamic outcomes.

Detection of significant antiviral drug effects on COVID-19 with reasonable sample sizes in randomized controlled trials: A modeling study.

Development of an effective antiviral drug for Coronavirus Disease 2019 (COVID-19) is a global health priority. Although several candidate drugs have been identified through in vitro and in vivo models, consistent and compelling evidence from clinical studies is limited. The lack of evidence from clinical trials may stem in part from the imperfect design of the trials. We investigated how clinical trials for antivirals need to be designed, especially focusing on the sample size in randomized controlled trials. A modeling study was conducted to help understand the reasons behind inconsistent clinical trial findings and to design better clinical trials. We first analyzed longitudinal viral load data for Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) without antiviral treatment by use of a within-host virus dynamics model. The fitted viral load was categorized into 3 different groups by a clustering approach. Comparison of the estimated parameters showed that the 3 distinct groups were characterized by different virus decay rates (p-value < 0.001). The mean decay rates were 1.17 d-1 (95% CI: 1.06 to 1.27 d-1), 0.777 d-1 (0.716 to 0.838 d-1), and 0.450 d-1 (0.378 to 0.522 d-1) for the 3 groups, respectively. Such heterogeneity in virus dynamics could be a confounding variable if it is associated with treatment allocation in compassionate use programs (i.e., observational studies). Subsequently, we mimicked randomized controlled trials of antivirals by simulation. An antiviral effect causing a 95% to 99% reduction in viral replication was added to the model. To be realistic, we assumed that randomization and treatment are initiated with some time lag after symptom onset. Using the duration of virus shedding as an outcome, the sample size to detect a statistically significant mean difference between the treatment and placebo groups (1:1 allocation) was 13,603 and 11,670 (when the antiviral effect was 95% and 99%, respectively) per group if all patients are enrolled regardless of timing of randomization. The sample size was reduced to 584 and 458 (when the antiviral effect was 95% and 99%, respectively) if only patients who are treated within 1 day of symptom onset are enrolled. We confirmed the sample size was similarly reduced when using cumulative viral load in log scale as an outcome. We used a conventional virus dynamics model, which may not fully reflect the detailed mechanisms of viral dynamics of SARS-CoV-2. The model needs to be calibrated in terms of both parameter settings and model structure, which would yield more reliable sample size calculation. In this study, we found that estimated association in observational studies can be biased due to large heterogeneity in viral dynamics among infected individuals, and statistically significant effect in randomized controlled trials may be difficult to be detected due to small sample size. The sample size can be dramatically reduced by recruiting patients immediately after developing symptoms. We believe this is the first study investigated the study design of clinical trials for antiviral treatment using the viral dynamics model.

Stability of an HTLV-HIV coinfection model with multiple delays and CTL-mediated immunity

In the literature, several mathematical models have been formulated and developed to describe the within-host dynamics of either human immunodeficiency virus (HIV) or human T-lymphotropic virus type I (HTLV-I) monoinfections. In this paper, we formulate and analyze a novel within-host dynamics model of HTLV-HIV coinfection taking into consideration the response of cytotoxic T lymphocytes (CTLs). The uninfected mathrm{CD} 4^{+}mathrm{T} cells can be infected via HIV by two mechanisms, free-to-cell and infected-to-cell. On the other hand, the HTLV-I has two modes for transmission, (i) horizontal, via direct infected-to-cell touch, and (ii) vertical, by mitotic division of active HTLV-infected cells. It is well known that the intracellular time delays play an important role in within-host virus dynamics. In this work, we consider six types of distributed-time delays. We investigate the fundamental properties of solutions. Then, we calculate the steady states of the model in terms of threshold parameters. Moreover, we study the global stability of the steady states by using the Lyapunov method. We conduct numerical simulations to illustrate and support our theoretical results. In addition, we discuss the effect of multiple time delays on stability of the steady states of the system.

The threshold for a stochastic within-host CHIKV virus model with saturated incidence rate

This paper deals with stochastic Chikungunya (CHIKV) virus model along with saturated incidence rate. We show that there exists a unique global positive solution and also we obtain the conditions for the disease to be extinct. We also discuss about the existence of a unique ergodic stationary distribution of the model, through a suitable Lyapunov function. The stationary distribution validates the occurrence of disease; through that, we find the threshold value for prevail and disappear of disease within host. With the help of numerical simulations, we validate the stochastic reproduction number [Formula: see text] as stated in our theoretical findings.