Virus Dynamics Model Research Articles

A quantitative model used to compare within-host SARS-CoV-2, MERS-CoV, and SARS-CoV dynamics provides insights into the pathogenesis and treatment of SARS-CoV-2.

The scientific community is focused on developing antiviral therapies to mitigate the impacts of the ongoing novel coronavirus disease 2019 (COVID-19) outbreak. This will be facilitated by improved understanding of viral dynamics within infected hosts. Here, using a mathematical model in combination with published viral load data, we compare within-host viral dynamics of SARS-CoV-2 with analogous dynamics of MERS-CoV and SARS-CoV. Our quantitative analyses using a mathematical model revealed that the within-host reproduction number at symptom onset of SARS-CoV-2 was statistically significantly larger than that of MERS-CoV and similar to that of SARS-CoV. In addition, the time from symptom onset to the viral load peak for SARS-CoV-2 infection was shorter than those of MERS-CoV and SARS-CoV. These findings suggest the difficulty of controlling SARS-CoV-2 infection by antivirals. We further used the viral dynamics model to predict the efficacy of potential antiviral drugs that have different modes of action. The efficacy was measured by the reduction in the viral load area under the curve (AUC). Our results indicate that therapies that block de novo infection or virus production are likely to be effective if and only if initiated before the viral load peak (which appears 2-3 days after symptom onset), but therapies that promote cytotoxicity of infected cells are likely to have effects with less sensitivity to the timing of treatment initiation. Furthermore, combining a therapy that promotes cytotoxicity and one that blocks de novo infection or virus production synergistically reduces the AUC with early treatment. Our unique modeling approach provides insights into the pathogenesis of SARS-CoV-2 and may be useful for development of antiviral therapies.

Estimation of the incubation period of COVID-19 using viral load data

The incubation period, or the time from infection to symptom onset, of COVID-19 has usually been estimated by using data collected through interviews with cases and their contacts. However, this estimation is influenced by uncertainty in the cases’ recall of exposure time. We propose a novel method that uses viral load data collected over time since hospitalization, hindcasting the timing of infection with a mathematical model for viral dynamics. As an example, we used reported data on viral load for 30 hospitalized patients from multiple countries (Singapore, China, Germany, and Korea) and estimated the incubation period. The median, 2.5, and 97.5 percentiles of the incubation period were 5.85 days (95 % CI: 5.05, 6.77), 2.65 days (2.04, 3.41), and 12.99 days (9.98, 16.79), respectively, which are comparable to the values estimated in previous studies. Using viral load to estimate the incubation period might be a useful approach, especially when it is impractical to directly observe the infection event.

Stability Analysis of the Corona Virus (Covid-19) Dynamics SEIR Model in Indonesia

Covid-19 is a type of virus that infects the respiratory tract or is also known as severe acute respiratory syndrome Corona virus-2 (SARS-CoV-2). Researchers through this study were trying to build a mathematical model of the spread of the Covid-19 virus and analyzed the stability of its critical points. This virus dynamic model was built based on the interaction between the suspect group with the exposed group and the interaction with the infected group. The virus spread model in this study consists of two critical points, namely a disease-free critical point and a disease endemic critical point. The two critical points will be stable if they meet the requirements for certain parameter values. Numerical simulations of virus dynamics in Indonesia were carried out using data on the number of susceptible people, the number under monitoring, the number of the infected, the number of cures and the number of deaths due to the virus. These data were obtained from the Ministry of Health of the Republic of Indonesia. Based on the data obtained, it was found that the simulation model of stability reached a critical point in a very long time. Therefore, treatment or vaccines are needed as a step to reduce the dynamics of Covid-19.

The within-host fitness of HIV-1 increases with age in ART-na\xefve HIV-1 subtype C infected children

As the immune system develops with age, children combat infections better. HIV-1, however, targets an activated immune system, potentially rendering children increasingly permissive to HIV-1 infection as they grow. How HIV-1 fitness changes with age in children is unknown. Here, we estimated the within-host basic reproductive ratio, R0, a marker of viral fitness, in HIV-1 subtype C-infected children in India, aged between 84 days and 17 years. We measured serial viral load and CD4 T cell counts in 171 children who initiated first-line ART. For 25 children, regular and frequent measurements provided adequate data points for analysis using a mathematical model of viral dynamics to estimate R0. For the rest, we used CD4 counts for approximate estimation of R0. The viral load decline during therapy was biphasic. The mean lifespans of productively and long-lived infected cells were 1.4 and 27.8 days, respectively. The mean R0 was 1.5 in children aged < 5 years, increased with age, and approached 6.0 at 18 years, close to 5.8 estimated previously for adults. The tolerogenic immune environment thus compromises HIV-1 fitness in young children. Early treatment initiation, when the R0 is small, will likely improve viral control, in addition to suppressing the latent reservoir.

Global sensitivity analysis of a single-cell HBV model for viral dynamics in the liver.

The predictive accuracy of mathematical models representing anything ranging from the meteorological to the biological system profoundly depends on the quality of model parameters derived from experimental data. Hence, robust sensitivity analysis (SA) of these critical model parameters aids in sifting the influential from the negligible out of typically vast parameter regimes, thus illuminating key components of the system under study. We here move beyond traditional local sensitivity analysis to the adoption of global SA techniques. Partial rank correlation coefficient (PRCC) based on Latin hypercube sampling is compared with the variance-based Sobol method. We selected for this SA investigation an infection model for the hepatitis-B virus (HBV) that describes infection dynamics and clearance of HBV in the liver [Murray & Goyal, 2015]. The model tracks viral particles such as the tenacious and nearly ineradicable covalently closed circular DNA (cccDNA) embedded in infected nuclei and an HBV protein known as p36. Our application of these SA methods to the HBV model illuminates, especially over time, the quantitative relationships between cccDNA synthesis rate and p36 synthesis and export. Our results reinforce previous observations that the viral protein, p36, is by far the most influential factor for cccDNA replication. Moreover, both methods are capable of finding crucial parameters of the model. Though the Sobol method is independent of model structure (e.g., linearity and monotonicity) and well suited for SA, our results ensure that LHS-PRCC suffices for SA of a non-linear model if it is monotonic.

A discrete viral infection model with both modes of transmission and distributed delays

The aim of this work is to propose and analyse a discrete virus dynamics model with distributed delays and both modes of transmission, one by virus-to-cell infection and the other by cell-to-cell transfer. In the proposed model, the first distributed delays describes the time needed for infected cells to produce new virions, and the second portrays the time necessary for the newly produced virions to become mature and infectious. In addition, the infection transmission process is modelled by general incidence functions for both modes. Furthermore, we prove that the proposed discrete model has the same dynamics as the corresponding continuous model, such as positivity, boundedness and global behaviours of solutions with no restriction on the time step size. Moreover, numerical simulations are given to illustrate and confirm our main analytical results.

Global Stability and Hopf Bifurcation for a Virus Dynamics Model with General Incidence Rate and Delayed CTL Immune Response

In this work, we investigate an HIV-1 infection model with a general incidence rate and delayed CTL immune response. The model admits three possible equilibria, an infection-free equilibrium E*0, CTL-inactivated infection equilibrium E*1 and CTL-activated infection equilibrium E*2. We prove that in the absence of CTL immune delay, the model has exactly the basic behaviour model, for all positive intracellular delays, the global dynamics are determined by two threshold parameters R0 and R1, if R0 ≤ 1, E*0 is globally asymptotically stable, if R1 ≤ 1 R0, E*1 is globally asymptotically stable and if R1 >1, E*2 is globally asymptotically stable. But if the CTL immune response delay is different from zero, then the behaviour of the model at E*2 changes completely, although R1 > 1, a Hopf bifurcation at E*2 is established. In the end, we present some numerical simulations.

Examining HIV progression mechanisms via mathematical approaches

&#x0D; &#x0D; &#x0D; The progression of HIV infection to AIDS is unclear and under examined. Many mechanisms have been proposed, including a decline in immune response, increase in replication rate, involution of the thymus, syncytium inducing capacity, activation of the latently infected cell pool, chronic activation of the immune system, and the ability of the virus to infect other immune system cells. The significance of each mechanism in combination has not been studied. We develop a simple HIV viral dynamics model incorporating proposed mechanisms as parameters that are allowed to vary. In the entire parameter space, we derive two formulae for the basic reproduction number (R0) by considering the infection starting with a single infected CD4 T cell and a single virion, respectively. We show that both formulae are equivalent. We derive analytical conditions for the occurrence of backward and forward bifurcations. To investigate the influence of the proposed mechanisms to the HIV progression, we perform uncertainty and sensitivity analysis for all parameters and conduct a bifurcation analysis on all parameters that are shown to be significant, in combination, to explore various HIV/AIDS progression dynamics.&#x0D; &#x0D; &#x0D;

Approximate analytical solution to a model of virus dynamics in computer network

Approximate analytical solution to a model of virus dynamics in computer network

On the generalized Chikungunya virus dynamics model with distributed time delays

In this paper, a stability analysis of a general nonlinear Chikungunya virus dynamics model is presented. Two kinds of infected cells, namely latently infected and actively infected are incorporated into the model. It is assumed that, the incidence rate of infection as well as the production, removal and proliferation rates of all compartments are modeled by general nonlinear functions that satisfy sufficient conditions. The model contains two distributed time delays. The nonnegativity and boundedness of the solutions of the model are investigated. Constructions of suitable Lyapunov functionals are established to prove the global stability of the steady states of the model. Numerical simulations are performed to confirm the validity of the established theoretical results.

What drives the dynamics of HBV RNA during treatment?

Hepatitis B virus RNA (HBV RNA)-containing particles are encapsidated pre-genomic RNA (pgRNA) detectable in chronically infected patients in addition to virions (HBV DNA) that have been suggested as a marker of the treatment efficacy. This makes promising the use of core protein allosteric modulators, such as RG7907, which disrupt the nucleocapsid assembly and profoundly reduce HBV RNA. Here, we developed a multiscale model of HBV extending the standard viral dynamic models to analyse the kinetics of HBV DNA and HBV RNA in 35 patients treated with RG7907 for 28days. We compare the predictions with those obtained in patients treated with the nucleotide analog tenofovir. RG7907 blocked 99.3% of pgRNA encapsidation (range: 92.1%-99.9%) which led to a decline of both HBV DNA and HBV RNA. As a consequence of its mode of action, the first phase of decline of HBV RNA was rapid, uncovering the clearance of viral particles with half-life of 45min. In contrast, HBV DNA decline was predicted to be less rapid, due to the continuous secretion of already formed viral capsids (t1/2 =17±6h). After few days, both markers declined at the same rate, which was attributed to the loss of infected cells (t1/2 ≅6±0.8days). By blocking efficiently RNA reverse transcription but not its encapsidation, nucleotide analog in contrast was predicted to lead to a transient accumulation of HBV RNA both intracellularly and extracellularly. The model brings a conceptual framework for understanding the differences between HBV DNA and HBV RNA dynamics. Integration of HBV RNA in viral dynamic models may be helpful to better quantify the treatment effect, especially in viral-suppressed patients where HBV DNA is no longer detectable.

Mathematical modelling of multiple target cells with delay

Target cells contagion has sparked the necessity of a multiple target cell model with chronic infection and intracellular delay (MTC-CI-ID). This paper seeks to advance a viral dynamical model with multiple target cells and corroborate the global stability of their steady states. Hence, the affiliation of the virus with two classes of target cells, CD4 + Tcells and macrophage. The time delay amidst viral entry and the output of virions were intimated and the basic reproductive number was procured, as the long term behavior of the model and less than unity. The contagious free equilibrium E0 was unveiled as locally and globally asymptotically stable. The conditions of an infected CD4 + Tcell and macrophage on viral production were engaged. It was ascertained that CD4 + Tcell accounts for larger amounts of virions in the blood as per macrophage cells. Hence, varying time delay has no impact on peak viral levels, but only shelves the viral peaking time. The adopted model has unrestrained bearing on HIV-1 therapy.

Probability of Disease Extinction or Outbreak in a Stochastic Epidemic Model for West Nile Virus Dynamics in Birds.

Thresholds for disease extinction provide essential information for the prevention and control of diseases. In this paper, a stochastic epidemic model, a continuous-time Markov chain, for the transmission dynamics of West Nile virus in birds is developed based on the assumptions of its analogous deterministic model. The branching process is applied to derive the extinction threshold for the stochastic model and conditions for disease extinction or persistence. The probability of disease extinction computed from the branching process is shown to be in good agreement with the probability approximated from numerical simulations. The disease dynamics of both models are compared to ascertain the effect of demographic stochasticity on West Nile virus dynamics. Analytical and numerical results show differences in model predictions and asymptotic dynamics between stochastic and deterministic models that are crucial for the prevention of disease outbreaks. It is found that there is a high probability of disease extinction if the disease emerges from exposed mosquitoes unlike if it emerges from infectious mosquitoes and birds. Finite-time to disease extinction is estimated using sample paths and it is shown that the epidemic duration is shortest if the disease is introduced by exposed mosquitoes.

Dynamics of an oncolytic virus model

An ODE model for oncolytic virus dynamics with four parameters is discussed. Although it is hard to obtain the explicit expressions of coordinates of equilibria, we find distribution of equilibria qualitatively, and obtain the exact number of equilibria and their qualitative properties. We further give a complete analysis on local bifurcations such as saddle–node, Bogdanov–Takens, and Hopf bifurcations. Resultant elimination is applied to decompose the semi-algebraic varieties of Lyapunov quantities under the restriction of biological meaning, and we show that the weak focus is of order at most 3.

Efficient Methods for Parameter Estimation of Ordinary and Partial Differential Equation Models of Viral Hepatitis Kinetics.

Parameter estimation in mathematical models that are based on differential equations is known to be of fundamental importance. For sophisticated models such as age-structured models that simulate biological agents, parameter estimation that addresses all cases of data points available presents a formidable challenge and efficiency considerations need to be employed in order for the method to become practical. In the case of age-structured models of viral hepatitis dynamics under antiviral treatment that deal with partial differential equations, a fully numerical parameter estimation method was developed that does not require an analytical approximation of the solution to the multiscale model equations, avoiding the necessity to derive the long-term approximation for each model. However, the method is considerably slow because of precision problems in estimating derivatives with respect to the parameters near their boundary values, making it almost impractical for general use. In order to overcome this limitation, two steps have been taken that significantly reduce the running time by orders of magnitude and thereby lead to a practical method. First, constrained optimization is used, letting the user add constraints relating to the boundary values of each parameter before the method is executed. Second, optimization is performed by derivative-free methods, eliminating the need to evaluate expensive numerical derivative approximations. The newly efficient methods that were developed as a result of the above approach are described for hepatitis C virus kinetic models during antiviral therapy. Illustrations are provided using a user-friendly simulator that incorporates the efficient methods for both the ordinary and partial differential equation models.

Comparison of empirical and dynamic models for HIV viral load rebound after treatment interruption.

To compare empirical and mechanistic modeling approaches for describing HIV-1 RNA viral load trajectories after antiretroviral treatment interruption and for identifying factors that predict features of viral rebound process. We apply and compare two modeling approaches in analysis of data from 346 participants in six AIDS Clinical Trial Group studies. From each separate analysis, we identify predictors for viral set points and delay in rebound. Our empirical model postulates a parametric functional form whose parameters represent different features of the viral rebound process, such as rate of rise and viral load set point. The viral dynamics model augments standard HIV dynamics models-a class of mathematical models based on differential equations describing biological mechanisms-by including reactivation of latently infected cells and adaptive immune response. We use Monolix, which makes use of a Stochastic Approximation of the Expectation-Maximization algorithm, to fit non-linear mixed effects models incorporating observations that were below the assay limit of quantification. Among the 346 participants, the median age at treatment interruption was 42. Ninety-three percent of participants were male and sixty-five percent, white non-Hispanic. Both models provided a reasonable fit to the data and can accommodate atypical viral load trajectories. The median set points obtained from two approaches were similar: 4.44 log10 copies/mL from the empirical model and 4.59 log10 copies/mL from the viral dynamics model. Both models revealed that higher nadir CD4 cell counts and ART initiation during acute/recent phase were associated with lower viral set points and identified receiving a non-nucleoside reverse transcriptase inhibitor (NNRTI)-based pre-ATI regimen as a predictor for a delay in rebound. Although based on different sets of assumptions, both models lead to similar conclusions regarding features of viral rebound process.

Early exposure to broadly neutralizing antibodies may trigger a dynamical switch from progressive disease to lasting control of SHIV infection.

Antiretroviral therapy (ART) for HIV-1 infection is life-long. Stopping therapy typically leads to the reignition of infection and progressive disease. In a major breakthrough, recent studies have shown that early initiation of ART can lead to sustained post-treatment control of viremia, raising hopes of long-term HIV-1 remission. ART, however, elicits post-treatment control in a small fraction of individuals treated. Strikingly, passive immunization with broadly neutralizing antibodies (bNAbs) of HIV-1 early in infection was found recently to elicit long-term control in a majority of SHIV-infected macaques, suggesting that HIV-1 remission may be more widely achievable. The mechanisms underlying the control elicited by bNAb therapy, however, remain unclear. Untreated infection typically leads to progressive disease. We hypothesized that viremic control represents an alternative but rarely realized outcome of the infection and that early bNAb therapy triggers a dynamical switch to this outcome. To test this hypothesis, we constructed a model of viral dynamics with bNAb therapy and applied it to analyse clinical data. The model fit quantitatively the complex longitudinal viral load data from macaques that achieved lasting control. The model predicted, consistently with our hypothesis, that the underlying system exhibited bistability, indicating two potential outcomes of infection. The first had high viremia, weak cytotoxic effector responses, and high effector exhaustion, marking progressive disease. The second had low viremia, strong effector responses, and low effector exhaustion, indicating lasting viremic control. Further, model predictions suggest that early bNAb therapy elicited lasting control via pleiotropic effects. bNAb therapy lowers viremia, which would also limit immune exhaustion. Simultaneously, it can improve effector stimulation via cross-presentation. Consequently, viremia may resurge post-therapy, but would encounter a primed effector population and eventually get controlled. ART suppresses viremia but does not enhance effector stimulation, explaining its limited ability to elicit post-treatment control relative to bNAb therapy.

Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells

In this paper, a delayed viral dynamical model that considers two different transmission methods of the virus and apoptosis of bystander cells is proposed and investigated. The basic reproductive numberR0of the model is derived. Based on the basic reproductive number, we prove that the disease-free equilibriumE0is globally asymptotically stable forR0&lt;1by constructing suitable Lyapunov functional. ForR0&gt;1, by regarding the time delay as bifurcation parameter, the existence of local Hopf bifurcation is investigated. The results show that time delay can change the stability of endemic equilibrium and cause periodic oscillations. Finally, we give some numerical simulations to illustrate the theoretical findings.

Inferred duration of infectious period of SARS-CoV-2: rapid scoping review and analysis of available evidence for asymptomatic and symptomatic COVID-19 cases

ObjectivesOur objective was to review the literature on the inferred duration of the infectious period of COVID-19, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus, and provide an...

Viral Infection Dynamics Model Based on a Markov Process with Time Delay between Cell Infection and Progeny Production

Many human virus infections including those with the human immunodeficiency virus type 1 (HIV) are initiated by low numbers of founder viruses. Therefore, random effects have a strong influence on the initial infection dynamics, e.g., extinction versus spread. In this study, we considered the simplest (so-called, ‘consensus’) virus dynamics model and incorporated a delay between infection of a cell and virus progeny release from the infected cell. We then developed an equivalent stochastic virus dynamics model that accounts for this delay in the description of the random interactions between the model components. The new model is used to study the statistical characteristics of virus and target cell populations. It predicts the probability of infection spread as a function of the number of transmitted viruses. A hybrid algorithm is suggested to compute efficiently the system dynamics in state space domain characterized by the mix of small and large species densities.