Virus Dynamics Model Research Articles

Stability dynamics of a delayed generalized Chikungunya virus infection model

In this paper, a general nonlinear Chikungunya virus (CHIKV) dynamics model is formulated and analyzed. We assume that, the production, removal and proliferation rates of all compartments as well as the incidence rate of infection are modeled by general nonlinear functions that satisfy a set of reasonable conditions. The model is incorporated by two types of discrete time delays. We prove the nonnegativity and boundedness of the solutions of the model. We established the global stability of the steady states of the model by constructing suitable Lyapunov functionals. The numerical simulations are performed to illustrate our theoretical results. The effect of time delay on the virus dynamics is studied.

Stability preserving NSFD scheme for a general virus dynamics model with antibody and cell-mediated responses

Abstract Nonstandard finite difference (NSFD) is one of the efficient computational methods that has been used to discretize various viral infection models. In this paper we present a NSFD scheme for a virus dynamics model with antibody and cell-mediated responses. Two types of infected cells are incorporated into the model, namely latently infected and actively infected cells. The incidence rate of infection as well as the production and removal rates of all compartments are modeled by general nonlinear functions. We prove that NSFD preserves the positivity and boundedness of the solutions of the model. Based on four threshold parameters the existence of five equilibria is established. We perform global stability of all equilibria of the model by using Lyapunov approach. Numerical simulations are carried out to illustrate our theoretical results. A comparison between NSFD method and Runge-Kutta method is presented.

A theoretical framework for transitioning from patient-level to population-scale epidemiological dynamics: influenza A as a case study.

Multi-scale epidemic forecasting models have been used to inform population-scale predictions with within-host models and/or infection data collected in longitudinal cohort studies. However, most multi-scale models are complex and require significant modelling expertise to run. We formulate an alternative multi-scale modelling framework using a compartmental model with multiple infected stages. In the large-compartment limit, our easy-to-use framework generates identical results compared to previous more complicated approaches. We apply our framework to the case study of influenza A in humans. By using a viral dynamics model to generate synthetic patient-level data, we explore the effects of limited and inaccurate patient data on the accuracy of population-scale forecasts. If infection data are collected daily, we find that a cohort of at least 40 patients is required for a mean population-scale forecasting error below 10%. Forecasting errors may be reduced by including more patients in future cohort studies or by increasing the frequency of observations for each patient. Our work, therefore, provides not only an accessible epidemiological modelling framework but also an insight into the data required for accurate forecasting using multi-scale models.

Global stability of delay‐distributed viral infection model with two modes of viral transmission and B‐cell impairment

This paper formulates a virus dynamics model with impairment of B‐cell functions. The model incorporates two modes of viral transmission: cell‐free and cell‐to‐cell. The cell‐free and cell‐cell incidence rates are modeled by general functions. The model incorporates both, latently and actively, infected cells as well as three distributed time delays. Nonnegativity and boundedness properties of the solutions are proven to show the well‐posedness of the model. The model admits two equilibria that are determined by the basic reproduction number R0. The global stability of each equilibrium is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations. The effect of impairment of B‐cell functions and time delays on the virus dynamics are studied. We have shown that if the functions of B‐cell is impaired, then the concentration of viruses is increased in the plasma. Moreover, we have observed that increasing the time delay will suppress the viral replication.

Modelling the impact of antibody-dependent enhancement on disease severity of Zika virus and dengue virus sequential and co-infection.

Human infections with viruses of the genus Flavivirus, including dengue virus (DENV) and Zika virus (ZIKV), are of increasing global importance. Owing to antibody-dependent enhancement (ADE), secondary infection with one Flavivirus following primary infection with another Flavivirus can result in a significantly larger peak viral load with a much higher risk of severe disease. Although several mathematical models have been developed to quantify the virus dynamics in the primary and secondary infections of DENV, little progress has been made regarding secondary infection of DENV after a primary infection of ZIKV, or DENV-ZIKV co-infection. Here, we address this critical gap by developing compartmental models of virus dynamics. We first fitted the models to published data on dengue viral loads of the primary and secondary infections with the observation that the primary infection reaches its peak much more gradually than the secondary infection. We then quantitatively show that ADE is the key factor determining a sharp increase/decrease of viral load near the peak time in the secondary infection. In comparison, our simulations of DENV and ZIKV co-infection (simultaneous rather than sequential) show that ADE has very limited influence on the peak DENV viral load. This indicates pre-existing immunity to ZIKV is the determinant of a high level of ADE effect. Our numerical simulations show that (i) in the absence of ADE effect, a subsequent co-infection is beneficial to the second virus; and (ii) if ADE is feasible, then a subsequent co-infection can induce greater damage to the host with a higher peak viral load and a much earlier peak time for the second virus, and for the second peak for the first virus.

Ribavirin does not potentiate favipiravir antiviral activity against Ebola virus in non-human primates

BackgroundIn spite of recurrent and dramatic outbreaks, there are no therapeutics approved against Ebola virus disease. Favipiravir, a RNA polymerase inhibitor active against several RNA viruses, recently demonstrated significant but not complete protection in a non-human primate model of Ebola virus disease. In this study, we assessed the benefit of the combination of favipiravir and ribavirin, another broad spectrum antiviral agent, in the same model. Methods15 female cynomolgus macaques were challenged intramuscularly with 1,000 FFU of Ebola virus Gabon 2001 strain and followed for 21 days. All animals received favipiravir 180 mg/kg twice a day (BID), either as monotherapy (n = 5) or in combination with ribavirin (n = 10). Ribavirin was given either at the dose 10 mg/kg BID (n = 5) or 5 mg/kg BID (n = 5). Favipiravir and ribavirin were initiated two and one days before viral challenge respectively and treatment were continued for 14 days. Treatment effects on viral and hematological markers were assessed using a mathematical model. Survival rate of 0% and 20% were obtained in macaques receiving favipiravir plus ribavirin 10 and 5 mg/kg BID, respectively, compared to 40% in the favipiravir monotherapy group (P = 0.061 when comparing monotherapy and bitherapy, log rank). Viral dynamic modeling analysis did not identify an association between plasma concentrations of ribavirin and viral load levels. Using a model of erythropoiesis, plasma concentrations of ribavirin were strongly associated with a hemoglobin drop (p = 0.0015). ConclusionRibavirin plus favipiravir did not extend survival rates and did not lower viral replication rate compared to favipiravir monotherapy in this animal model. Patients receiving this combination in other indications, such as Lassa fever, should be closely monitored to prevent potential toxicity associated with anemia.

Model Averaging in Viral Dynamic Models.

The paucity of experimental data makes both inference and prediction particularly challenging in viral dynamic models. In the presence of several candidate models, a common strategy is model selection (MS), in which models are fitted to the data but only results obtained with the "best model" are presented. However, this approach ignores model uncertainty, which may lead to inaccurate predictions. When several models provide a good fit to the data, another approach is model averaging (MA) that weights the predictions of each model according to its consistency to the data. Here, we evaluated by simulations in a nonlinear mixed-effect model framework the performances of MS and MA in two realistic cases of acute viral infection, i.e., (1) inference in the presence of poorly identifiable parameters, namely, initial viral inoculum and eclipse phase duration, (2) uncertainty on the mechanisms of action of the immune response. MS was associated in some scenarios with a large rate of false selection. This led to a coverage rate lower than the nominal coverage rate of 0.95 in the majority of cases and below 0.50 in some scenarios. In contrast, MA provided better estimation of parameter uncertainty, with coverage rates ranging from 0.72 to 0.98 and mostly comprised within the nominal coverage rate. Finally, MA provided similar predictions than those obtained with MS. In conclusion, parameter estimates obtained with MS should be taken with caution, especially when several models well describe the data. In this situation, MA has better performances and could be performed to account for model uncertainty.

A within-host drug resistance model with continuous state-dependent viral strains

Drug resistance can hamper the success of antiviral therapy for virus infection. Many mathematical models studying within-host drug resistance only consider two viral strains: wild-type (or drug-sensitive) and drug-resistant strains. However, the level of drug resistance can be continuous. Using HIV infection as an example, we developed a new within-host viral dynamic model that structures the virus population continuously on the basis of the level of drug resistance. We derived the basic reproduction number, which was shown to completely determine the global stability of the steady states. This model serves as a new continuous modeling framework to study the emergence and evolution of drug resistance during the therapy of virus infection.

Analysis of a multiscale HIV-1 model coupling within-host viral dynamics and between-host transmission dynamics.

There are many challenges to constitute the linkage from the macroscale to the microscale and analyze the multiscale model. We proposed a bidirectional coupling model with standard incidence which includes the interaction of between-host transmission dynamics and within-host viral dynamics, and investigated the dynamic behaviors of the multiscale system on two time-scales. We found that the multiscale system exhibits more complex dynamics including backward bifurcation, which means that the usual thresholds for infection control or virus elimination obtained from the epidemiological model or virus dynamic model may not act as threshold parameter under a certain condition. There may be multiple epidemic equilibriums, one of which is stable, although the basic reproduction number is less than 1. We numerically examine the synergistic impact between the macro and micro dynamics. In particular, increasing the drug efficacy can decrease the prevalence of disease. The contact rate may affect the number and size of equilibria of viral dynamics model by inducing the occurrence of backward bifurcation. The finding suggests that the effective control measures may include both the reduction in contact rate or transmission rate at the population level and the increase in drug efficacy at the individual level, and using these control measures together can effectively control the diseases.

Global dynamics of a delayed diffusive virus infection model with cell-mediated immunity and cell-to-cell transmission.

In this paper, we propose and analyze a delayed diffusive viral dynamic model incorporating cell-mediated immunity and both cell-free and cell-to-cell transmission. After discussing the well-posedness, we provide some preliminary results on solutions. Then we study the existence and uniqueness of homogeneous steady states, which turned out to be completely determined by the basic reproduction number of infection R0 and the basic reproduction number of immunity R1. Note that when R1 is defined, it is necessary that R0 > 1. The main result is a threefold dynamics. Roughly speaking, when R0 < 1 the infection-free steady state is globally asymptotically stable; when R1 ≤ 1 < R0 the immunity-free infected steady state is globally asymptotically stable; when R1 > 1 the infected-immune steady state is globally asymptotically stable. The approaches are linearization technique and the Lyapunov functional method. The theoretical results are also illustrated with numerical simulations.

The within-host viral kinetics of SARS-CoV-2.

In this work, we use a within-host viral dynamic model to describe the SARS-CoV-2 kinetics in the host. Chest radiograph score data are used to estimate the parameters of that model. Our result shows that the basic reproductive number of SARS-CoV-2 in host growth is around 3.79. Using the same method we also estimate the basic reproductive number of MERS virus is 8.16 which is higher than SARS-CoV-2. The PRCC method is used to analyze the sensitivities of model parameters. Moreover, the drug effects on virus growth and immunity effect of patients are also implemented to analyze the model.

Impact of adaptive immune response and cellular infection on delayed virus dynamics with multi-stages of infected cells

In this investigation, we propose and analyze a virus dynamics model with multi-stages of infected cells. The model incorporates the effect of both humoral and cell-mediated immune responses. We consider two modes of transmissions, virus-to-cell and cell-to-cell. Multiple intracellular discrete-time delays have been integrated into the model. The incidence rate of infection as well as the generation and removal rates of all compartments are described by general nonlinear functions. We derive five threshold parameters which determine the existence of the equilibria of the model under consideration. A set of conditions on the general functions has been established which is sufficient to investigate the global stability of the five equilibria of the model. The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle’s invariance principle. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions.

Mathematical model of zika virus dynamics with vector control and sensitivity analysis

In this paper, we have developed and analyzed a deterministic Zika model considering both vector and sexual transmission route with the effect of human awareness and vector control in the absence of disease induce death. To formulate the model, we assume that the Zika virus is being first transmitted to human by mosquito bite, and then it is being transmitted to his or her sexual partner. The system contains at most three equilibrium points among them one is the disease free and other two are endemic equilibrium points, exists under certain conditions. The theoretical analysis shows that the diseases-free equilibrium is locally and globally asymptotically stable if the basic reproduction number is less than one. Theatrically we have established that endemic equilibrium point which is locally asymptotically stable if the basic reproduction number is greater than one. The system exhibits backward bifurcation when the transmission probability per biting of susceptible mosquito with infected humans crosses the critical value. We estimate the model parameters and validate the model by fitting the model with the reported Zika infected human data from 1 to 36 week of 2016 Zika outbreak in Colombia. Furthermore, using the normalised forward sensitivity index method we have established that the model parameter mosquito biting rate, recruitment rate of mosquito, transmission probability per biting of Susceptible (infected) humans with infected (susceptible) mosquito, rate of awareness in host population, recovery rates of infected human are most sensitive parameters of the considered Zika model. Lastly, some conclusions are given to control the spreading of the Zika disease.

Global properties of virus dynamics with B-cell impairment

Abstract In this paper we construct a class of virus dynamics models with impairment of B-cell functions. Two forms of the incidence rate have been considered, saturated and general. The well-posedness of the models is justified. The models admit two equilibria which are determined by the basic reproduction number R0. The global stability of each equilibrium is proven by utilizing Lyapunov function and LaSalle’s invariance principle. The theoretical results are illustrated by numerical simulations.

Stability of a general adaptive immunity virus dynamics model with multistages of infected cells and two routes of infection

This paper studies an (n+4)‐dimensional nonlinear virus dynamics model that characterizes the interactions of the viruses, susceptible host cells,n‐stages of infected cells, B cells and cytotoxic T lymphocyte (CTL) cells. Both viral and cellular infections have been incorporated into the model. The infected‐susceptible and virus‐susceptible infection rates as well as the generation and removal rates of all compartments are described by general nonlinear functions. Five threshold parameters are computed, which insure the existence of the equilibria of the model under consideration. A set of conditions on the general functions has been established, which is sufficient to investigate the global dynamics of the model. The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions.

Global properties of saturated chikungunya virus dynamics models with cellular infection and delays

This paper studies the global properties of chikungunya virus (CHIKV) dynamics models with both CHIKV-to-monocytes and infected-to-monocyte transmissions. We assume that the infection rate of modeling CHIKV infection is given by saturated mass action. The effect of antibody immune response on the virus dynamics is modeled. The models included three types of time delays, discrete or distributed. The first type of delay is the time between CHIKV entry an uninfected monocyte to be latently infected monocyte. The second time delay is the time between CHIKV entry an uninfected monocyte and the emission of immature CHIKV. The third time delay represents the CHIKV’s maturation time. Lyapunov method is utilized and LaSalle’s invariance principle is applied to address the global stability of equilibria. The model is numerically simulated to support theoretical results.

A numerical method for a diffusive virus model with general incidence function, cell-to-cell transmission and time delay

In this paper, we propose a numerical method for a diffusive virus dynamics model with general incidence function, cell-to-cell transmission and time delay. We justify the wellposedness of the numerical model, and prove that the proposed method preserves the global stability of equilibria by constructing suitable discrete Lyapunov functionals with no constraints on the time and space step sizes. we perform numerical simulation to verify our theoretic results. Epidemiologically, we deduce that the spatial heterogeneity of transmission rate can enlarge the risk of disease outbreaks, and the larger time delay is conductive to cure diseases.

Estimating the approximate analytical solution of HIV viral dynamic model by using homotopy analysis method

Abstract Viruses have different mechanisms in causing a disease in an organism, which largely depend on the viral species. The recent advancement, through coupling data analysis and mathematical modeling, has allowed the identification and characterization of the nature of the virus. In the present paper, the homotopy analysis method is applied to provide an approximate solution of the basic HIV viral dynamic model describing the viral dynamics in a susceptible population. The proposed method allows for the solution of the governing system of differential equations to be calculated in the form of an infinite series with components which can be easily calculated. The homotopy analysis method utilizes a simple method to adjust and control the convergence region of the infinite series solution by using an auxiliary parameter. By using the homotopy series solutions, firstly, several β − curves using an appropriate ratio are plotted to demonstrate the regions of convergence and the optimum value of ℏ, then the residual and absolute errors are obtained for different values of these regions. Secondly, the residual error functions are applied to show the accuracy of the applied homotopy analysis method. Also, the convergence theorem of homotopy analysis method for the HIV viral dynamic model is proved. Mathematica software is used for the calculations and numerical results. The results obtained show the effectiveness and strength of the homotopy analysis method.

Asymptotic expansions of solutions in the model of virus dynamics with immune response

This paper deals with the model of virus dynamics with immune response. Consisting of three integro–differential equations with partial derivatives with two small parameters the singularly perturbed system describes the model. By Vasil’eva – Tikhonov boundary function method, asymptotic expansions of the solutions of the initial boundary value problem are constructed.

Optimal control of the mathematical viral dynamic model of different hepatitis B infected individuals with numerical simulation

The viral infection of hepatitis B virus (HBV) is a dangerous problem for health around the globe and counted in the top leading causes of death. To explore the viral dynamics of this infection, an HBV epidemic model has been developed by dividing the infected compartment into three subclasses, acute, chronically infected and carrier individuals with both vertical as well as horizontal transmission. After formulating the model, we prove that the positive solution of the model exists. The next generation matrix approach has been used to investigate the threshold quantity known as basic reproduction number. The global stability conditions at endemic equilibria (EE) and disease-free equilibrium (DFE) are established by using the method of geometrical approach and Castillo-Chavez, respectively. We use the optimization theory and the three time-dependent control variables to establish the control program. By the help of this control policy, we reduce the number of susceptible, acute, chronically hepatitis B infected and carrier persons, while the numbers of recovered and vaccinated populations are maximized. Finally, numerical results will be found out for the support and feasibility of the analytical results.