Within-host Model Research Articles

Analysis of a Stochastic Within-Host Model of Dengue Infection with Immune Response and Ornstein–Uhlenbeck Process

Analysis of a Stochastic Within-Host Model of Dengue Infection with Immune Response and Ornstein–Uhlenbeck Process

Identifiability investigation of within-host models of acute virus infection

<p>Uncertainty in parameter estimates from fitting within-host models to empirical data limits the model's ability to uncover mechanisms of infection, disease progression, and to guide pharmaceutical interventions. Understanding the effect of model structure and data availability on model predictions is important for informing model development and experimental design. To address sources of uncertainty in parameter estimation, we used four mathematical models of influenza A infection with increased degrees of biological realism. We tested the ability of each model to reveal its parameters in the presence of unlimited data by performing structural identifiability analyses. We then refined the results by predicting practical identifiability of parameters under daily influenza A virus titers alone or together with daily adaptive immune cell data. Using these approaches, we presented insight into the sources of uncertainty in parameter estimation and provided guidelines for the types of model assumptions, optimal experimental design, and biological information needed for improved predictions.</p>

A novel within-host model of HIV and nutrition.

In this paper we develop a four compartment within-host model of nutrition and HIV. We show that the model has two equilibria: an infection-free equilibrium and infection equilibrium. The infection free equilibrium is locally asymptotically stable when the basic reproduction number $ \mathcal{R}_0 < 1 $, and unstable when $ \mathcal{R}_0 > 1 $. The infection equilibrium is locally asymptotically stable if $ \mathcal{R}_0 > 1 $ and an additional condition holds. We show that the within-host model of HIV and nutrition is structured to reveal its parameters from the observations of viral load, CD4 cell count and total protein data. We then estimate the model parameters for these 3 data sets. We have also studied the practical identifiability of the model parameters by performing Monte Carlo simulations, and found that the rate of clearance of the virus by immunoglobulins is practically unidentifiable, and that the rest of the model parameters are only weakly identifiable given the experimental data. Furthermore, we have studied how the data frequency impacts the practical identifiability of model parameters.

Using mixture density networks to emulate a stochastic within-host model of Francisella tularensis infection.

For stochastic models with large numbers of states, analytical techniques are often impractical, and simulations time-consuming and computationally demanding. This limitation can hinder the practical implementation of such models. In this study, we demonstrate how neural networks can be used to develop emulators for two outputs of a stochastic within-host model of Francisella tularensis infection: the dose-dependent probability of illness and the incubation period. Once the emulators are constructed, we employ Markov Chain Monte Carlo sampling methods to parameterize the within-host model using records of human infection. This inference is only possible through the use of a mixture density network to emulate the incubation period, providing accurate approximations of the corresponding probability distribution. Notably, these estimates improve upon previous approaches that relied on bacterial counts from the lungs of macaques. Our findings reveal a 50% infectious dose of approximately 10 colony-forming units and we estimate that the incubation period can last for up to 11 days following low dose exposure.

Within-host mathematical model of malaria parasite with cell-mediated and antibody-mediated immune systems

ABSTRACT Malaria is a serious health problem in the world. Nearly half of the world’s population is at risk of disease. In this study, a mathematical model was developed to understand and analyze the dynamics of the malaria parasite within host cells with cell-mediated and antibody-mediated immune systems. The model categorizes the population into six compartments. The study provides a concise representation of the interaction between the parasite and red blood cells, as well as the responses of the immune system, including both antibody-mediated and cell-mediated responses. The research examines the biological visibility and well-posedness of the model, ensuring that the solutions remain bounded and positive. The basic reproduction number, which indicates the potential spread of the parasite is determined. The stability analysis of the parasite-free equilibrium point was also conducted, revealing that the parasite-free state is locally and globally stable if the basic reproduction number, R 0 < 1 . Furthermore, bifurcation and sensitivity analysis are performed. Finally, to complement the theoretical findings and illustrate the impact of immunological effectiveness, numerical simulations are conducted under different scenarios. The result shows that the cell-mediated and antibody-mediated immune response helps to eliminate the parasite within the human host.

Mathematical model on HIV and nutrition

ABSTRACT HIV continues to be a major global health issue, having claimed millions of lives in the last few decades. While several empirical studies support the fact that proper nutrition is useful in the fight against HIV, very few studies have focused on developing and using mathematical modelling approaches to assess the association between HIV, human immune response to the disease, and nutrition. We develop a within-host model for HIV that captures the dynamic interactions between HIV, the immune system and nutrition. We find that increased viral activity leads to increased serum protein levels. We also show that the viral production rate is positively correlated with HIV viral loads, as is the enhancement rate of protein by virus. Although our numerical simulations indicate a direct correlation between dietary protein intake and serum protein levels in HIV-infected individuals, further modelling and clinical studies are necessary to gain comprehensive understanding of the relationship.

Insights into unexpected relapse and recovery in HCV-infected patients by studying a stochastic within-host HCV model

The causes of viral rebound leading to disease relapse in some chronic hepatitis C virus-infected patients at the end of treatment with direct-acting antiviral drugs are still unclear, which poses a challenge to further improve the permanent cure rate of HCV-infected patients. In this paper, a stochastic within-host HCV model is studied in detail to gain insights into the phenomena of unexpected relapse and recovery in HCV-infected patients. Theoretically, the existence of an ergodic stationary distribution, which also reflects the long-term coexistence of uninfected hepatocytes and free viruses, is proved by constructing suitable stochastic Lyapunov functions at a threshold condition related to the basic reproduction number of the corresponding deterministic model. In addition, the sufficient conditions for the extinction of free viruses is also given, which implies that the viral load eventually drops to zero and HCV-infected patients are cured. In the numerical simulations, the phenomenon of unexpected relapse and recovery in HCV-infected patients is demonstrated by a few simple examples. By Monte Carlo method, under certain conditions, it is observed that the increase in noise intensities makes the phenomena of unexpected relapse and recovery in HCV-infected patients increase as well.

Numerical assessment of the impact of hemozoin on the dynamics of a within-host malaria model

Phagocytosis of infected red blood cells by macrophages can lead to the elimination of malaria parasites. However, the phagocytic function of macrophages can be diminished when they ingest the malarial pigment called hemozoin. In this study, we consider an in-host malaria model which assesses the impact of the ingestion or uptake of hemozoin by macrophages on the dynamics of malaria in a human host. It is shown that the model undergoes the backward bifurcation phenomenon. This phenomenon is induced by the suppression or inhibition of the phagocytic function of macrophages resulting from their interaction with hemozoin. More so, it is shown numerically that the model can undergo a Hopf bifurcation with periodic solutions appearing in all compartments of the model when the suppression rate of the phagocytic function of macrophages by hemozoin is sufficiently small.

Global Dynamics of a Within-Host Model for Usutu Virus

We propose a within-host mathematical model for the dynamics of Usutu virus infection, incorporating Crowley–Martin functional response. The basic reproduction number R0 is found by applying the next-generation matrix approach. Depending on this threshold, parameter, global asymptotic stability of one of the two possible equilibria is also established via constructing appropriate Lyapunov functions and using LaSalle’s invariance principle. We present numerical simulations to illustrate the results and a sensitivity analysis of R0 was also completed. Finally, we fit the model to actual data on Usutu virus titers. Our study provides new insights into the dynamics of Usutu virus infection.

Analysis of Within-Host Mathematical Models of Toxoplasmosis That Consider Time Delays

In this paper, we investigate two within-host mathematical models that are based on differential equations. These mathematical models include healthy cells, tachyzoites, and bradyzoites. The first model is based on ordinary differential equations and the second one includes a discrete time delay. We found the models’ steady states and computed the basic reproduction number R0. Two equilibrium points exist in both models: the first is the disease-free equilibrium point and the second one is the endemic equilibrium point. We found that the initial quantity of uninfected cells has an impact on the basic reproduction number R0. This threshold parameter also depends on the contact rate between tachyzoites and uninfected cells, the contact rate between encysted bradyzoite and the uninfected cells, the conversion rate from tachyzoites to bradyzoites, and the death rate of the bradyzoites- and tachyzoites-infected cells. We investigated the local and global stability of the two equilibrium points for the within-host models that are based on differential equations. We perform numerical simulations to validate our analytical findings. We also demonstrated that the disease-free equilibrium point cannot lose stability regardless of the value of the time delay. The numerical simulations corroborated our analytical results.

An agent-based multi-level model to study the spread of gonorrhea in different and interacting risk groups

IntroductionMathematical modeling has emerged as a crucial component in understanding the epidemiology of infectious diseases. In fact, contemporary surveillance efforts for epidemic or endemic infections heavily rely on mathematical and computational methods. This study presents a novel agent-based multi-level model that depicts the transmission dynamics of gonorrhea, a sexually transmitted infection (STI) caused by the bacterium Neisseria gonorrhoeae. This infection poses a significant public health challenge as it is endemic in numerous countries, and each year sees millions of new cases, including a concerning number of drug-resistant cases commonly referred to as gonorrhea superbugs or super gonorrhea. These drug-resistant strains exhibit a high level of resistance to recommended antibiotic treatments.MethodsThe proposed model incorporates a multi-layer network of agents' interaction representing the dynamics of sexual partnerships. It also encompasses a transmission model, which quantifies the probability of infection during sexual intercourse, and a within-host model, which captures the immune activation following gonorrhea infection in an individual. It is a combination of agent-based modeling, which effectively captures interactions among various risk groups, and probabilistic modeling, which enables a theoretical exploration of sexual network characteristics and contagion dynamics.ResultsNumerical simulations of the dynamics of gonorrhea infection using the complete agent-based model are carried out. In particular, some examples of possible epidemic evolution are presented together with an application to a real case study. The goal was to construct a virtual population that closely resembles the target population of interest.DiscussionThe uniqueness of this research lies in its objective to accurately depict the influence of distinct sexual risk groups and their interaction on the prevalence of gonorrhea. The proposed model, having interpretable and measurable parameters from epidemiological data, facilitates a more comprehensive understanding of the disease evolution.

Estimating seroconversion rates accounting for repeated infections by approximate Bayesian computation.

This study presents a novel approach for inferring the incidence of infections by employing a quantitative model of the serum antibody response. Current methodologies often overlook the cumulative effect of an individual's infection history, making it challenging to obtain a marginal distribution for antibody concentrations. Our proposed approach leverages approximate Bayesian computation to simulate cross-sectional antibody responses and compare these to observed data, factoring in the impact of repeated infections. We then assess the empirical distribution functions of the simulated and observed antibody data utilizing Kolmogorov deviance, thereby incorporating a goodness-of-fit check. This new method not only matches the computational efficiency of preceding likelihood-based analyses but also facilitates the joint estimation of antibody noise parameters. The results affirm that the predictions generated by our within-host model closely align with the observed distributions from cross-sectional samples of a well-characterized population. Our findings mirror those of likelihood-based methodologies in scenarios of low infection pressure, such as the transmission of pertussis in Europe. However, our simulations reveal that in settings of higher infection pressure, likelihood-based approaches tend to underestimate the force of infection. Thus, our novel methodology presents significant advancements in estimating infection incidence, thereby enhancing our understanding of disease dynamics in the field of epidemiology.

Modelling the viral dynamics of the SARS-CoV-2 Delta and Omicron variants in different cell types.

We use viral kinetic models fitted to viral load data from in vitro studies to explain why the SARS-CoV-2 Omicron variant replicates faster than the Delta variant in nasal cells, but slower than Delta in lung cells, which could explain Omicron's higher transmission potential and lower severity. We find that in both nasal and lung cells, viral infectivity is higher for Omicron but the virus production rate is higher for Delta, with an estimated approximately 200-fold increase in infectivity and 100-fold decrease in virus production when comparing Omicron with Delta in nasal cells. However, the differences are unequal between cell types, and ultimately lead to the basic reproduction number and growth rate being higher for Omicron in nasal cells, and higher for Delta in lung cells. In nasal cells, Omicron alone can enter via a TMPRSS2-independent pathway, but it is primarily increased efficiency of TMPRSS2-dependent entry which accounts for Omicron's increased activity. This work paves the way for using within-host mathematical models to understand the transmission potential and severity of future variants.

Competing Heterogeneities in Vaccine Effectiveness Estimation.

Understanding the waning of vaccine-induced protection is important for both immunology and public health. Population heterogeneities in underlying (pre-vaccination) susceptibility and vaccine response can cause measured vaccine effectiveness (mVE) to change over time, even in the absence of pathogen evolution and any actual waning of immune responses. We use multi-scale agent-based models parameterized using epidemiological and immunological data, to investigate the effect of these heterogeneities on mVE as measured by the hazard ratio. Based on our previous work, we consider the waning of antibodies according to a power law and link it to protection in two ways: (1) motivated by correlates of risk data and (2) using a within-host model of stochastic viral extinction. The effect of the heterogeneities is given by concise and understandable formulas, one of which is essentially a generalization of Fisher's fundamental theorem of natural selection to include higher derivatives. Heterogeneity in underlying susceptibility accelerates apparent waning, whereas heterogeneity in vaccine response slows down apparent waning. Our models suggest that heterogeneity in underlying susceptibility is likely to dominate. However, heterogeneity in vaccine response offsets <10% to >100% (median of 29%) of this effect in our simulations. Our study suggests heterogeneity is more likely to 'bias' mVE downwards towards the faster waning of immunity but a subtle bias in the opposite direction is also plausible.

Global Stability and Bifurcation Analysis of a Virus Infection Model with Nonlinear Incidence and Multiple Delays

In order to investigate the impact of general nonlinear incidence, cellular infection, and multiple time delays on the dynamical behaviors of a virus infection model, a within-host model describing the virus infection is formulated and studied by taking these factors into account in a single model. Qualitative analysis of the global properties of the equilibria is carried out by utilizing the methods of Lyapunov functionals. The existence and properties of local and global Hopf bifurcations are discussed by regarding immune delay as the bifurcation parameter via the normal form, center manifold theory, and global Hopf bifurcation theorem. This work reveals that the immune delay is mainly responsible for the existence of the Hopf bifurcation and rich dynamics rather than the intracellular delays, and the general nonlinear incidence does not change the global stability of the equilibria. Moreover, ignoring the cell-to-cell infection may underevaluate the infection risk. Numerical simulations are carried out for three kinds of incidence function forms to show the rich dynamics of the model. The bifurcation diagrams and the identification of the stability region show that increasing the immune delay can destabilize the immunity-activated equilibrium and induce a Hopf bifurcation, stability switches, and oscillation solutions. The obtained results are a generalization of some existing models.

An artesunate pharmacometric model to explain therapeutic responses in falciparum malaria.

The artemisinins are potent and widely used antimalarial drugs that are eliminated rapidly. A simple concentration-effect pharmacometric model does not explain why dosing more frequently than once daily fails to augment parasite clearance and improve therapeutic responses in vivo. Artemisinins can induce a temporary non-replicative or 'dormant' drug refractory state in Plasmodium falciparum malaria parasites which may explain recrudescences observed in clinical trials despite full drug susceptibility, but whether it explains the dosing-response relationship is uncertain. To propose a revised model of antimalarial pharmacodynamics that incorporates reversible asexual parasite injury and temporary drug refractoriness in order to explain the failure of frequent dosing to augment therapeutic efficacy in falciparum malaria. The model was fitted using a Bayesian Markov Chain Monte Carlo approach with the parasite clearance data from 39 patients with uncomplicated falciparum malaria treated with artesunate from western Cambodia and 40 patients from northwestern Thailand reported previously. The revised model captured the dynamics of parasite clearance data. Its predictions are consistent with observed therapeutic responses. A within-host pharmacometric model is proposed in which it is hypothesized that some malaria parasites enter a temporary drug refractory state after exposure to artemisinin antimalarials, which is followed by delayed parasite death or reactivation. The model fitted the observed sequential parasite density data from patients with acute P. falciparum malaria, and it supported reduced ring stage activity in artemisinin-resistant infections.

Viral kinetics, stability and sensitivity analysis of the within-host COVID-19 model

This paper delves into the investigation of the COVID-19 dynamics within a host using the Target-Latent-Infected-Virus (TLIV) model, presenting a fresh approach compared to previous studies. Our model introduces a latent class and explores sensitivity analysis, aspects that have received limited attention in prior research. A significant contribution of this study is the analysis of both local and global stability of equilibrium states, subject to specific sufficient conditions based on the basic reproduction number R_0. By examining these stability properties, we aim to gain insights into the factors underlying variations observed in the findings of different studies. Additionally, we identify the death rate of infected cells as the parameter most susceptible to influence in our model. To minimize its impact and facilitate recovery, it is crucial to implement appropriate medical therapies and consume immune-boosting foods. Some computer simulations are carried out to strengthen the theoretical results.

A General Approach to Modeling Covid-19

The present work shows that it is possible to analytically solve a general model to explain the transmission dynamics of SARS-CoV-2. First, the within-host model is described, and later a between-host model, where the coupling between them is the viral load of SARS-CoV-2. The within-host model describes the equations involved in the life cycle of SARS-CoV-2, and also the immune response; while that the between-Host model analyzes the dynamics of virus spread from the original source of contagion associated with bats, subsequently transmitted to a host, and then reaching the reservoir (Huanan Seafood Wholesale Market in Wuhan ), until finally infecting the human population.

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.

Within-host models of dengue virus transmission with immune response

AbstractDengue fever is an infectious viral fever. The complex behavior of the virus within the body can be explained through mathematical models to understand the virus’s dynamics. We propose two different with-in host models of dengue virus transmission with humoral immune response. The proposed models differ from one another because one of the models assumes that newly formed viruses infect healthy cells again. To understand the dynamics of the proposed models, we perform a comparative study of stability analysis, numerical simulation, and sensitivity analysis. The basic reproduction number (BRN) of the two models is computed using next-generation matrix method. The local stability (l.s) analysis is discussed using the linearization method. The Lyapunov’s direct method is used to check the global stability (g.s) of the models. It has been found that both the equilibrium states for both the models, namely, virus-free equilibrium state and endemic equilibrium state, are globally stable, based on the value of BRN. Results show the influence of immune response on the cell dynamics and virus particles. The virus neutralization rate by antibodies and rate that affects the antibody growth are highly sensitive for the two models. Optimal control is applied to explore the possible control strategies to prevent virus spread in the host system. It is evident from the results that the strategy to administrate antibiotic drugs and home remedies slow down the virus spread in the host.