Modelling and analysis of dynamics of viral infection of cells and of interferon resistance

Interferons are active biomolecules, which help fight viral infections by spreading from infected to uninfected cells and activate effector molecules, which confer resistance from the virus on cells. We propose a new model of dynamics of viral infection, including endocytosis, cell death, production of interferon and development of resistance. The novel element is a specific biologically justified mechanism of interferon action, which results in dynamics different from other infection models. The model reflects conditions prevailing in liquid cultures (ideal mixing), and the absence of cells or virus influx from outside. The basic model is a nonlinear system of five ordinary differential equations. For this variant, it is possible to characterise global behaviour, using a conservation law. Analytic results are supplemented by computational studies. The second variant of the model includes age-of-infection structure of infected cells, which is described by a transport-type partial differential equation for infected cells. The conclusions are: (i) If virus mortality is included, the virus becomes eventually extinct and subpopulations of uninfected and resistant cells are established. (ii) If virus mortality is not included, the dynamics may lead to extinction of uninfected cells. (iii) Switching off the interferon defense results in a decrease of the sum total of uninfected and resistant cells. (iv) Infection-age structure of infected cells may result in stabilisation or destabilisation of the system, depending on detailed assumptions. Our work seems to constitute the first comprehensive mathematical analysis of the cell-virus-interferon system based on biologically plausible hypotheses.     

Modeling the dynamical impact of HIV on the immune system: Viral clearance,infection, and AIDS

A phenomenological model simulating the time-dependent consequences of the HIV challenge on the immune system is presented. One of the important features of the model is its ability to handle T helper cell production and apoptosis (genetically determined suicide). The values of the independent, generally time-dependent, model parameters were chosen to be compatible with known experimental data. A new approach to the numerical solution of the resulting coupled, nonlinear model equations is presented, and simulations of a typical viral challenge that is cleared and one that leads to infection and AIDS are exhibited.It is shown that a change in the saturated value of a single model parameter is sufficient to change a simulated challenge on its way to being cleared into one that leads to infection instead (and vice versa). If the saturated values of all of the independent model parameters are known at the beginning of a challenge, the outcome of the challenge can be predicted in advance. If the virulence of the HIV strain (defined in this paper) is above a critical threshold at inoculation, infection will result regardless of the initial viral load. This latter result could explain why accidental HIV contaminated needle sticks sometime result in infection regardless of the counter-measures undertaken.A model simulating the time evolution of the collapse of the T helper cell density leading to AIDS is introduced. This model consists of immunological and mathematical parts and is compatible with experimental data. The immediate cause of the beginning of this collapse is postulated to be a spontaneous mutation of the virus into a more virulent form that not only leads to an explosion in the viral load but also to a dramatic increase in the level of induced apoptosis of T helper cells. The results of this model are consistent with the known experimental behavior of the viral load and T helper cell densities in the final stage of HIV infection.     

HIV low viral load persistence under treatment: Insights from a model of cell-to-cell viral transmission

HIV infection persists despite long-term administration of antiretroviral therapy. The mechanisms underlying HIV persistence are not fully understood. Direct viral transmission from infected to uninfected cells (cell-to-cell transmission) may be one of them. During cell-to-cell transmission, multiple virions are delivered to an uninfected cell, making it possible that at least one virion can escape HIV drugs and establish infection. In this paper, we develop a mathematical model that includes cell-to-cell viral transmission to study HIV persistence. During cell-to-cell transmission, it is assumed that various number of virus particles are transmitted with different probabilities and antiretroviral therapy has different effectiveness in blocking their infection. We analyze the model by deriving the basic reproduction number and investigating the stability of equilibria. Sensitivity analysis and numerical simulation show that the viral load is still sensitive to the change of the treatment effectiveness in blocking cell-free virus infection. To reduce this sensitivity, we modify the model by including density-dependent infected cell death or HIV latent infection. The model results suggest that although cell-to-cell transmission may have reduced susceptibility to HIV drugs, HIV latency represents a major reason for HIV persistence in patients on suppressive treatment.     

Spreading and generalized propagating speeds of discrete KPP models in time varying environments

The current paper deals with spatial spreading and front propagating dynamics for spatially discrete KPP (Kolmogorov, Petrovsky and Paskunov) models in time recurrent environments, which include time periodic and almost periodic environments as special cases. The notions of spreading speed interval, generalized propagating speed interval, and traveling wave solutions are first introduced, which are proper modifications of those introduced for spatially continuous KPP models in time almost periodic environments. Among others, it is then shown that the spreading speed interval in a given direction is the minimal generalized propagating speed interval in that direction. Some important upper and lower bounds for the spreading and generalized propagating speed intervals are provided. When the environment is unique ergodic and the so called linear determinacy condition is satisfied, it is shown that the spreading speed interval in any direction is a singleton (called the spreading speed), which equals the classical spreading speed if the environment is actually periodic. Moreover, in such a case, a variational principle for the spreading speed is established and it is shown that there is a front of speed c in a given direction if and only if c is greater than or equal to the spreading speed in that direction.      

Dynamics of an HIV infection model with virus diffusion and latently infected cell activation

Effective combination therapy usually reduces the plasma viral load of HIV to below the detection limit, but it cannot eradicate the virus. The latently infected cell activation is considered to be the main obstacle to completely eradicating HIV infection. In this paper, we consider an HIV infection model with latently infected cell activation, virus diffusion and spatial heterogeneity under Neumann boundary condition. The basic reproduction ratio is characterized by the principal eigenvalue of the related elliptic eigenvalue problem. Besides, by constructing Lyapunov functionals and using Green’s first identity, the global threshold dynamics of the system are completely established. Numerical simulations are carried out to illustrate the theoretical results, in particular, the influence of virus diffusion rate on the basic reproduction ratio is addressed.     

A note on fast approximate minimum degree orderings for symmetric matrices with some dense rows

Recently, a number of variants of the approximate minimum degree algorithm have been proposed that aim to efficiently order symmetric matrices containing some dense rows. We compare the performance of these variants on a range of problems and highlight their potential limitations. This leads us to propose a new variant that offers both speed and robustness. Copyright © 2009 John Wiley & Sons, Ltd.     

一类HIV病毒动力学模型的全局稳定性与周期解

建立了一类较广泛的HIV感染CD4+T细胞病毒动力学模型,给出了一个感染细胞在其整个感染期内产生的病毒的平均数(基本再生数)R0的表达式,运用Lyapunov原理和Routh-Hurwitz判据得到了该模型的未感染平衡点与感染平衡点的存在性与稳定性条件.同时也得到了模型存在轨道渐近稳定周期解和系统持续生存的条件,并通过数值模拟验证了所得到的结果.     

Conceptual Representations of Flu and Microbial Illness Held by Students,Teachers, and Medical Professionals

This study describes 5 th, 8th, and 11th‐grade students', teachers', and medical professionals' conceptions of flu and microbial illness. Participants constructed a concept map on “flu” and participated in a semi‐structured interview. The results showed that these groups of students, teachers and medical professionals held and structured their conceptions about microbes differently. A progression toward more accurate and complete knowledge existed across the groups but this trajectory was not always a predictable, linear developmental path from novice to expert. Across the groups, participants were most knowledgeable about symptoms of microbial illness, treatments of symptoms, and routes of transmission for respiratory illnesses. This knowledge was tightly linked to participants' prior experiences with colds and flu. There were typically large gaps in participants' (children and teachers) understandings of vaccines, immune system responses, treatments (including the mechanisms of pain medications and the functions of antibiotics), and transmission of non‐respiratory microbial illness. A common misconception held by students was the belief that antibiotics can cure viral infections.     

Fast Implementation for Normal Mixed Effects Models With Censored Response

We propose an EM algorithm for computing the maximum likelihood and restricted maximum likelihood for linear and nonlinear mixed effects models with censored response. In contrast with previous developments, this algorithm uses closed-form expressions at the E-step, as opposed to Monte Carlo simulation. These expressions rely on formulas for the mean and variance of a truncated multinormal distribution, and can be computed using available software. This leads to an improvement in the speed of computation of up to an order of magnitude. A wide class of mixed effects models is considered, including the Laird–Ware model, and extensions to different structures for the variance components, heteroscedastic and autocorrelated errors, and multilevel models. We apply the methodology to two case studies from our own biostatistical practice, involving the analysis of longitudinal HIV viral load in two recent AIDS studies.

The proposed algorithm is implemented in the R package lmec. An appendix which includes further mathematical details, the R code, and datasets for examples and simulations are available as the online supplements.     

Propagation of computer virus both across the Internet and external computers: A complex-network approach

Based on the assumption that external computers (particularly, infected external computers) are connected to the Internet, and by considering the influence of the Internet topology on computer virus spreading, this paper establishes a novel computer virus propagation model with a complex-network approach. This model possesses a unique (viral) equilibrium which is globally attractive. Some numerical simulations are also given to illustrate this result. Further study shows that the computers with higher node degrees are more susceptible to infection than those with lower node degrees. In this regard, some appropriate protective measures are suggested.     

具有饱和发生率和免疫响应的病毒感染模型的稳定性分析

提出了具有饱和发生率和免疫响应的病毒感染数学模型,得到了基本再生数R_0的表达式.当R_01时,证明了无病平衡点是全局渐近稳定的;当R_01时,得到了免疫耗竭平衡点和持续带毒平衡点局部渐近稳定的条件.     

A free boundary problem for Aedes aegypti mosquito invasion

An advection–reaction–diffusion model with free boundary is proposed to investigate the invasive process of Aedes aegypti mosquitoes. By analyzing the free boundary problem, we show that there are two main scenarios of invasive regime: vanishing regime or spreading regime, depending on a threshold in terms of model parameters. Once the mortality rate of the mosquito becomes large with a small specific rate of maturation, the invasive mosquito will go extinct. By introducing the definition of asymptotic spreading speed to describe the spreading front, we provide an estimate to show that the boundary moving speed cannot be faster than the minimal traveling wave speed. By numerical simulations, we consider that the mosquitoes invasive ability and wind driven advection effect on the boundary moving speed. The greater the mosquito invasive ability or advection, the larger the boundary moving speed. Our results indicate that the mosquitoes asymptotic spreading speed can be controlled by modulating the invasive ability of winged mosquitoes.     

Spreading speeds and traveling wavefronts for second order integrodifference equations

This paper is concerned with the spreading speeds and traveling wavefronts for second order integrodifference equations. By introducing an auxiliary integrodifference system, the spreading speed is established for the integrodifference equation. It is shown that the spreading speed coincides with the minimal wave speed for monotonic traveling wavefronts. Furthermore, we prove that the traveling wavefronts are stable by applying the squeezing technique. Finally, we analyze the different effects of the delay term appearing in the integrodifference equation from the viewpoint of ecology.     

A simulation framework to investigate in vitro viral infection dynamics

Virus infection is a complex biological phenomenon for which in vitro experiments provide a uniquely concise view where data is often obtained from a single population of cells, under controlled environmental conditions. Nonetheless, data interpretation and real understanding of viral dynamics is still hampered by the sheer complexity of the various intertwined spatio-temporal processes. In this paper we present a tool to address these issues: a cellular automata model describing critical aspects of in vitro viral infections taking into account spatial characteristics of virus spreading within a culture well. The aim of the model is to understand the key mechanisms of SARS-CoV infection dynamics during the first 24 h post infection. Using a simulated annealing algorithm we tune free parameters with data from SARS-CoV infection of cultured lung epithelial cells. We also interrogate the model using a Latin Hypercube sensitivity analysis to identify which mechanisms are critical to the observed infection of host cells and the release of measured virus particles.     

A with-in host Dengue infection model with immune response

A model of viral infection of monocytes population by Dengue virus is formulated here. The model can capture phenomena that dengue virus is quickly cleared in approximately 7 days after the onset of the symptoms. The model takes into account the immune response. It is shown that the quantity of free virus is decreasing when the viral invasion rate is increasing. The basic reproduction ratio of model without immune response is reduced significantly by adding the immune response. Numerical simulations indicate that the growth of immune response and the invasion rate are very crucial in identification of the intensity of infection.     

Topology independent SIS process: An engineering viewpoint

A Susceptible-Infected-Susceptible (SIS) spreading process, occurring on complex networks that are characterized by a special form of contact dynamics called “acquisition exclusivity”, is studied. Assuming statistical independence of joint events, we find analytic solutions for the stationary probabilities that network nodes are infected, and more importantly, find that these solutions are independent of the network topology. We explore the possibilities to use the studied set-up as an engineering solution for controlled spreading on technological networks. In that context, an example for controlled sharing of viral countermeasures in networks is presented. Considering the high epidemic threshold that characterizes the process, “acquisition exclusivity” is suggested as a method for eradication of viral infections from networks.     

Probability of a major infection in a stochastic within-host model with multiple stages

Establishment or spread of a viral infection within healthy individuals depends on exposure to a viral source, either through virus particles or through cells that have been infected. We assume that a potential infection has reached the site of the healthy target cells and we apply stochastic within-host models and multitype branching processes to investigate whether a major infection becomes established. The model includes multiple latent and actively infected stages. It is shown that the probability of a major infection is generally more likely after the virus has entered the target cell and the cell is actively infected. In some cases, the probability of a major infection is less likely if the burst size of actively infected cells is small.     

Spreading speeds and traveling waves for a time periodic DS-I-A epidemic model

This paper is devoted to studying the speed of asymptotic spreading and minimal wave speed of traveling wave solutions for a time periodic and diffusive DS-I-A epidemic model, which describes the propagation threshold of disease spreading. The main feature of this model is the possible deficiency of the classical comparison principle such that many known results do not directly work. The speed of asymptotic spreading is estimated by constructing auxiliary equations and applying the classical theory of asymptotic spreading for Fisher type equation. The minimal wave speed is established by proving the existence and nonexistence of the nonconstant traveling wave solutions. Moreover, some numerical examples are presented to model the propagation dynamics of this system.     

Classical Gauge Theory of Gravity

The classical theory of gravity is formulated as a gauge theory on a frame bundle with spontaneous symmetry breaking caused by the existence of Dirac fermionic fields. The pseudo-Reimannian metric (tetrad field) is the corresponding Higgs field. We consider two variants of this theory. In the first variant, gravity is represented by the pseudo-Reimannian metric as in general relativity theory; in the second variant, it is represented by the effective metric as in Logunov's relativistic theory of gravity. The configuration space, Dirac operator, and Lagrangians are constructed for both variants.     

Enhancing PSO methods for global optimization

The Particle Swarm Optimization (PSO) method is a well-established technique for global optimization. During the past years several variations of the original PSO have been proposed in the relevant literature. Because of the increasing necessity in global optimization methods in almost all fields of science there is a great demand for efficient and fast implementations of relative algorithms. In this work we propose three modifications of the original PSO method in order to increase the speed and its efficiency that can be applied independently in almost every PSO variant. These modifications are: (a) a new stopping rule, (b) a similarity check and (c) a conditional application of some local search method. The proposed were tested using three popular PSO variants and a variety test functions. We have found that the application of these modifications resulted in significant gain in speed and efficiency.