Cell-free transmission of human adenovirus by passive mass transfer in cell culture simulated in a computer model

Viruses spread between cells, tissues, and organisms by cell-free and cell-cell transmissions. Both mechanisms enhance disease development, but it is difficult to distinguish between them. Here, we analyzed the transmission mode of human adenovirus (HAdV) in monolayers of epithelial cells by wet laboratory experimentation and a computer simulation. Using live-cell fluorescence microscopy and replication-competent HAdV2 expressing green fluorescent protein, we found that the spread of infection invariably occurred after cell lysis. It was affected by convection and blocked by neutralizing antibodies but was independent of second-round infections. If cells were overlaid with agarose, convection was blocked and round plaques developed around lytic infected cells. Infected cells that did not lyse did not give rise to plaques, highlighting the importance of cell-free transmission. Key parameters for cell-free virus transmission were the time from infection to lysis, the dose of free viruses determining infection probability, and the diffusion of single HAdV particles in aqueous medium. With these parameters, we developed an in silico model using multiscale hybrid dynamics, cellular automata, and particle strength exchange. This so-called white box model is based on experimentally determined parameters and reproduces viral infection spreading as a function of the local concentration of free viruses. These analyses imply that the extent of lytic infections can be determined by either direct plaque assays or can be predicted by calculations of virus diffusion constants and modeling.     

Population dynamics of botanical epidemics involving primary and secondary infection

In this paper we study the dynamical properties of models for botanical epidemics, especially for soil-borne fungal infection. The models develop several new concepts, involving dual sources of infection, host and inoculum dynamics. Epidemics are modelled with respect to the infection status of whole plants and plant organs (the G model) or to lesion density and size (the SW model). The infection can originate in two sources, either from the initial inoculum (primary infection) or by a direct transmission between plant tissue (secondary infection). The first term corresponds to the transmission through the free-living stages of macroparasites or an external source of infection in certain medical models, whereas the second term is equivalent to direct transmission between the hosts in microparasitic infections. The models allow for dynamics of host growth and inoculum decay. We show that the two models for root and lesion dynamics can be derived as special cases of a single generic model. Analytical and numerical methods are used to analyse the behaviour of the models for static, unlimited (exponential) and asymptotically limited host growth with and without secondary infection, and with and without decay of initial inoculum. The models are shown to exhibit a range of epidemic behaviour within single seasons that extends from simple monotonic increase with saturation of the host population, through temporary plateaux as the system switches from primary to secondary infection, to effective elimination of the pathogen by the host outgrowing the fungal infection. For certain conditions, the equilibrium values are shown to depend on initial conditions. These results have important consequences for the control of plant disease. They can be applied beyond soil-borne plant pathogens to mycorrhizal fungi and aerial pathogens while the principles of primary and secondary infection with host and inoculum dynamics may be used to link classical models for both microparasitic and macroparasitic infections.     

Innate Immunity and the Inter-exposure Interval Determine the Dynamics of Secondary Influenza Virus Infection and Explain Observed Viral Hierarchies

Influenza is an infectious disease that primarily attacks the respiratory system. Innate immunity provides both a very early defense to influenza virus invasion and an effective control of viral growth. Previous modelling studies of virus–innate immune response interactions have focused on infection with a single virus and, while improving our understanding of viral and immune dynamics, have been unable to effectively evaluate the relative feasibility of different hypothesised mechanisms of antiviral immunity. In recent experiments, we have applied consecutive exposures to different virus strains in a ferret model, and demonstrated that viruses differed in their ability to induce a state of temporary immunity or viral interference capable of modifying the infection kinetics of the subsequent exposure. These results imply that virus-induced early immune responses may be responsible for the observed viral hierarchy. Here we introduce and analyse a family of within-host models of re-infection viral kinetics which allow for different viruses to stimulate the innate immune response to different degrees. The proposed models differ in their hypothesised mechanisms of action of the non-specific innate immune response. We compare these alternative models in terms of their abilities to reproduce the re-exposure data. Our results show that 1) a model with viral control mediated solely by a virus-resistant state, as commonly considered in the literature, is not able to reproduce the observed viral hierarchy; 2) the synchronised and desynchronised behaviour of consecutive virus infections is highly dependent upon the interval between primary virus and challenge virus exposures and is consistent with virus-dependent stimulation of the innate immune response. Our study provides the first mechanistic explanation for the recently observed influenza viral hierarchies and demonstrates the importance of understanding the host response to multi-strain viral infections. Re-exposure experiments provide a new paradigm in which to study the immune response to influenza and its role in viral control.     

Influence of confinement on the spreading of bacterial populations

The spreading of bacterial populations is central to processes in agriculture, the environment, and medicine. However, existing models of spreading typically focus on cells in unconfined settings—despite the fact that many bacteria inhabit complex and crowded environments, such as soils, sediments, and biological tissues/gels, in which solid obstacles confine the cells and thereby strongly regulate population spreading. Here, we develop an extended version of the classic Keller-Segel model of bacterial spreading via motility that also incorporates cellular growth and division, and explicitly considers the influence of confinement in promoting both cell-solid and cell-cell collisions. Numerical simulations of this extended model demonstrate how confinement fundamentally alters the dynamics and morphology of spreading bacterial populations, in good agreement with recent experimental results. In particular, with increasing confinement, we find that cell-cell collisions increasingly hinder the initial formation and the long-time propagation speed of chemotactic pulses. Moreover, also with increasing confinement, we find that cellular growth and division plays an increasingly dominant role in driving population spreading—eventually leading to a transition from chemotactic spreading to growth-driven spreading via a slower, jammed front. This work thus provides a theoretical foundation for further investigations of the influence of confinement on bacterial spreading. More broadly, these results help to provide a framework to predict and control the dynamics of bacterial populations in complex and crowded environments.     

Zika virus dynamics: Effects of inoculum dose,the innate immune response and viral interference

Experimental Zika virus infection in non-human primates results in acute viral load dynamics that can be well-described by mathematical models. The inoculum dose that would be received in a natural infection setting is likely lower than the experimental infections and how this difference affects the viral dynamics and immune response is unclear. Here we study a dataset of experimental infection of non-human primates with a range of doses of Zika virus. We develop new models of infection incorporating both an innate immune response and viral interference with that response. We find that such a model explains the data better than models with no interaction between virus and the immune response. We also find that larger inoculum doses lead to faster dynamics of infection, but approximately the same total amount of viral production.     

Increased burst size in multiply infected cells can alter basic virus dynamics

ABSTRACT: BACKGROUND: The dynamics of viral infections have been studied extensively in a variety of settings, both experimentally and with mathematical models. The majori-ty of mathematical models assumes that only one virus can infect a given cell at a time. It is, however, clear that especially in the context of high viral load, cells can become infected with multiple copies of a virus, a process called coinfection. This has been best demonstrated experimentally for human immunodeficiency virus (HIV), although it is thought to be equally relevant for a number of other viral infections. In a previously explored mathematical model, the viral output from an infected cell does not depend on the number of viruses that reside in the cell, i.e. viral replication is limited by cellular rather than viral factors. In this case, basic virus dynamics properties are not altered by coinfection. Results: Here, we explore the alternative assumption that multiply infected cells are characterized by an increased burst size and find that this can fundamentally alter model predictions. Under this scenario, establishment of infection may not be solely determined by the basic reproductive ratio of the virus, but can depend on the initial virus load. Upon infection, the virus population need not follow straight exponential growth. Instead, the exponential rate of growth can increase over time as virus load becomes larger. Moreover, the model suggests that the ability of anti-viral drugs to suppress the virus population can depend on the virus load upon initiation of therapy. This is because more coinfected cells, which produce more virus, are present at higher virus loads. Hence, the degree of drug resistance is not only determined by the viral genotype, but also by the prevalence of coinfected cells. Conclusions: Our work shows how an increased burst size in multiply infected cells can alter basic infection dynamics. This forms the basis for future experimental testing of model assumptions and predictions that can distinguish between the different scenarios.     

Modeling Within-Host Evolution of HIV: Mutation,Competition and Strain Replacement

Virus evolution during infection of a single individual is a well-known feature of disease progression in chronic viral diseases. However, the simplest models of virus competition for host resources show the existence of a single dominant strain that grows most rapidly during the initial period of infection and competitively excludes all other virus strains. Here, we examine the dynamics of strain replacement in a simple model that includes a convex trade-off between rapid virus reproduction and long-term host cell survival. Strains are structured according to their within-cell replication rate. Over the course of infection, we find a progression in the dominant strain from fast- to moderately-replicating virus strains featuring distinct jumps in the replication rate of the dominant strain over time. We completely analyze the model and provide estimates for the replication rate of the initial dominant strain and its successors. Our model lays the groundwork for more detailed models of HIV selection and mutation. We outline future directions and application of related models to other biological situations.     

A probability cellular automaton model for hepatitis B viral infections

The existing models of hepatitis B virus (HBV) infection dynamics are based on the assumption that the populations of viruses and cells are uniformly mixed. However, the real virus infection system is actually not homogeneous and some spatial factors might play a nontrivial role in governing the development of HBV infection and its outcome. For instance, the localized populations of dead cells might adversely affect the spread of infection. To consider this kind of inhomogeneous feature, a simple 2D (dimensional) probability Cellular Automaton model was introduced to study the dynamic process of HBV infection. The model took into account the existence of different types of HBV infectious and non-infectious particles. The simulation results thus obtained showed that the Cellular Automaton model could successfully account for some important features of the disease, such as its wide variety in manifestation and its age dependency. Meanwhile, the effects of the model's parameters on the dynamical process of the infection were also investigated. It is anticipated that the Cellular Automaton model may be extended to serve as a useful vehicle for studying, among many other complicated dynamic biological systems, various persistent infections with replicating parasites.     

Dynamics of CD8+ T cell responses during acute and chronic lymphocytic choriomeningitis virus infection

Infection of mice with lymphocytic choriomeningitis virus (LCMV) is frequently used to study the underlying principles of viral infections and immune responses. We fit a mathematical model to recently published data characterizing Ag-specific CD8+ T cell responses during acute (Armstrong) and chronic (clone 13) LCMV infection. This allows us to analyze the differences in the dynamics of CD8+ T cell responses against different types of LCMV infections. For the four CD8+ T cell responses studied, we find that, compared with the responses against acute infection, responses against chronic infection are generally characterized by an earlier peak and a faster contraction phase thereafter. Furthermore, the model allows us to give a new interpretation of the effect of thymectomy on the dynamics of CD8+ T cell responses during chronic LCMV infection: a smaller number of naive precursor cells is sufficient to account for the observed differences in the responses in thymectomized mice. Finally, we compare data characterizing LCMV-specific CD8+ T cell responses from different laboratories. Although the data were derived from the same experimental model, we find quantitative differences that can be solved by introducing a scaling factor. Also, we find kinetic differences that are at least partly due to the infrequent measurements of CD8+ T cells in the different laboratories.     

The differential infectivity and staged progression models for the transmission of HIV

Recent studies of HIV RNA in infected individuals show that viral levels vary widely between individuals and within the same individual over time. Individuals with higher viral loads during the chronic phase tend to develop AIDS more rapidly. If RNA levels are correlated with infectiousness, these variations explain puzzling results from HIV transmission studies and suggest that a small subset of infected people may be responsible for a disproportionate number of infections. We use two simple models to study the impact of variations in infectiousness. In the first model, we account for different levels of virus between individuals during the chronic phase of infection, and the increase in the average time from infection to AIDS that goes along with a decreased viral load. The second model follows the more standard hypothesis that infected individuals progress through a series of infection stages, with the infectiousness of a person depending upon his current disease stage. We derive and compare threshold conditions for the two models and find explicit formulas of their endemic equilibria. We show that formulas for both models can be put into a standard form, which allows for a clear interpretation. We define the relative impact of each group as the fraction of infections being caused by that group. We use these formulas and numerical simulations to examine the relative importance of different stages of infection and different chronic levels of virus to the spreading of the disease. The acute stage and the most infectious group both appear to have a disproportionate effect, especially on the early epidemic. Contact tracing to identify super-spreaders and alertness to the symptoms of acute HIV infection may both be needed to contain this epidemic.     

Exploring cell tropism as a possible contributor to influenza infection severity

Several mechanisms have been proposed to account for the marked increase in severity of human infections with avian compared to human influenza strains, including increased cytokine expression, poor immune response, and differences in target cell receptor affinity. Here, the potential effect of target cell tropism on disease severity is studied using a mathematical model for in-host influenza viral infection in a cell population consisting of two different cell types. The two cell types differ only in their susceptibility to infection and rate of virus production. We show the existence of a parameter regime which is characterized by high viral loads sustained long after the onset of infection. This finding suggests that differences in cell tropism between influenza strains could be sufficient to cause significant differences in viral titer profiles, similar to those observed in infections with certain strains of influenza A virus. The two target cell mathematical model offers good agreement with experimental data from severe influenza infections, as does the usual, single target cell model albeit with biologically unrealistic parameters. Both models predict that while neuraminidase inhibitors and adamantanes are only effective when administered early to treat an uncomplicated seasonal infection, they can be effective against more severe influenza infections even when administered late.     

Within-Host Models of High and Low Pathogenic Influenza Virus Infections: The Role of Macrophages

The World Health Organization identifies influenza as a major public health problem. While the strains commonly circulating in humans usually do not cause severe pathogenicity in healthy adults, some strains that have infected humans, such as H5N1, can cause high morbidity and mortality. Based on the severity of the disease, influenza viruses are sometimes categorized as either being highly pathogenic (HP) or having low pathogenicity (LP). The reasons why some strains are LP and others HP are not fully understood. While there are likely multiple mechanisms of interaction between the virus and the immune response that determine LP versus HP outcomes, we focus here on one component, namely macrophages (MP). There is some evidence that MP may both help fight the infection and become productively infected with HP influenza viruses. We developed mathematical models for influenza infections which explicitly included the dynamics and action of MP. We fit these models to viral load and macrophage count data from experimental infections of mice with LP and HP strains. Our results suggest that MP may not only help fight an influenza infection but may contribute to virus production in infections with HP viruses. We also explored the impact of combination therapies with antivirals and anti-inflammatory drugs on HP infections. Our study suggests a possible mechanism of MP in determining HP versus LP outcomes, and how different interventions might affect infection dynamics.     

Stochastic models for virus and immune system dynamics

New stochastic models are developed for the dynamics of a viral infection and an immune response during the early stages of infection. The stochastic models are derived based on the dynamics of deterministic models. The simplest deterministic model is a well-known system of ordinary differential equations which consists of three populations: uninfected cells, actively infected cells, and virus particles. This basic model is extended to include some factors of the immune response related to Human Immunodeficiency Virus-1 (HIV-1) infection. For the deterministic models, the basic reproduction number, R₀, is calculated and it is shown that if R₀<1, the disease-free equilibrium is locally asymptotically stable and is globally asymptotically stable in some special cases. The new stochastic models are systems of stochastic differential equations (SDEs) and continuous-time Markov chain (CTMC) models that account for the variability in cellular reproduction and death, the infection process, the immune system activation, and viral reproduction. Two viral release strategies are considered: budding and bursting. The CTMC model is used to estimate the probability of virus extinction during the early stages of infection. Numerical simulations are carried out using parameter values applicable to HIV-1 dynamics. The stochastic models provide new insights, distinct from the basic deterministic models. For the case R₀>1, the deterministic models predict the viral infection persists in the host. But for the stochastic models, there is a positive probability of viral extinction. It is shown that the probability of a successful invasion depends on the initial viral dose, whether the immune system is activated, and whether the release strategy is bursting or budding.     

The Problem of Auto-Correlation in Parasitology

Explaining the contribution of host and pathogen factors in driving infection dynamics is a major ambition in parasitology. There is increasing recognition that analyses based on single summary measures of an infection (e.g., peak parasitaemia) do not adequately capture infection dynamics and so, the appropriate use of statistical techniques to analyse dynamics is necessary to understand infections and, ultimately, control parasites. However, the complexities of within-host environments mean that tracking and analysing pathogen dynamics within infections and among hosts poses considerable statistical challenges. Simple statistical models make assumptions that will rarely be satisfied in data collected on host and parasite parameters. In particular, model residuals (unexplained variance in the data) should not be correlated in time or space. Here we demonstrate how failure to account for such correlations can result in incorrect biological inference from statistical analysis. We then show how mixed effects models can be used as a powerful tool to analyse such repeated measures data in the hope that this will encourage better statistical practices in parasitology.     

Reproducibility and usability of chronic virus infection model using agent-based simulation; comparing with a mathematical model

We created agent-based models that visually simulate conditions of chronic viral infections using two software. The results from two models were consistent, when they have same parameters during the actual simulation. The simulation results comprise a transient phase and an equilibrium phase, and unlike the mathematical model, virus count transit smoothly to the equilibrium phase without overshooting which correlates with actual biology in vivo of certain viruses. We investigated the effects caused by varying all the parameters included in concept; increasing virus lifespan, uninfected cell lifespan, uninfected cell regeneration rate, virus production count from infected cells, and infection rate had positive effects to the virus count during the equilibrium period, whereas increasing the latent period, the lifespan-shortening ratio for infected cells, and the cell cycle speed had negative effects. Virus count at the start did not influence the equilibrium conditions, but it influenced the infection development rate. The space size had no intrinsic effect on the equilibrium period, but virus count maximized when the virus moving speed was twice the space size. These agent-based simulation models reproducibly provide a visual representation of the disease, and enable a simulation that encompasses parameters those are difficult to account for in a mathematical model.     

From elaborate to compact seasonal plant epidemic models and back: is competitive exclusion in the details?

Seasonality, or periodic host absence, is a central feature in plant epidemiology. In this respect, seasonal plant epidemic models take into account the way the parasite overwinters and generates new infections. These are termed primary infections. In the literature, one finds two classes of models: high-dimensional elaborate models and low-dimensional compact models, where primary infection dynamics are explicit and implicit, respectively. Investigating a compact model allowed previous authors to show the existence of a competitive exclusion principle. However, the way compact models derive from elaborate models has not been made explicit yet. This makes it unclear whether results such as competitive exclusion extend to elaborate models as well. Here, we show that assuming primary infection dynamics are fast in a standard elaborate model translates into a compact form. Yet, it is not that usually found in the literature. Moreover, we numerically show that coexistence is possible in this original compact form. Reversing the question, we show that the usual compact form approximates an alternate elaborate model, which differs from the earlier one in that primary infection dynamics are density dependent. We discuss to which extent these results shed light on coexistence within soil- and air-borne plant parasites, such as within the take-all disease of wheat and the grapevine powdery mildew cryptic species complexes, respectively.     

Sustainability of culture-driven population dynamics

We consider models of the interactions between human population dynamics and cultural evolution, asking whether they predict sustainable or unsustainable patterns of growth. Phenomenological models predict either unsustainable population growth or stabilization in the near future. The latter prediction, however, is based on extrapolation of current demographic trends and does not take into account causal processes of demographic and cultural dynamics. Most existing causal models assume (or derive from simplified models of the economy) a positive feedback between cultural evolution and demographic growth, and predict unlimited growth in both culture and population. We augment these models taking into account that: (1) cultural transmission is not perfect, i.e., culture can be lost; (2) culture does not always promote population growth. We show that taking these factors into account can cause radically different model behavior, such as population extinction rather than stability, and extinction rather than growth. We conclude that all models agree that a population capable of maintaining a large amount of culture, including a powerful technology, runs a high risk of being unsustainable. We suggest that future work must address more explicitly both the dynamics of resource consumption and the cultural evolution of beliefs implicated in reproductive behavior (e.g., ideas about the preferred family size) and in resource use (e.g., environmentalist stances).     

Estimating the impact of vaccination on acute simian-human immunodeficiency virus/simian immunodeficiency virus infections

The dynamics of HIV infection have been studied in humans and in a variety of animal models. The standard model of infection has been used to estimate the basic reproductive ratio of the virus, calculated from the growth rate of virus in acute infection. This method has not been useful in studying the effects of vaccination, since, for the vaccines developed so far, early growth rates of virus do not differ between control and vaccinated animals. Here, we use the standard model of viral dynamics to derive the reproductive ratio from the peak viral load and nadir of target cell numbers in acute infection. We apply this method to data from studies of vaccination in SHIV and SIV infection and demonstrate that vaccination can reduce the reproductive ratio by 2.3- and 2-fold, respectively. This method allows the comparison of vaccination efficacies among different viral strains and animal models in vivo.     

Arrested spread of vesicular stomatitis virus infections in vitro depends on interferon-mediated antiviral activity

A quantitative understanding of the innate immune response will enable its recruitment against emerging, poorly characterized, or weaponized viral pathogens. To gain insights into how the innate responses can limit viral spread, we used quantitative focal infections to study how the spread of recombinant vesicular stomatitis viruses (VSV) on baby hamster kidney (BHK) and delayed brain tumor (DBT) cell monolayers is affected by innate cellular antiviral responses. We observed that rates of infection spread correlated with one-step growth rankings for four ectopic VSV strains: N1, N2, N3, and N4. However, this correlation was lost for M51R, a recombinant VSV mutant that lacks the ability to shut-off host gene expression. In BHK cells, M51R spread at two-thirds the rate of the recombinant control virus, XK3.1, even though their one-step growth was comparable. In DBT cells, M51R infections failed to spread beyond the site of inoculation. Addition of anti-interferon antibody restored M51R spread and one-step growth to wild-type levels. Interestingly, the antibody enhanced the spread of wild-type virus but not its growth. These results suggest that while the rate of viral spread generally correlates with the rate of viral growth, the induction of cellular antiviral activities can be in some cases, the overriding factor in both spread and growth. In summary, focal infections enabled us to visualize and quantify how viral spread was inhibited by cellular antiviral activities. This study demonstrates a mechanism for quantifying how innate cellular responses can mitigate infection spread in vitro.