The Role of Viral Infection in Pest Control: A Mathematical Study

In this paper, we propose a mathematical model of viral infection in pest control. As the viral infection induces host lysis which releases more virus into the environment, on the average ‘κ’ viruses per host, κ∈(1,∞), so the ‘virus replication parameter’ is chosen as the main parameter on which the dynamics of the infection depends. There exists a threshold value κ ₀ beyond which the infection persists in the system. Still for increasing the value of κ, the endemic equilibrium bifurcates towards a periodic solution, which essentially indicates that the viral pesticide has a density-dependent ‘numerical response’ component to its action. Investigation also includes the dependence of the process on predation of natural enemy into the system. A concluding discussion with numerical simulation of the model is also presented.     

Role of latency period in viral infection: a pest control model

The interrelationship of latency period in viral infection and overall infection process in host community are of critical importance in context of pest control programme. Both of them regulate the overall system stability as they are dynamically linked to predation by natural enemies in the system. The present paper deals with the role of latency period in viral infection through mathematical modeling and analysis. We propose a four dimensional mathematical model with delayed infection in pest community. It is shown that there exists a certain value of delay, say T( *) such that for T>T( *) the system exhibits global stability towards disease-free equilibrium. But for T相似文献   

Antibody Responses during Hepatitis B Viral Infection

Hepatitis B is a DNA virus that infects liver cells and can cause both acute and chronic disease. It is believed that both viral and host factors are responsible for determining whether the infection is cleared or becomes chronic. Here we investigate the mechanism of protection by developing a mathematical model of the antibody response following hepatitis B virus (HBV) infection. We fitted the model to data from seven infected adults identified during acute infection and determined the ability of the virus to escape neutralization through overproduction of non-infectious subviral particles, which have HBs proteins on their surface, but do not contain nucleocapsid protein and viral nucleic acids. We showed that viral clearance can be achieved for high anti-HBV antibody levels, as in vaccinated individuals, when: (1) the rate of synthesis of hepatitis B subviral particles is slow; (2) the rate of synthesis of hepatitis B subviral particles is high but either anti-HBV antibody production is fast, the antibody affinity is high, or the levels of pre-existent HBV-specific antibody at the time of infection are high, as could be attained by vaccination. We further showed that viral clearance can be achieved for low equilibrium anti-HBV antibody levels, as in unvaccinated individuals, when a strong cellular immune response controls early infection.     

Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells

A mathematical model that describes HIV infection of CD4(+) T cells is analyzed. Global dynamics of the model is rigorously established. We prove that, if the basic reproduction number R(0) < or = 1, the HIV infection is cleared from the T-cell population; if R(0) > 1, the HIV infection persists. For an open set of parameter values, the chronic-infection equilibrium P* can be unstable and periodic solutions may exist. We establish parameter regions for which P* is globally stable.     

Transmission selects for HIV-1 strains of intermediate virulence: a modelling approach

Recent data shows that HIV-1 is characterised by variation in viral virulence factors that is heritable between infections, which suggests that viral virulence can be naturally selected at the population level. A trade-off between transmissibility and duration of infection appears to favour viruses of intermediate virulence. We developed a mathematical model to simulate the dynamics of putative viral genotypes that differ in their virulence. As a proxy for virulence, we use set-point viral load (SPVL), which is the steady density of viral particles in blood during asymptomatic infection. Mutation, the dependency of survival and transmissibility on SPVL, and host effects were incorporated into the model. The model was fitted to data to estimate unknown parameters, and was found to fit existing data well. The maximum likelihood estimates of the parameters produced a model in which SPVL converged from any initial conditions to observed values within 100-150 years of first emergence of HIV-1. We estimated the 1) host effect and 2) the extent to which the viral virulence genotype mutates from one infection to the next, and found a trade-off between these two parameters in explaining the variation in SPVL. The model confirms that evolution of virulence towards intermediate levels is sufficiently rapid for it to have happened in the early stages of the HIV epidemic, and confirms that existing viral loads are nearly optimal given the assumed constraints on evolution. The model provides a useful framework under which to examine the future evolution of HIV-1 virulence.     

具有三时滞Lotka-Volterra互惠系统的Hopf分支

建立了具有三个时滞的Lotka-Volterra互惠系统;获得了正平衡点和Hopf分支存在的条件等;并对所获得的结果进行了数值模拟．     

Some basic properties of immune selection

We analyze models for the evolutionary dynamics of viral or other infectious agents within a host. We study how the invasion of a new strain affects the composition and diversity of the viral population. We show that--under strain-specific immunity--the equilibrium abundance of uninfected cells declines during viral evolution. In addition, for cytotoxic immunity the absolute force of infection, and for non-cytotoxic immunity the absolute cellular virulence increases during viral evolution. We prove global stability by means of Lyapunov functions. These unidirectional trends of virus evolution under immune selection do not hold for general cross-reactive immune responses, which introduce frequency-dependent selection among viral strains. Therefore, appropriate cross-reactive immunity can lead to a viral evolution within a host which limits the extent of the disease.     

Sustained and transient oscillations and chaos induced by delayed antiviral immune response in an immunosuppressive infection model

Sustained and transient oscillations are frequently observed in clinical data for immune responses in viral infections such as human immunodeficiency virus, hepatitis B virus, and hepatitis C virus. To account for these oscillations, we incorporate the time lag needed for the expansion of immune cells into an immunosuppressive infection model. It is shown that the delayed antiviral immune response can induce sustained periodic oscillations, transient oscillations and even sustained aperiodic oscillations (chaos). Both local and global Hopf bifurcation theorems are applied to show the existence of periodic solutions, which are illustrated by bifurcation diagrams and numerical simulations. Two types of bistability are shown to be possible: (i) a stable equilibrium can coexist with another stable equilibrium, and (ii) a stable equilibrium can coexist with a stable periodic solution.     

Existence and bifurcation of stable equilibrium in two-prey,one-predator communities

In this paper, stability of two-prey, one-predator communities is investigated by Lyapunov's direct method and Hopf's bifurcation theory. Three patterns of three-species coexistence are possible. A globally stable non-negative equilibrium exists for the system even if two competing prey species without a predator cannot coexist. The stable equilibrium bifurcates to a periodic motion with a small amplitude when the predation rate increases. It is also shown that a chaotic motion emerges from the periodic motion when one of two prey has greater competitive abilities than the other. This predator-mediated coexistence can be realized by the intimate relationship between preferences of a predator and competitive abilities of two prey.     

一类食饵捕食系统的Hopf分岔及周期解的稳定性

首先建立了具有时滞的三种群食饵捕食模型,并研究了平衡点的存在性,接着应用规范化方法和中心流行定理研究了Hopf分岔以及分岔周期解的稳定性.并举例论证.     

Modeling within-host and aerosol dynamics of SARS-CoV-2: The relationship with infectiousness

The relationship between transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and the amount of virus present in the proximity of a susceptible host is not understood. Here, we developed a within-host and aerosol mathematical model and used it to determine the relationship between viral kinetics in the upper respiratory track, viral kinetics in the aerosols, and new transmissions in golden hamsters challenged with SARS-CoV-2. We determined that infectious virus shedding early in infection correlates with transmission events, shedding of infectious virus diminishes late in the infection, and high viral RNA levels late in the infection are a poor indicator of transmission. We further showed that viral infectiousness increases in a density dependent manner with viral RNA and that their relative ratio is time-dependent. Such information is useful for designing interventions.     

A mathematical design of vector vaccine against autoimmune disease

Viruses have been implicated in the initiation, progression, and exacerbation of several human autoimmune diseases. Evidence also exists that viruses can protect against autoimmune disease. Several proposed mechanisms explain the viral effects. One mechanism is “molecular mimicry” which represents a shared immunologic epitope with a microbe and the host. We consider, using a simple mathematical model, whether and how a viral infection with molecular mimicry can be beneficial or detrimental for autoimmune disease. Furthermore, we consider the possibility of development of a vector therapeutic vaccine that can relieve autoimmune disease symptoms. Our findings demonstrate that vaccine therapy success necessitates (i) appropriate immune response function, (ii) appropriate affinities with self and non-self antigen, and (iii) a replicative vector vaccine. Moreover, the model shows that the viral infection can cause autoimmune relapses.     

A new theory of cytotoxic T-lymphocyte memory: implications for HIV treatment

We use simple mathematical models to examine the dynamics of primary and secondary cytotoxic T-lymphocyte (CTL) responses to viral infections. In particular, we are interested in conditions required to resolve the infection and to protect the host upon secondary challenge. While protection against reinfection is only effective in a restricted set of circumstances, we find that resolution of the primary infection requires persistence of CTL precursors (GTLp), as well as a fast rate of activation of the CTLp. Since these are commonly the defining characteristics of CTL memory, we propose that CTL memory may have evolved in order to clear the virus during primary challenge. We show experimental data from lymphocytic choriomeningitis virus infection in mice, supporting our theory on CTL memory. We adapt our models to HIV and find that immune impairment during the primary phase of the infection may result in the failure to establish CTL memory which in turn leads to viral persistence. Based on our models we suggest conceptual treatment regimes which ensure establishment of CTL memory. This would allow the immune response to control HIV in the long term in the absence of continued therapy.     

LPP-1 Infection of the Blue-Green Alga Plectonema boryanum: II. Viral Deoxyribonucleic Acid Synthesis and Host Deoxyribonucleic Acid Breakdown

Host and viral deoxyribonucleic acid (DNA) metabolism in LPP-1-infected Plectonema boryanum was studied by equilibrium centrifugation in CsCl gradients. Approximately 50% of the host DNA is degraded to acid-soluble material between 3 and 7 hr after infection. Most of the acid-soluble product is reincorporated into viral DNA. Incorporation of exogenous (3)H-adenine into viral DNA can be detected very early after infection (within the first 2 hr), but the bulk of viral DNA synthesis occurs between 6 and 8 hr. Both the breakdown of host DNA and the synthesis of viral DNA require protein synthesis during the first few hours of infection.     

The evolution of virus-induced apoptosis.

Viruses from several different families are able to exploit their host''s cell death programmes so as to maximize viral fitness. Consideration of the evolution of such strategies has lead to the suggestion that the virus should inhibit apoptosis, in order to prolong the life of the cell and thereby maximize the number of progeny virions. The host, on the other hand, should stimulate apoptosis thereby inhibiting viral growth and blocking viral spread. For example, the function of the latent membrane protein I (LMPI) of the Epstein-Barr virus and the bcl-2 homologue gene A179L of African swine fever virus is to inhibit apoptosis. However, in other cases it is the virus that stimulates cell death or the host that benefits from inhibiting apoptosis, such as in fatal alphavirus encephalitis. This has been explained by assuming that virus-induced apoptosis in non-regenerating cells would be detrimental to the host. We present a mathematical framework for understanding virus-induced apoptosis which accounts for these two opposite solutions to virus infection with respect to the mode of virus replication and the life cycle of the target cell.     

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.     

The dynamics of T-cell fratricide: application of a robust approach to mathematical modelling in immunology

Fratricide between CD8(+) T lymphocytes is known to occur in HTLV-I and possibly HSV-1 and HIV-1 infection. However it is not known what effect, if any, T-cell fratricide has on the course of infection. Here we present simple mathematical techniques to investigate T-cell fratricide with particular reference to HTLV-I infection. Using a general model we predict the qualitative and quantitative effect of fratricide on HTLV-I equilibrium proviral load. We also investigate the effect of fratricide on the probability of viral clearance. We show that, surprisingly, fratricide can lead either to an increase or a decrease in equilibrium proviral load. We derive the conditions necessary for fratricide to cause a decrease in load and deduce that, for the five HTLV-I-positive patients considered here, fratricide has probably caused an increase in equilibrium load. We also estimate the percentage increase in load that is attributable to fratricide and determine the parameters that should be measured in order to improve this estimate. Finally, we show that fratricide reduces the probability of viral clearance. Mathematical modelling of HTLV-I infection, as is often the case in biology, is severely hampered by a lack of experimental data. Consequently it is difficult to know what functional form a model should take. The behaviour of complex nonlinear systems is highly model-dependent. Predictions based on theoretical models are therefore sensitive to the choice of model; this is a very severe problem that undermines and limits the success of the application of mathematics to immunology. In this paper we reduce the model dependency of the results in two ways-by considering (analytically) a general model with a minimal number of assumptions and, where this is not possible, by checking (numerically) that a wide range of models yield the same results. We therefore begin to develop two practical methods for dealing with the problem of robustness in mathematical models of the immune system.     

Structural organization of DNA in chlorella viruses

Chlorella viruses have icosahedral capsids with an internal membrane enclosing their large dsDNA genomes and associated proteins. Their genomes are packaged in the particles with a predicted DNA density of ca. 0.2 bp nm(-3). Occasionally infection of an algal cell by an individual particle fails and the viral DNA is dynamically ejected from the capsid. This shows that the release of the DNA generates a force, which can aid in the transfer of the genome into the host in a successful infection. Imaging of ejected viral DNA indicates that it is intimately associated with proteins in a periodic fashion. The bulk of the protein particles detected by atomic force microscopy have a size of ～60 kDa and two proteins (A278L and A282L) of about this size are among 6 basic putative DNA binding proteins found in a proteomic analysis of DNA binding proteins packaged in the virion. A combination of fluorescence images of ejected DNA and a bioinformatics analysis of the DNA reveal periodic patterns in the viral DNA. The periodic distribution of GC rich regions in the genome provides potential binding sites for basic proteins. This DNA/protein aggregation could be responsible for the periodic concentration of fluorescently labeled DNA observed in ejected viral DNA. Collectively the data indicate that the large chlorella viruses have a DNA packaging strategy that differs from bacteriophages; it involves proteins and share similarities to that of chromatin structure in eukaryotes.     

Correlates of cytotoxic T-lymphocyte-mediated virus control: implications for immunosuppressive infections and their treatment

A very important question in immunology is to determine which factors decide whether an immune response can efficiently clear or control a viral infection, and under what circumstances we observe persistent viral replication and pathology. This paper summarizes how mathematical models help us gain new insights into these questions, and explores the relationship between antiviral therapy and long-term immunological control in human immunodeficiency virus (HIV) infection. We find that cytotoxic T lymphocyte (CTL) memory, defined as antigen-independent persistence of CTL precursors, is necessary for the CTL response to clear an infection. The presence of such a memory response is associated with the coexistence of many CTL clones directed against multiple epitopes. If CTL memory is inefficient, then persistent replication can be established. This outcome is associated with a narrow CTL response directed against only one or a few viral epitopes. If the virus replicates persistently, occurrence of pathology depends on the level of virus load at equilibrium, and this can be determined by the overall efficacy of the CTL response. Mathematical models suggest that controlled replication is reflected by a positive correlation between CTLs and virus load. On the other hand, uncontrolled viral replication results in higher loads and the absence of a correlation between CTLs and virus load. A negative correlation between CTLs and virus load indicates that the virus actively impairs immunity, as observed with HIV. Mathematical models and experimental data suggest that HIV persistence and pathology are caused by the absence of sufficient CTL memory. We show how mathematical models can help us devise therapy regimens that can restore CTL memory in HIV patients and result in long-term immunological control of the virus in the absence of life-long treatment.