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.     

Mathematical modeling of viral kinetics under immune control during primary HIV-1 infection

Primary human immunodeficiency virus (HIV) infection is characterized by an initial exponential increase of viral load in peripheral blood reaching a peak, followed by a rapid decline to the viral setpoint. Although the target-cell-limited model can account for part of the viral kinetics observed early in infection [Phillips, 1996. Reduction of HIV concentration during acute infection: independence from a specific immune response. Science 271 (5248), 497-499], it frequently predicts highly oscillatory kinetics after peak viremia, which is not typically observed in clinical data. Furthermore, the target-cell-limited model is unable to predict long-term viral kinetics, unless a delayed immune effect is assumed [Stafford et al., 2000. Modeling plasma virus concentration during primary HIV infection. J. Theor. Biol. 203 (3), 285-301]. We show here that extending the target-cell-limited model, by implementing a saturation term for HIV-infected cell loss dependent upon infected cell levels, is able to reproduce the diverse observed viral kinetic patterns without the assumption of a delayed immune response. Our results suggest that the immune response may have significant effect on the control of the virus during primary infection and may support experimental observations that an anti-HIV immune response is already functional during peak viremia.     

Oscillations in cyclical neutropenia: new evidence based on mathematical modeling

We present a dynamical model of the production and regulation of circulating blood neutrophil number. This model is derived from physiologically relevant features of the hematopoietic system, and is analysed using both analytic and numerical methods. Supercritical Hopf bifurcations and saddle-node bifurcations of limit cycles are shown to exist. We make the estimation of kinetic parameters for dogs and then apply the model to cyclical neutropenia (CN) in the grey collie, a rare disorder in which oscillations in all blood cell counts are found. We conclude that the major cause of the oscillations in CN is an increased rate of apoptosis of neutrophil precursors which leads to a destabilization of the hematopoietic stem cell compartment.     

非线性红松林生态系统的定性与分支研究(英文)

利用系统分析的方法研究了一类非线性红松林生态系统的稳定性,讨论了其鞍结分支和Hopf分支,且对Hopf分支周期解进行了详细的分析和计算,指出了红松林生态系统中松籽、鼠类和幼苗三种群数量具有周期波动的特征.     

害虫的基因沉默控制

作为现代分子生物学的重大突破性成果之一,基因沉默是人为调控基因表达的重要途径之一。本文介绍了基因沉默的发现历史、作用机制及其在昆虫中的研究进展,以及利用基因沉默原理进行害虫控制的探索,并展望害虫基因沉默控制的应用前景。     

Quantitative analysis of the Hopf bifurcation in the Goodwin n-dimensional metabolic control system

We study, from a quantitative point of view, the Hopf bifurcation in an ODE model of feedback control type introduced by Goodwin (1963) to describe the dynamics of end-product inhibition of gene activity. We formally prove that the exchange of linear stability of the positive equilibrium in the n-dimensional Goodwin system with equal reaction constants coexists with a Hopf bifurcation of nontrivial periodic solutions emanating from this equilibrium, without any further restriction on the dimension n 3 or on the Hill coefficient . The direction of the bifurcation, and the stability and the period of the bifurcating orbits are estimated by means of the algorithm proposed by Hassard et al. (1981).Supported by MURST 40/60%     

Immune impairment in HIV infection: Existence of risky and immunodeficiency thresholds

Results of several studies show that some DC populations are susceptible to HIV. Modulation of DCs by HIV infection, in particular interference of the antigen-presenting function of DCs, is a key aspect in viral pathogenesis and contributes to viral evasion from immunity because the loss of the DC function engenders some impairment effects for a proliferation of CTL responses, which play an important role in the immune response to HIV. As described herein, we use a simple mathematical model to examine virus-immune dynamics over the course of HIV infection in the context of the immune impairment effects. A decrease of the DC number and function during the course of HIV-1 infection is observed. Therefore, we simply assumed that the immune impairment rate increases over the HIV infection. Under the assumption, four processes of the disease progression dynamics of our model are classifiable according to their virological properties. It is particularly interesting a typical disease progression presents a “risky threshold” and an “immunodeficiency threshold”. Regarding the former, the immune system might collapse when the impairment rate of HIV exceeds a threshold value (which corresponds to a transcritical bifurcation point). For the latter, the immune system always collapses when the impairment rate exceeds the value (which corresponds to a saddle-node bifurcation point). To test our theoretical framework, we investigate the existence and distribution of these thresholds in 10 patients.     

Cancer immunotherapy, mathematical modeling and optimal control

Clinical immunologists, among other problems, routinely face a question: what is the best time and dose for a certain therapeutic agent to be administered to the patient in order to decrease/eradicate the pathological condition? In cancer immunotherapies the therapeutic agent is something able to elicit an immune response against cancer. The immune response has its own dynamics that depends on the immunogenicity of the therapeutic agent and on the duration of the immune response. The question then is "how can we decide when and how much of the drug to inject so to have a prolonged and effective immune response to the cancer?". This question can be addressed in mathematical terms in two stages: first one construct a mathematical model describing the cancer-immune interaction and secondly one applies the theory of optimal control to determine when and to which extent to stimulate the immune system by means of an immunotherapeutic agent administered in discrete variable doses within the therapeutic period. The solution of this mathematical problem is described and discussed in this article. We show that the method employed can be applied to find the optimal protocol in a variety of clinical problems where the kinetics of the drug or treatment and its influence on the physiologic/pathologic functions have been described by a system of ordinary differential equations.     

Adaptive modeling of viral diseases in bats with a focus on rabies

Many emerging and reemerging viruses, such as rabies, SARS, Marburg, and Ebola have bat populations as disease reservoirs. Understanding the spillover from bats to humans and other animals, and the associated health risks requires an analysis of the disease dynamics in bat populations. Traditional compartmental epizootic models, which are relatively easy to implement and analyze, usually impose unrealistic aggregation assumptions about disease-related structure and depend on parameters that frequently are not measurable in field conditions. We propose a novel combination of computational and adaptive modeling approaches that address the maintenance of emerging diseases in bat colonies through individual (intra-host) models of the response of the host to a viral challenge. The dynamics of the individual models are used to define survival, susceptibility and transmission conditions relevant to epizootics as well as to develop and parametrize models of the disease evolution into uniform and diverse populations. Applications of the proposed approach to modeling the effects of immunological heterogeneity on the dynamics of bat rabies are presented.     

Effect of temperature on viral infection and its control: a mathematical approach

The interrelationship of the host-virus-environment is of critical importance in determining the amount of virus production per insect and its consequences in the overall infection process in insect community. Lower temperature inhibits the virus replication and thus infection does not persist into the system. On the other hand, virus production per insect increases with temperature increase within certain limit, and this increase of virus production brings some unforeseen consequences in the infection dynamics in pest control. We deal the problem by applying non-vulnerability concept on the mathematical model of viral infection that linked up with the temperature-viral developmental model. Using Lyapunov-like function, we determine a range of temperature and show that the system would become endemic and remain in stable situation if temperature could be maintained in this prescribed range, whereas that range depends on other parameters of the system.     

Biological control through provision of additional food to predators: a theoretical study

In this paper we analyze a variation of a standard predator-prey model with type II functional response which represents predator-prey dynamics in the presence of some additional food to the predator. The aim is to study the consequences of providing additional food on the system dynamics. We conclude that handling times for the available foods play a key role in determining the eventual state of the ecosystem. It is interesting to observe that by varying the quality and quantity of additional food we can not only control and limit the prey, but also limit and eradicate the predators. In the context of biological pest control, the results caution the manager on the choice of quality and quantity of the additional food used for this purpose. An arbitrary choice may have opposite effects leading to increase in pest concentration and eradication of the predator. This study offers insight into the possible management strategies that involve manipulation of quality and supply level of additional food to predators, for the benefit of biological control. The theoretical conclusions agree with results of some practical biological control experiments.     

Vitamin D deficiency in community-acquired pneumonia: low levels of 1,25(OH)2 D are associated with disease severity

Objectives

We aimed to explore the association between vitamin D levels and the severity, mortality and microbiological etiology of community-acquired pneumonia.

Methods

Vitamin D levels (both, the reservoir form 25-OH and the activated form 1,25-OH2) of 300 randomly selected patients with community-acquired pneumonia due to pre-specified pathogens included in the German competence network (CAPNETZ) study were measured. Prior to statistical analysis, values of 25-OH and 1,25-OH2 were power-transformed to achieve parametric distribution. All further analyses were performed with seasonally and age adjusted values.

Results

There was only a modest (Spearman Coefficient 0.38) positive correlation between 25-OH and 1,25-OH2. For 1,25-OH2 but not 25-OH, the general linear model revealed a significant inverse correlation between serum concentration and CURB score (p = 0.011). Liver and respiratory co-morbidity were associated with significantly lower 25-OH values and renal co-morbidity with significantly lower 1,25-OH2 values. No significant differences of 1,25-OH2 or 25-OH between different pathogens (influenza virus, Legionella spp., Streptococcus pneumoniae) were detected.

Conclusion

For 1,25-OH2, we found a significant and independent (controlled for age, season and pathogen) negative correlation to pneumonia severity. Therefore, supplementation of non-activated vitamin D to protect from pneumonia may be non-sufficient in patients that have a decreased capacity to hydroxylate 25-OH to 1,25-OH2.     

Mathematical models of the early embryonic cell cycle: the role of MPF activation and cyclin degradation

Recent advances in cell biology indicate that the interactions between two proteins, cdc2 and cyclin, together with the activity of the cdc2/cyclin complex called MPF in the cytoplasm form the basis of a universal biochemical control mechanism for the cell division cycle in eukaryotes. Based on experimental facts that total cdc2 level is constant throughout the cell cycle and that onset of mitosis is subsequent to activation of MPF, we propose and analyze two different but related models — an ordinary differential equations model and a delay differential equations model — for the control of the early embryonic cell division cycle. Assuming very general reaction terms in the model equations, it is shown that MPF activation and rapid cyclin degradation triggered by active MPF drive cells to alternate between interphase and mitosis, the two phases of the cell cycle.S. Busenberg passed away on April 3, 1993 from complications of ALS (Lou Gehrig's disease). His research was supported by NSF Grant DMS-9112821Research was carried out at Harvey Mudd College and was supported by NSF Grant HRD-9252994     

Dynamics and bifurcation of a model for hormonal control of the menstrual cycle with inhibin delay

A system of 13 ordinary differential equations with 42 parameters is presented to model hormonal regulation of the menstrual cycle. For an excellent fit to clinical data, the model requires a 36 h time delay for the effect of inhibin on the synthesis of follicle stimulating hormone. Biological and mathematical reasons for this delay are discussed. Bifurcations with respect to changes in three important parameters are examined. One parameter represents the level of estradiol adequate for significant synthesis of luteinizing hormone. Bifurcation diagrams with respect to this parameter reveal an interval of parameter values for which a unique stable periodic solution exists and this solution represents a menstrual cycle during which ovulation occurs. The second parameter measures mass transfer between the first two stages of ovarian development and is indicative of healthy follicular growth. The third parameter is the time delay. Changes in the second parameter and the time delay affect the size of the uniqueness interval defined with respect to the first parameter. Saddle-node, transcritical and degenerate Hopf bifurcations are studied.     

Respiratory viral infection predisposing for bacterial disease: a concise review

Although bacterial superinfection in viral respiratory disease is a clinically well documented phenomenon, the pathogenic mechanisms are still poorly understood. Recent studies have revealed some of the mechanisms involved. Physical damage to respiratory cells as a result of viral infection may lead to opportunistic adherence of bacteria. Enhanced bacterial adherence by specific mechanisms has been documented for respiratory cells infected with influenza A virus, respiratory syncytial virus and adenovirus in both in vitro and in vivo models. To date, results of various experimental studies indicate that different mechanisms for increased bacterial adherence induced by viruses are operating for specific viral-bacterial combinations. In the present review, a number of key findings obtained during the past two decades is presented and discussed.     

Infectivity of Anticarsia gemmatalis nucleopolyhedrovirus to different insect cell lines: Morphology, viral production, and protein synthesis

The Anticarsia gemmatalis nucleopolyhedrovirus (AgMNPV) is currently used as an efficient biological pesticide for the control of the velvetbean caterpillar (A. gemmatalis), an important pest of soybean in Brazil. Until now, production of the virus has been achieved mainly by infection of larvae on local soybean farms. Studies for the development of in vitro systems and the optimization of mass production in insects reared on artificial diets is now important to help to meet the actual demand for the bioinsecticide. We therefore, investigated the infectivity of AgMNPV in cell culture, which might contribute to the selection of suitable cell lines that may be used for in vitro production of this virus. The cytopathic effects induced by the virus, the production of viral particles and the synthesis of viral polypeptides were examined and compared in the cell lines from A. gemmatalis (UFL-AG-286), Trichoplusia ni (BTI-Tn-5B1-4 and TN-368), Spodoptera frugiperda (IPLB-SF-21AE and Sf9), Lymantria dispar (IPLB-LD-652Y), and Bombyx mori (BM-5). Whereas, Tn-5B1-4 and AG-286 cells produced large numbers of occlusion bodies, no polyhedra were visualized in either Ld-652Y or BM-5 cells, although extensive cell lysis was observed in BM-5. Analysis of the kinetics of viral protein synthesis by SDS–PAGE after pulse labeling with [³⁵S]methionine, showed similar protein patterns in most of the cell lines tested. Exceptions were the LD-652Y and BM-5 cells, in which viral polypeptides, including polyhedrin, were not synthesized. In parallel, measurement of viral titers (budded virus) by the endpoint dilution method showed that Tn-5B1-4, AG-286, and SF-21AE cells were highly productive. Their TCID₅₀ values, at 48 h p.i., were about 10⁷ IU/ml. In addition to the lower formation of polyhedra, the viral titers determined in Sf9 and TN-368 cells were about 5 to10-fold lower. As expected, the viral titers obtained in LD-652Y and BM-5 cells were similar to basal levels.     

Integrative models of bat rabies immunology, epizootiology and disease demography

Bats are natural reservoirs of rabies. We address the maintenance of the disease in bat colonies by developing individual and population models that generate indicators of risk of rabies to bats, that provide dynamic estimates of effects of rabies on population densities, and that suggest consequences of viral exposures and infections in bats relative to physiological and ecological characteristics of bats in different habitats. We present individual models (within host) for the immune responses to a rabies virus challenge, an immunotypic disease model that describes the evolution of the disease and a disease demographics model, which is structured by immunotypic response governed by immune system efficiency. Model simulations are consistent with available data, characterized by relatively low prevalence of the virus in colonies and much higher prevalence of rabies virus-neutralizing antibodies. Under model conditions, there is a robust non-clinical state that can be attained by the exposed individual that allows persistence of the disease in the population.     

Damage and ecological characteristics of termite Neotermes koshunensis on Taiwan cherry tree Cerasus campanulata in Okinawa Island

Termites are typical house pests that can also be harmful pests for living trees, although this topic has not received much attention. To clarify the damage to trees caused by dry-wood termites (Neotermes koshunensis), and the ecological characteristics of such damage, we conducted a study on Taiwan cherry trees (Cerasus campanulata) grown in parks, historical sites, and streets in the central-southern area of Okinawa Island, a subtropical region. Damage by N. koshunensis was confirmed in 21 of the 36 sites surveyed (58.3%) and in 76 of the 1076 trees surveyed (7.1%). However, damage by Formosan subterranean termites (Coptotermes formosanus), a house pest, was only observed at six sites (16.7%), and 10 trees (0.9%), indicating that most damage was caused by N. koshunensis. Furthermore, the probability of the presence of damaged trees close to other damaged trees was significantly higher than the probability of the presence of damaged trees close to undamaged trees, implying that destructive colonies spread from damaged trees to other trees nearby. Therefore, care for trees in the initial stages of termite invasion seems to be the best method for preventing the spread N. koshunensis damage to other trees in the same area. To our knowledge, this study is the first to report that dry-wood termite N. koshunensis are harmful pests for Taiwan cherry trees in Okinawa Island. Our results could be used to establish dry-wood termite countermeasures for garden tree species.     

A network approach to modeling population aggregation and genetic control of pest insects

Historically, models of the invasion and biological control of insect pests have omitted heterogeneities in the spatial structure of the targeted populations. In this study, we use stochastic network simulations to examine explicitly population heterogeneity as a function of landscape structure and insect behavior. We show that when insects are distributed non-randomly across a heterogeneous landscape, control can be significantly hindered. However, when insect populations are clustered as a result of limited dispersal, genetic control efficiency can be enhanced. In developing the model, we relax a key assumption of previous theoretical studies of genetic control: that released genetic control insects remain homogenously distributed irrespective of the spatial structure of the wild type populations. Here, this behavior (termed the ‘coverage proportion’) is parameterized and its properties are explored. We show that landscape heterogeneity and limited dispersal have little effect on the critical coverage proportion necessary for control.