An SIS epidemic model with variable population size and a delay

The SIS epidemiological model has births, natural deaths, disease-related deaths and a delay corresponding to the infectious period. The thresholds for persistence, equilibria and stability are determined. The persistence of the disease combined with the disease-related deaths can cause the population size to decrease to zero, to remain finite, or to grow exponentially with a smaller growth rate constant. For some parameter values, the endemic infective-fraction equilibrium is asymptotically stable, but for other parameter values, it is unstable and a surrounding periodic solution appears by Hopf bifurcation.Research Supported in part by NSERC grant A-8965 and the University of Victoria Committee on Faculty Research & Travel     

An epidemiological model with a delay and a nonlinear incidence rate

An epidemiological model with both a time delay in the removed class and a nonlinear incidence rate is analysed to determine the equilibria and their stability. This model is for diseases where individuals are first susceptible, then infected, then removed with temporary immunity and then susceptible again when they lose their immunity. There are multiple equilibria for some parameter values, and, for certain of these, periodic solutions arise by Hopf bifurcation from the large nontrivial equilibrium state.Research supported in parts by Centers for Disease Control Contract 200-87-0515Research supported in part by NSERC A-8965     

Optimal HIV treatment by maximising immune response

We present an optimal control model of drug treatment of the human immunodeficiency virus (HIV). Our model is based upon ordinary differential equations that describe the interaction between HIV and the specific immune response as measured by levels of natural killer cells. We establish stability results for the model. We approach the treatment problem by posing it as an optimal control problem in which we maximise the benefit based on levels of healthy CD4+ T cells and immune response cells, less the systemic cost of chemotherapy. We completely characterise the optimal control and compute a numerical solution of the optimality system via analytic continuation.Research supported by the Natural Science and Engineering Research Council (NSERC) and the Mathematics of Information Technology and Complex Systems (MITACS) of Canada     

Transmission dynamics of West Nile virus in mosquitoes and corvids and non-corvids

There are more than 300 avian species that can transmit West Nile virus (WNv). In general, the corvid and non-corvid families of birds have different responses to the virus, with corvids suffering a higher disease-induced mortality rate. By taking both corvids and non-corvids as the primary reservoir hosts and mosquitoes as vectors; we formulate and study a system of ordinary differential equations to model a single season of the transmission dynamics of WNv in the mosquito–bird cycle. We calculate the basic reproduction number and analyze the existence and stability of the equilibria. The existence of a backward bifurcation gives a further sub-threshold condition beyond the basic reproduction number for the spread of the virus. We also discuss the role of corvids and non-corvids in spreading the virus. We conclude that knowledge of the relative abundance of corvid bird species and other mammals assist us in accurate estimation of the epidemic of WNv.     

A Periodic Droop Model for Two Species Competition in A Chemostat

Both uniform persistence and the existence of periodic coexistence state are established for a periodically forced Droop model on two phytoplankton species competition in a chemostat under some appropriate conditions. Numerical simulations using biological data are presented as well to illustrate the main result. Research supported in part by the NSERC of Canada and the MITACS of Canada.     

NMR Analysis of the Dynamic Exchange of the NS2B Cofactor between Open and Closed Conformations of the West Nile Virus NS2B-NS3 Protease

Background

The two-component NS2B-NS3 proteases of West Nile and dengue viruses are essential for viral replication and established targets for drug development. In all crystal structures of the proteases to date, the NS2B cofactor is located far from the substrate binding site (open conformation) in the absence of inhibitor and lining the substrate binding site (closed conformation) in the presence of an inhibitor.

Methods

In this work, nuclear magnetic resonance (NMR) spectroscopy of isotope and spin-labeled samples of the West Nile virus protease was used to investigate the occurrence of equilibria between open and closed conformations in solution.

Findings

In solution, the closed form of the West Nile virus protease is the predominant conformation irrespective of the presence or absence of inhibitors. Nonetheless, dissociation of the C-terminal part of the NS2B cofactor from the NS3 protease (open conformation) occurs in both the presence and the absence of inhibitors. Low-molecular-weight inhibitors can shift the conformational exchange equilibria so that over 90% of the West Nile virus protease molecules assume the closed conformation. The West Nile virus protease differs from the dengue virus protease, where the open conformation is the predominant form in the absence of inhibitors.

Conclusion

Partial dissociation of NS2B from NS3 has implications for the way in which the NS3 protease can be positioned with respect to the host cell membrane when NS2B is membrane associated via N- and C-terminal segments present in the polyprotein. In the case of the West Nile virus protease, discovery of low-molecular-weight inhibitors that act by breaking the association of the NS2B cofactor with the NS3 protease is impeded by the natural affinity of the cofactor to the NS3 protease. The same strategy can be more successful in the case of the dengue virus NS2B-NS3 protease.     

Big Science vs. Little Science: How Scientific Impact Scales with Funding

Agencies that fund scientific research must choose: is it more effective to give large grants to a few elite researchers, or small grants to many researchers? Large grants would be more effective only if scientific impact increases as an accelerating function of grant size. Here, we examine the scientific impact of individual university-based researchers in three disciplines funded by the Natural Sciences and Engineering Research Council of Canada (NSERC). We considered four indices of scientific impact: numbers of articles published, numbers of citations to those articles, the most cited article, and the number of highly cited articles, each measured over a four-year period. We related these to the amount of NSERC funding received. Impact is positively, but only weakly, related to funding. Researchers who received additional funds from a second federal granting council, the Canadian Institutes for Health Research, were not more productive than those who received only NSERC funding. Impact was generally a decelerating function of funding. Impact per dollar was therefore lower for large grant-holders. This is inconsistent with the hypothesis that larger grants lead to larger discoveries. Further, the impact of researchers who received increases in funding did not predictably increase. We conclude that scientific impact (as reflected by publications) is only weakly limited by funding. We suggest that funding strategies that target diversity, rather than “excellence”, are likely to prove to be more productive.     

A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay

 We consider a two-dimensional model of cell-to-cell spread of HIV-1 in tissue cultures, assuming that infection is spread directly from infected cells to healthy cells and neglecting the effects of free virus. The intracellular incubation period is modeled by a gamma distribution and the model is a system of two differential equations with distributed delay, which includes the differential equations model with a discrete delay and the ordinary differential equations model as special cases. We study the stability in all three types of models. It is shown that the ODE model is globally stable while both delay models exhibit Hopf bifurcations by using the (average) delay as a bifurcation parameter. The results indicate that, differing from the cell-to-free virus spread models, the cell-to-cell spread models can produce infective oscillations in typical tissue culture parameter regimes and the latently infected cells are instrumental in sustaining the infection. Our delayed cell-to-cell models may be applicable to study other types of viral infections such as human T-cell leukaemia virus type 1 (HTLV-1). Received: 18 November 2000 / Published online: 28 February 2003 RID="*" ID="*" Research was partially supported by the NSERC and MITACS of Canada and a start-up fund from the College of Arts and Sciences at the University of Miami. On leave from Dalhousie University, Halifax, Nova Scotia, Canada. Current address: Department of Mathematics, Clarke College, Dubuque, Iowa 52001, USA Key words or phrases: HIV-1 – Cell-to-cell spread – Time delay – Stability – Hopf bifurcation – Periodicity     

The dynamics of two-species allelopathic competition with optimal harvesting

This paper analyses a bionomic model of two competitive species in the presence of toxicity with different harvesting efforts. An interesting dynamics in the first quadrant is analysed and two saddle-node bifurcations are detected for different bifurcation parameters. It is noted that under certain parametric restrictions, the model has a unique positive equilibrium point that is globally asymptotically stable whenever it is locally stable. It is also noted that the model can have zero, one or two feasible equilibria appearing through saddle-node bifurcations. The non-existence of a limit cycle in the interior of the first quadrant is also discussed using the Poincare–Dulac criteria. The saddle-node bifurcations are studied using Sotomayor's theorem. Numerical simulations are carried out to validate the analytical findings. The conditions for the existence of bionomic equilibria are discussed and an optimal harvesting policy is derived using Pontryagin's maximum principle.     

Fluorescence banding patterns of the rat chromosomes

The quinacrine-fluorescence karyotype was analysed in 7 rats of Wistar-King A (WKA/Mk) and Wistar (W/Mk) strains. All 20 pairs of autosomes and the X and Y chromosomes have been identified. No polymorphic band has been found within or between the strains. The characteristic banding pattern of each pair was described, and the idiogram of WKA/Mk rat was presented.Contribution from the Chromosome Research Unit, Hokkaido University. Supported by grants from the Scientific Research Fund of the Ministry of Education and from the Princess Takamatsu Cancer Research Fund.     

The dynamics of two-species allelopathic competition with optimal harvesting

This paper analyses a bionomic model of two competitive species in the presence of toxicity with different harvesting efforts. An interesting dynamics in the first quadrant is analysed and two saddle-node bifurcations are detected for different bifurcation parameters. It is noted that under certain parametric restrictions, the model has a unique positive equilibrium point that is globally asymptotically stable whenever it is locally stable. It is also noted that the model can have zero, one or two feasible equilibria appearing through saddle-node bifurcations. The non-existence of a limit cycle in the interior of the first quadrant is also discussed using the Poincare-Dulac criteria. The saddle-node bifurcations are studied using Sotomayor's theorem. Numerical simulations are carried out to validate the analytical findings. The conditions for the existence of bionomic equilibria are discussed and an optimal harvesting policy is derived using Pontryagin's maximum principle.     

The backward bifurcation in compartmental models for West Nile virus

In all of the West Nile virus (WNV) compartmental models in the literature, the basic reproduction number serves as a crucial control threshold for the eradication of the virus. However, our study suggests that backward bifurcation is a common property shared by the available compartmental models with a logistic type of growth for the population of host birds. There exists a subthreshold condition for the outbreak of the virus due to the existence of backward bifurcation. In this paper, we first review and give a comparison study of the four available compartmental models for the virus, and focus on the analysis of the model proposed by Cruz-Pacheco et al. to explore the backward bifurcation in the model. Our comparison study suggests that the mosquito population dynamics itself cannot explain the occurrence of the backward bifurcation, it is the higher mortality rate of the avian host due to the infection that determines the existence of backward bifurcation.     

The complete classification for dynamics in a homosexually-transmitted disease model

A sexually-transmitted disease model for two strains of pathogen in a one-sex, heterogeneously-mixing population was proposed by Li et al. in (J Math Biol 10:1037–1052, 1986). The sufficient and necessary conditions for coexistence and the sufficient conditions for stability of the boundary equilibria were provided. This paper will present a thorough classification of dynamics for this model in terms of the first and second so called reproductive numbers of infection in strains I and J. This classification not only solves a conjecture proposed in (Li et al., J Math Biol 10:1037–1052, 1986) but also gives the sufficient and necessary conditions for the competitive exclusion. Supported by the NSF of China grants 10531030 and 10671143.     

A disease transmission model in a nonconstant population

A general SIRS disease transmission model is formulated under assumptions that the size of the population varies, the incidence rate is nonlinear, and the recovered (removed) class may also be directly reinfected. For a class of incidence functions it is shown that the model has no periodic solutions. By contrast, for a particular incidence function, a combination of analytical and numerical techniques are used to show that (for some parameters) periodic solutions can arise through homoclinic loops or saddle connections and disappear through Hopf bifurcations.Supported in part by NSERC grant A-8965, the University of Victoria Committee on Faculty Research & Travel, and the Institute for Mathematics and its Applications, Minneapolis, MN, with funds provided by NSF     

West Nile fever/encephalitis as one of the arboviral infections

West Nile virus maintains natural infection cycle between birds and mosquitoes. It has been known that about 200 species of birds are infected with West Nile virus and the virus is isolated from more than 40 species of mosquitoes. This suggests that West Nile virus has an ability to be transmitted by many species of mosquitoes and infect many kinds of animals. Approximately 20% of infected humans develop symptoms. West Nile fever, an acute febrile illness, is the main disease, and meningitis and encephalitis (meningoencephalitis) occasionally occur. Cases with flaccid paralysis or polyneuritis have been recently reported. Thus, West Nile virus causes multiple types of symptoms in humans. The endemic area has expanded in North America and Siberia. West Nile virus may enter Japan in the near future; therefore, we should keep paying attention to the endemic and epidemic situations in the world.     

Infection of mouse neurones by West Nile virus is modulated by the interferon-inducible 2'-5' oligoadenylate synthetase 1b protein

Over the past 7 years, West Nile zoonosis has been an emerging concern for public health in Europe, Middle East and more recently in North America. West Nile virus causes epidemic outbreaks in humans and infected patients may exhibit severe neurological symptoms. Because susceptibility and sensitivity to West Nile virus infections may depend on host genetic factors, a mouse model has been established to investigate the genetic determinism of host susceptibility to West Nile virus. A nonsense mutation in gene encoding the 1b isoform of the 2'-5'oligoadenylate synthetase (OAS1b) was constantly associated with the susceptibility of mouse strains to experimental West Nile virus infection. Oligoadenylate synthetase are interferon-inducible proteins playing a role in the endogeneous antiviral pathway. It was of interest to establish whether interferon-alpha and OAS 1B were sufficient to mediate resistance to West Nile virus infection. In the present study, we showed that interferon-alpha had the ability to modulate West Nile virus infection in mouse. In vitro, interferon-alpha protected mouse neuroblastoma cells against West Nile virus infection if cells have been pretreated with the cytokine for several hours. As a consequence of the presence of a stop codon, the Oas1b gene of the susceptible mice encodes a truncated and presumably inactive form, while resistant mice have a normal copy of the gene. Stable mouse neuroblastoma cell clones overexpressing mutant or wild-type OAS 1B were established. Replication of West Nile virus was less efficient in cells that produce the normal copy of OAS 1B as compared to those expressing the truncated form. Our data illustrate the notion that interferon-alpha and Oas genes may be critical for West Nile virus pathogenesis.     

Changes in cytoplasmic and lysosomal enzyme activities in cultured rat heart cells: The relationship to cell differentiation and cell population in culture

Summary Postnatal rat heart cells in culture enriched with respect to muscle cells were obtained by either high density seeding or by the replating technique. [³H]Thymidine incorporation to DNA and the enzymatic pattern of cytoplasmic and lysosomal enzymes have been studied as a function of the culture’s age, of seeding density, and replating. It was shown that (a) replating maintains predominance of myocyte population for at least 2 wk in culture; (b) heavy seeding density allows homogeneous myocyte population for the 1st wk in culture; and (c) the enzyme profile of the culture may serve as an indicator for the type of cell population in culture and its state of differentiation. This study was done as partial fulfilment of the M.Sc. thesis in Biochemistry (SY). Supported by grants from The Chief Scientist, Ministry of Health, State of Israel; The Ministry of Education and Sciences, State of Niedersachssen (FRG); and The Foundation for Heart Research from Mr. and Mrs. D. Vidal-Madjar, Paris, France.     

Population collapse to extinction: the catastrophic combination of parasitism and Allee effect

Infectious diseases are responsible for the extinction of a number of species. In conventional epidemic models, the transition from endemic population persistence to extirpation takes place gradually. However, if host demographics exhibits a strong Allee effect (AE) (population decline at low densities), extinction can occur abruptly in a catastrophic population crash. This might explain why species suddenly disappear even when they used to persist at high endemic population levels. Mathematically, the tipping point towards population collapse is associated with a saddle-node bifurcation. The underlying mechanism is the simultaneous population size depression and the increase of the extinction threshold due to parasite pathogenicity and Allee effect. Since highly pathogenic parasites cause their own extinction but not that of their host, there can be another saddle-node bifurcation with the re-emergence of two endemic equilibria. The implications for control interventions are discussed, suggesting that effective management may be possible for ?(0)?1.     

胃排空检测方法的研究及展望

胃排空是衡量消化道功能的一个重要指标,在探讨消化道疾病病因学、药物动力学以及疾病的诊断和治疗方面有着不可或缺的作用。近年来,一系列成熟的检测方法已经被用来测量人体胃排空,包括插管法、实时超声、放射性显像及呼吸试验等,但这些检测方法在实验动物及动物临床医学的应用还相对较少,正确评估实验动物胃排空能力的技术对于药物药理学、生物利用度和胃肠疾病诊断等的研究非常重要。本文就常用的几个胃排空检测方法做一阐述,希望这些方法能为动物胃排空检测提供新思路。     

Ecological correlates of risk and incidence of West Nile virus in the United States

West Nile virus, which was recently introduced to North America, is a mosquito-borne pathogen that infects a wide range of vertebrate hosts, including humans. Several species of birds appear to be the primary reservoir hosts, whereas other bird species, as well as other vertebrate species, can be infected but are less competent reservoirs. One hypothesis regarding the transmission dynamics of West Nile virus suggests that high bird diversity reduces West Nile virus transmission because mosquito blood-meals are distributed across a wide range of bird species, many of which have low reservoir competence. One mechanism by which this hypothesis can operate is that high-diversity bird communities might have lower community-competence, defined as the sum of the product of each species’ abundance and its reservoir competence index value. Additional hypotheses posit that West Nile virus transmission will be reduced when either: (1) abundance of mosquito vectors is low; or (2) human population density is low. We assessed these hypotheses at two spatial scales: a regional scale near Saint Louis, MO, and a national scale (continental USA). We found that prevalence of West Nile virus infection in mosquito vectors and in humans increased with decreasing bird diversity and with increasing reservoir competence of the bird community. Our results suggest that conservation of avian diversity might help ameliorate the current West Nile virus epidemic in the USA