Stability in cyclic epidemic models

A general formulation for a family of cyclic epidemic models with density-dependent feedback mechanisms and removed classes is presented. A parameter, , related to the basic reproductive rate determines the asymptotic behaviour of solutions of the model. It is shown that if <1 the trivial solution is globally stable, and if >1 it is conditionally stable. The results are applied to a set of differential equations that has been used to model the life cycle of a parasite that has two hosts.     

General method for the derivation and numerical solution of epithelial transport models

Summary A general method is presented for the formulation and numerical evaluation of mathematical models describing epithelial transport. The method is based on the principles of conservation of mass, and maintenance of electroneutrality within the cells and bathing solutions. It is therefore independent of the specific membrane transport mechanisms, and can be used to evaluate different models describing arbitrary transport processes (including passive, active and cotransport processes). Detailed numerical methods are presented that allow computation of steady-state and transient responses under open-circuit, current-clamp and voltage-clamp conditions, using a general-purpose laboratory minicomputer. To evaluate the utility of this approach, a specific model is presented that is consistent with the Koefoed-Johnson and Ussing hypothesis of sodium transport in tight epithelia (Acta Physiol. Scand. 42:298–308, 1958). This model considers passive transport of an arbitrary number of permeant solutes, active transport of sodium and potassium, and osmotically induced water transport across the apical and basolateral membranes. Results of the model are compared to published experimental measurements in rabbit urinary bladder epithelium.     

Models for age structured populations with distributed maturation rates

In the use of age structured population models for agricultural applications such as the modeling of crop-pest interactions it is often essential that the model take into account the distribution in maturation rates present in some or all of the populations. The traditional method for incorporating distributed maturation rates into crop and pest models has been the so-called distributed delay method. In this paper we review the application of the distributed delay formalism to the McKendrick equation of an age structured population. We discuss the mathematical properties of the system of ordinary differential equations arising out of the distributed delay formalism. We then discuss an alternative method involving modification of the Leslie matrix.     

Studies on the prolonged storage of Metarhizium anisopliae conidia: effect of growth substrate on conidial survival and virulence against mosquitoes

Metarhizium anisopliae was grown on six complex mycological media and on three types of rice at three moisture levels to determine the effect of growth substrate on conidial yield, viability, and virulence against mosquitoes immediately after spore maturation and after the storage of conidia at four different temperature-relative humidity (RH) combinations over a 1-year period. Conidial yields varied with the mycological media, but the viability and virulence of conidia against mosquitoes produced on all substrates were similar when spores were stored under the same conditions. The storage conditions were more critical to spore survival and virulence than the substrate upon which conidia were produced. The comparison of rice types for conidial production indicated that conidial yield, viability, and virulence to mosquitoes were more dependent upon the moisture level during growth and on the storage conditions that upon the rice used. The best storage conditions among those tested for the retention of both spore viability and virulence against mosquitoes were 19°C–97% RH and 4°C–0% RH.     

Plasma levels of gonadotropin and 17α,20β-dihydroxy-4-pregnen-3-one in relation to spawning behaviour of rainbow trout, Oncorhynchus mykiss(Walbaum)

Manipulation of the opportunity to spawn was used to investigate the relationship between endocrine events, egg viability and spawning behaviour in female rainbow trout. Females were prevented from spawning by isolating them from males and gravel for up to 21 days after ovula- tion. Blood samples were taken before pairing with a male, at the onset of nesting activity, and at the completion of spawning. Plasma hormone levels of gonadotropin (GtH) and 17α,20β-dihydroxy-4-pregnen-3-one (17,2OP) were measured by specific radioimmunoassays. There were no qualitative or quantitative differences in the spawning behaviour of females paired on the day of ovulation or 7. 14, or 21 days after ovulation. There was a general decrease in the viability of eggs with increasing retention times. In females paired on the day of ovulation, or after 7 or 14 days, GtH levels increased with the onset of nesting behaviour and declined as fish reached the post-spawning condition. By day 21, GtH levels before pairing were significantly higher than prepairing levels in the other three treatment groups, and did not increase at the onset of nesting, or decrease in post-spawning fish. Plasma 17,20P remained high in prepairing and nesting samples of all four groups and declined to low levels in fish in post-spawning condition. In females paired on the day of ovulation there was a significant increase in 17,20P from the prepairing to the nesting stage. These results suggest that 17,20P plays a key role in the synchronization of behavioural and maturational events at the time of spawning.     

Simulated and measured nitrogen conditions in a manured and fertilised soil

The governing factors for soil nitrogen dynamics were identified with a simulation model. In addition, the model was used to interpret measurements from a plot fertilisation experiment in southwest Sweden.Simulated moisture and temperature conditions were the driving variables for the simulation of soil nitrogen dynamics and leaching during a 6-year period. The results of the simulation were compared with monthly observations on two plots with grain crops, one with liquid manure and commercial fertilisers applied and one with commercial fertilisers only.Simulated temporal variations of the nitrate and ammonium storages generally agreed with observations. The dominant role of the crops as a determinant of soil nitrogen conditions was demonstrated. A higher leaching loss from the plot with application of commerical fertilisers only occurred both in simulations and measurements compared to the plot with application of both commercial fertilisers and manure. The main reason was the higher N-application in the former treatment.The effect of water flows in macropores was interpreted as a delay of simulated leaching compared to observed leaching on some occasions in summer and early autumn. No direct effect of the macropores on the yearly rates of leaching could be seen.     

Modeling in the museum: On the role of remnant models in the work of Joseph Grinnell

Accounts of the relation between theories and models in biology concentrate on mathematical models. In this paper I consider the dual role of models as representations of natural systems and as a material basis for theorizing. In order to explicate the dual role, I develop the concept of a remnant model, a material entity made from parts of the natural system(s) under study. I present a case study of an important but neglected naturalist, Joseph Grinnell, to illustrate the extent to which mundane practices in a museum setting constitute theorizing. I speculate that historical and sociological analyses of institutions can play a specific role in the philosophical analysis of model-building strategies.     

Hydration of 3-cyanopyridine to nicotinamide by crude extract nitrile hydratase

Summary The kinetic and stability characteristics of crude extract nitrile hydratase fromBrevibacterium R-312 were studied for the hydration of 3-cyanopyridine to nicotinamide. The enzyme was substrate and product inhibited and had the following kinetic constants:K _m =28 mM;K _p =36 mM;K _s =155 mM;V _m =5.8 mol/min/mg protein (25°C). Itsmaximum temperature and pH (phosphate buffer) were 35°C and 8.0, respectively and it had half-lives of 50 days, 10 days and 1 day at 4°C, 10°C and 25°C, respectively. The crude extract also exhibited amidase activity on nicotinamide, but it became significant only at nicotinamide concentrations greater than 300 mM. Mathematical models for batch and fed-batch hydrations were developed to account for substrate and product inhibitions and for enzyme decay. They predicted to within 10% experimental results for initial substrate and final product concentrations up to 300 mM; the accuracies decreased at higher concentrations primarily because of the relatively rapid hydrolysis of nicotinamide.     

闽北地区四代三化螟发生动态Fuzzy预测模型研究

根据Fuzzy数学原理和三化螟生物学特性,组建了四代三化螟发生动态综合预测模型经对福建省将乐县16年四代三化螟发生期、发生量回报及1995年的预报,拟合率及正确率均达100％。