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The water distribution in hydrogel systems prepared from six different starches at different concentrations was analyzed by low-field nuclear magnetic resonance (LF-NMR) spectroscopy. The results showed that legume (corn and wheat) and legume (pea and mung bean) starch gels exhibited three water forms, while tuber (sweet potato and potato) starch gels exhibited only two water forms. Immobilized water (T23) was the major water form in the six starch gels. With increasing starch concentration (5%–14%), the transverse relaxation time decreased, and the ability of starch gels to bind immobilized water increased. At the same starch concentration, the ability of pea starch gels to bind water was the strongest, while that of potato starch gels was the weakest, and that of cereal starch gels was in the middle. With increasing starch concentration, the relative content of immobilized water in starch gels decreased, and the differences among legume, tuber and cereal starch gels became more obvious. This study provides a theoretical reference for the improvement of sensory texture in starch-based food processing.

We consider a two-species Lotka--Volterra competition-diffusion model with a shifting habitat. The growth rate of each species is nondecreasing along the x-axis, and it changes sign and shifts rightward at a speed c. We investigate the population dynamics of the model in the habitat suitable for growth of both species for two cases: (i) one species is competitively stronger and has a slower spreading speed, and (ii) both species coexist. We obtain conditions under which the outcome of competition depends critically on a number c(\infty) given by the model parameters. We show that under appropriate conditions, if c(\infty) > c, then the species with the faster spreading speed spreads into the open space at its own speed and the species with the slower spreading speed spreads into its rival at speed c(\infty), and if c(\infty) < c, then the species with the slower spreading speed eventually dies out in space. Our results particularly demonstrate the possibility that a competitively weaker species with a faster spreading speed can drive a competitively stronger species with a slower spreading speed to extinction. The mathematical proofs involve linear determinacy analysis, integral equations, and comparison. [ABSTRACT FROM AUTHOR]

Density dependence plays an important role in population regulation and is known to generate temporal fluctuations in population density. However, the ways in which density dependence affects spatial population processes, such as species invasions, are less understood. Although classical ecological theory suggests that invasions should advance at a constant speed, empirical work is illuminating the highly variable nature of biological invasions, which often exhibit nonconstant spreading speeds, even in simple, controlled settings. Here, we explore endogenous density dependence as a mechanism for inducing variability in biological invasions with a set of population models that incorporate density dependence in demographic and dispersal parameters. We show that density dependence in demography at low population densities—i.e., an Allee effect—combined with spatiotemporal variability in population density behind the invasion front can produce fluctuations in spreading speed. The density fluctuations behind the front can arise from either overcompensatory population growth or density-dependent dispersal, both of which are common in nature. Our results show that simple rules can generate complex spread dynamics and highlight a source of variability in biological invasions that may aid in ecological forecasting. [ABSTRACT FROM AUTHOR]

ObjectiveThe emergence of multi-drug resistance (MDR) in esophageal carcinoma has severely affected the effect of chemotherapy and shortened the survival of patients. To this end, we intend to develop a biomimetic nano-targeting drug modified by cancer cell membrane, and investigate its therapeutic effect.MethodsThe degradable poly(lactic-co-glycolic acid) (PLGA) nanoparticles (NPs) co-loaded with doxorubicin (DOX) and curcumin (Cur) were prepared by solvent evaporation method. TE10 cell membrane and Distearoyl phosphatidylethanolamine-polyethylene glycol (DSPE-PEG) were then coated on the PLGA NPs by membrane extrusion to prepare the PEG-TE10@PLGA@DOX-Cur NPs (PMPNs). Size and zeta potential of the PMPNs were analyzed by lazer particle analyzer, and the morphology of PMPNs was observed by transmission electron microscope. The TE10 cell membrane protein on PMPNs was analyzed by gel electrophoresis. The DOX-resistant esophageal cancer cell model TE10/DOX was established through high-dose induction. The In vitro homologous targeting ability of PMPNs was evaluated by cell uptake assay, and the in vitro anti-tumor effect of PMPNs was assessed through CCK-8, clone formation and flow cytometry. A Balb/c mouse model of TE10/DOX xenograft was constructed to evaluate the anti-tumor effect in vivo and the bio-safety of PMPNs.ResultsThe prepared cell membrane coated PMPNs had a regular spherical structure with an average diameter of 177 nm. PMPNs could directly target TE10 and TE10/DOX cells or TE10/DOX xenografted tumor and effectively inhibit the growth of DOX-resistant esophageal carcinoma. Besides, the PMPNs was confirmed to have high biosafety.ConclusionIn this study, a targeted biomimetic nano-drug delivery system PMPNs was successfully prepared, which overcome the MDR of esophageal carcinoma by co-delivering DOX and sensitizer curcumin.

We study a cooperative system of integro-differential equations. It is shown that the system in general has multiple spreading speeds, and when the linear determinacy conditions are satisfied all the spreading speeds are the same and equal to the spreading speed of the linearized system. The existence of traveling wave solutions is established via integral systems. It is shown that when the linear determinacy conditions are satisfied, if the unique spreading speed is not zero then it may be characterized as the slowest speed of a class of traveling wave solutions. Some examples are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

We propose a reaction-advection-diffusion model to study competition between two species in a stream. We divide each species into two compartments, individuals inhabiting the benthos and individuals drifting in the stream. We assume that the growth of and competitive interactions between the populations take place on the benthos and that dispersal occurs in the stream. Our system consists of two linear reaction-advection-diffusion equations and two ordinary differential equations. Here, we provide a thorough study for the corresponding single species model, which has been previously proposed. We next give formulas for the rightward spreading and leftward spreading speed for the model. We show that rightward spreading speed can be characterized as is the slowest speed of a class of traveling wave speeds. We provide sharp conditions for the spreading speeds to be positive. For the two species competition model, we investigate how a species spreads into its competitor's environment. Formulas for the spreading speeds are provided under linear determinacy conditions. We demonstrate that under certain conditions, the invading species can spread upstream. Lastly, we study the existence of traveling wave solutions for the two species competition model. [ABSTRACT FROM AUTHOR]

We study a reaction-diffusion model that describes the growth and spread of a species along a shifting habitat gradient on which the species' growth increases. It is assumed that the linearized species growth rate is positive near positive infinity and is negative near negative infinity. We show that the persistence and spreading dynamics depend on the speed of the shifting habitat edge c and a number c*(∞) that is determined by the maximum linearized growth rate and the diffusion coefficient. We demonstrate that if c > c*(∞), then the species will become extinct in the habitat, and that if c < c*(∞), then the species will persist and spread along the shifting habitat gradient at an asymptotic spreading speed c*(∞). [ABSTRACT FROM AUTHOR]

A ratio-dependent predator-prey model with a strong Allee effect in prey is studied. We show that the model has a Bogdanov-Takens bifur- cation that is associated with a catastrophic crash of the predator popula- tion. Our analysis indicates that an unstable limit cycle bifurcates from a Hopf bifurcation, and it disappears due to a homoclinic bifurcation which can lead to different patterns of global population dynamics in the model. We study the heteroclinic orbits and determine all possible phase portraits when the Bogdanov-Takens bifurcation occurs. We also provide the conditions for nonexistence of limit cycle under which the global dynamics of the model can be determined. [ABSTRACT FROM AUTHOR]

We formulate an integro-difference model to predict the growth and spatial spread of a plant population with an age-structured seed bank and juvenile cohort. We allow the seeds in the bank to be of any age, producing a system of infinitely many equations. We assume that juvenile plants mature into adults at a particular age. The production of new seeds can be density-dependent and so the function describing this growth is allowed to be nonmonotone. The functions describing the seed bank and juvenile plants are linear. We show that when the system has a positive equilibrium, there is a spreading speed that can be computed using model parameters and that this spreading speed can be characterized as the slowest speed of a class of traveling wave solutions. The spreading speed results are obtained through linearization and comparison to an analogous finite system, while the existence of traveling wave solutions is shown by using an asymptotic fixed point theorem. We conduct numerical simulations of a truncated version of this model. These simulations show that both the perennial term and the seed bank can have a stabilizing effect on the population. On the other hand, traveling wave solutions may exhibit different patterns of fluctuations including periodic oscillations and chaotic tails. [ABSTRACT FROM AUTHOR]

We establish the existence of travelling wave solutions for delayed cooperative recursions that are allowed to have more than two equilibria. We define an important extended real number that is used to determine the speeds of travelling wave solutions. The results can be applied to a large class of delayed cooperative reaction-diffusion models. We show that for a delayed Lotka-Volterra reaction-diffusion competition model, there exists a finite positive number c^*_+ that can be characterized as the slowest speed of travelling wave solutions connecting two mono-culture equilibria or connecting a mono-culture with the coexistence equilibrium. [ABSTRACT FROM AUTHOR]

Background: Cofactors, "nuisance" conditions or pathogens that affect the spread of a primary disease, are likely to be the norm rather than the exception in disease dynamics. Here we present a "simplest possible" demographic model that incorporates two distinct effects of cofactors: that on the transmission of the primary disease from an infected host bearing the cofactor, and that on the acquisition of the primary disease by an individual that is not infected with the primary disease but carries the cofactor. Methods: We constructed and analyzed a four-patch compartment model that accommodates a cofactor. We applied the model to HIV spread in the presence of the causal agent of genital schistosomiasis, Schistosoma hematobium, a pathogen commonly co-occurring with HIV in sub-Saharan Africa. Results: We found that cofactors can have a range of effects on primary disease dynamics, including shifting the primary disease from non-endemic to endemic, increasing the prevalence of the primary disease, and reversing demographic growth when the host population bears only the primary disease to demographic decline. We show that under parameter values based on the biology of the HIV/S. haematobium system, reduction of the schistosome-bearing subpopulations (e.g. through periodic use of antihelminths) can slow and even reverse the spread of HIV through the host population. Conclusions: Typical single-disease models provide estimates of future conditions and guidance for direct intervention efforts relating only to the modeled primary disease. Our results suggest that, in circumstances under which a cofactor affects the disease dynamics, the most effective intervention effort might not be one focused on direct treatment of the primary disease alone. The cofactor model presented here can be used to estimate the impact of the cofactor in a particular disease/cofactor system without requiring the development of a more complicated model which incorporates many other specific aspects of the chosen disease/cofactor pair. Simulation results for the HIV/S. haematobium system have profound implications for disease management in developing areas, in that they provide evidence that in some cases treating cofactors may be the most successful and cost-effective way to slow the spread of primary diseases. [ABSTRACT FROM AUTHOR]

A class of integral recursion models for the growth and spread of a synchronized single-species population is studied. It is well known that if there is no overcompensation in the fecundity function, the recursion has an asymptotic spreading speed c*, and that this speed can be characterized as the speed of the slowest non-constant traveling wave solution. A class of integral recursions with overcompensation which still have asymptotic spreading speeds can be found by using the ideas introduced by Thieme (J Reine Angew Math 306:94–121, 1979) for the study of space-time integral equation models for epidemics. The present work gives a large subclass of these models with overcompensation for which the spreading speed can still be characterized as the slowest speed of a non-constant traveling wave. To illustrate our results, we numerically simulate a series of traveling waves. The simulations indicate that, depending on the properties of the fecundity function, the tails of the waves may approach the carrying capacity monotonically, may approach the carrying capacity in an oscillatory manner, or may oscillate continually about the carrying capacity, with its values bounded above and below by computable positive numbers. [ABSTRACT FROM AUTHOR]

Abstract  We study a chemostat model that describes competition between two species for two essential resources based on storage. The model incorporates internal resource storage variables that serve the direct connection between species growth and external resource availability. Mathematical analysis for the global dynamics of the model is carried out by using the monotone dynamical system theory. It is shown that the limiting system of the model basically exhibits the familiar Lotka-Volterra alternatives: competitive exclusion, coexistence, and bi-stability, and most of these results can be carried over to the original model. [ABSTRACT FROM AUTHOR]

The existence of a heteroclinic bifurcation for the Michaelis—Menten-type ratio-dependent predator-prey system is rigorously established. Limit cycles related to the heteroclinic bifurcation are also discussed. It is shown that the heteroclinic bifurcation is characterized by the collision of a stable limit cycle with the origin, and the bifurcation triggers a catastrophic shift from the state of large oscillations of predator and prey populations to the state of extinction of both populations. It is also shown that the limit cycles related to the heteroclinic bifurcation originally bifurcate from the Hopf bifurcation. [ABSTRACT FROM AUTHOR]

Abstract  This work presents an example of a cooperative system of truncated linear recursions in which the interaction between species causes one of the species to have an anomalous spreading speed. By this we mean that this species spreads at a speed which is strictly greater than its spreading speed in isolation from the other species and the speeds at which all the other species actually spread. An ecological implication of this example is discussed in Sect. 5. Our example shows that the formula for the fastest spreading speed given in Lemma 2.3 of our paper (Weinberger et al. in J Math Biol 45:183–218, 2002) is incorrect. However, we find an extra hypothesis under which the formula for the faster spreading speed given in (Weinberger et al. in J Math Biol 45:183–218, 2002) is valid. We also show that the hypotheses of all but one of the theorems of (Weinberger et al. in J Math Biol 45:183–218, 2002) whose proofs rely on Lemma 2.3 imply this extra hypothesis, so that all but one of the theorems of (Weinberger et al. in J Math Biol 45:183–218, 2002) and all the examples given there are valid as they stand. [ABSTRACT FROM AUTHOR]

We consider the dynamics of the standard model of 3 species competing for 3 essential (non-substitutable) resources in a chemostat using Liebig's law of the minimum functional response. A subset of these systems which possess cyclic symmetry such that its three single-population equilibria are part of a heteroclinic cycle bounding the two-dimensional carrying simplex is examined. We show that a subcritical Hopf bifurcation from the coexistence equilibrium together with a repelling heteroclinic cycle leads to the existence of at least two limit cycles enclosing the coexistence equilibrium on the carrying simplex- the ``inside'' one is an unstable separatrix and the ``outside'' one is at least semi-stable relative to the carrying simplex. Numerical simulations suggest that there are exactly two limit cycles and that almost every positive solution approaches either the stable limit cycle or the stable coexistence equilibrium, depending on initial conditions. Bifurcation diagrams confirm this picture and show additional features. In an alternative scenario, we show that the subcritical Hopf together with an attracting heteroclinic cycle leads to an unstable periodic orbit separatrix. [ABSTRACT FROM AUTHOR]

Presents a chemostat model of n species competing for two perfectly complementary, growth-limiting nutrients. Sufficient conditions to be a single winning species and for two species to exist; Implications for applied mathematics.

In this paper, we consider a competition model between n species in a chemostat that incorporates both monotone and nonmonotone general response functions and distinct removal rates. We show that only the species with the lowest break-even concentration survives, provided that the variation of distinct removal rates relative to the flow rate of the chemostat can be controlled by either the difference between the two lowest break-even concentrations or by a parameter based on the structure of response functions. LaSalle's extension theorem of the Lyapunov stability theory and fluctuation lemma are the main tools. [ABSTRACT FROM AUTHOR]

A simple model for an autonomous pulsing drug delivery system was previously introduced. This model involves negative feedback action, with hysteresis, of an enzyme on the permeability of a membrane through which substrate, at constant external concentration, must diffuse to reach the enzyme. The qualitative dynamics of this model permit, depending on system parameters and external driving substrate concentration, two separate single steady state, double steady state, and permanently alternating (oscillatory) behaviors. The present contribution is concerned with rigorous proofs regarding the global stability of steady states when permanent alternation is precluded, and the existence and globally asymptotic stability of a limit cycle in the permanently alternating case. Also, we prove that more restrictive but often realistic conditions on the system parameters imply limitations on the number of alternations the system can undergo before reaching steady state. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]