A mathematical model for the population dynamics of army ants

A stochastic cellular automata model for the population dynamics of the army antEciton burchelli on Barro Colorado Island in Panama is set up. It is simulated on the computer and shown to give good agreement with biological data. It is analysed using two approximations akin to the mean field approximation in statistical mechanics, and good agreement with the simulations is obtained. Finally, the role of distance between successive statary phase bivouacs is discussed with regard to the rate of colony growth. There are two aspects of the biological system studied here that make it of general importance. First, the population is structured, since the size of each colony of army ants is crucial. Second, the spatial behaviour of the population, as in many others, is not diffusion-like, although it is random. This has implications for the kind of model that is chosen.     

A mathematical model of population dynamics for Batesian mimicry system

We analyse a mathematical model of the population dynamics among a mimic, a corresponding model, and their common predator populations. Predator changes its search-and-attack probability by forming and losing its search image. It cannot distinguish the mimic from the model. Once a predator eats a model individual, it comes to omit both the model and the mimic species from its diet menu. If a predator eats a mimic individual, it comes to increase the search-and-attack probability for both model and mimic. The predator may lose the repulsive/attractive search image with a probability per day. By analysing our model, we can derive the mathematical condition for the persistence of model and mimic populations, and then get the result that the condition for the persistence of model population does not depend on the mimic population size, while the condition for the persistence of mimic population does depend the predator's memory of search image.     

A mathematical model of population dynamics for Batesian mimicry system

We analyse a mathematical model of the population dynamics among a mimic, a corresponding model, and their common predator populations. Predator changes its search-and-attack probability by forming and losing its search image. It cannot distinguish the mimic from the model. Once a predator eats a model individual, it comes to omit both the model and the mimic species from its diet menu. If a predator eats a mimic individual, it comes to increase the search-and-attack probability for both model and mimic. The predator may lose the repulsive/attractive search image with a probability per day. By analysing our model, we can derive the mathematical condition for the persistence of model and mimic populations, and then get the result that the condition for the persistence of model population does not depend on the mimic population size, while the condition for the persistence of mimic population does depend the predator's memory of search image.     

Optimization of harvesting age in an integral age-dependent model of population dynamics

The paper deals with optimal control in a linear integral age-dependent model of population dynamics. A problem for maximizing the harvesting return on a finite time horizon is formulated and analyzed. The optimal controls are the harvesting age and the rate of population removal by harvesting. The gradient and necessary condition for an extremum are derived. A qualitative analysis of the problem is provided. The model shows the presence of a zero-investment period. A preliminary asymptotic analysis indicates possible turnpike properties of the optimal harvesting age. Biological interpretation of all results is provided.     

A model for the dynamics of an annual plant population

A model for the dynamics of a single species population of plants is proposed and its use demonstrated by the analysis of a simple example. The model incorporates the effects of microsite variation by allowing for individual differences in growth and death rates within each season. We demonstrate that an increase in the variance in individual growth rates may increase both the chances that a plant population will persist and the equilibrium size of that population. We also show that even if size-dependent death is occurring, it may not have a significant effect on the shape of the size frequency distribution. An extension of the model to multispecies communities of plants suggests an experimental procedure to determine whether competition is responsible for excluding a particular plant species from a community that appears otherwise to be suitable. A more detailed analysis of the model for a two-species community produces conditions for competitive coexistence reminiscent of those from the Lotka-Volterra competition equations. Another extension suggests that selection will favor those genotypes that maximize the product of germination probability and mass of seeds produced, if survivorship and growth are not substantially altered. Finally, an analog to r- and K-selection theory for animal populations is developed. Selection in low-density populations favors increasing growth rate, and in high-density populations favors minimizing the effect of neighbors on one's own growth rate.     

Implications of a simple mathematical model to cancer cell population dynamics

Recent research in cancer progression and treatment indicates that many forms of cancer arise from the development of a small subpopulation of abnormal cancer stem cells (CSCs) that promote cancer growth and spread. Many potential treatments preferentially interact with cells at certain stages of the cell cycle by either selective killing or halting the cell cycle, such as intense, nanosecond-duration pulsed electric fields (nsPEFs). Simple mathematical models of unfed cancer cell populations at the plateau of their growth characteristics may estimate the long-term consequences of these treatments on proliferating and quiescent cell populations. Applying such a model with no transition from the quiescent to proliferating state shows that it is possible for the proliferating cell population to fall below 1 if the quiescent cell population obtains a sufficient competitive advantage with respect to nutrient consumption and/or survival rate. Introducing small, realistic transition rates did not appreciably alter short-term or long-term population behaviour, indicating that the predicted small cell population behaviour (< 1 cell) is not an artefact of the simpler model. Experimental observations of nsPEF-induced effects on the cell cycle suggest that such a model may serve as a first step in assessing the viability of a given cancer treatment in vitro prior to clinical application.     

A mathematical model for the dynamics of malaria in mosquitoes feeding on a heterogeneous host population

We describe and develop a difference equation model for the dynamics of malaria in a mosquito population feeding on, infecting and getting infected from a heterogeneous population of hosts. Using the force of infection from different classes of humans to mosquitoes as parameters, we evaluate a number of entomological parameters, indicating malaria transmission levels, which can be compared to field data. By assigning different types of vector control interventions to different classes of humans and by evaluating the corresponding levels of malaria transmission, we can compare the effectiveness of these interventions. We show a numerical example of the effects of increasing coverage of insecticide-treated bed nets in a human population where the predominant malaria vector is Anopheles gambiae.     

A mathematical model for the dynamics of malaria in mosquitoes feeding on a heterogeneous host population

We describe and develop a difference equation model for the dynamics of malaria in a mosquito population feeding on, infecting and getting infected from a heterogeneous population of hosts. Using the force of infection from different classes of humans to mosquitoes as parameters, we evaluate a number of entomological parameters, indicating malaria transmission levels, which can be compared to field data. By assigning different types of vector control interventions to different classes of humans and by evaluating the corresponding levels of malaria transmission, we can compare the effectiveness of these interventions. We show a numerical example of the effects of increasing coverage of insecticide-treated bed nets in a human population where the predominant malaria vector is Anopheles gambiae.     

Effect of resource subsidies on predator-prey population dynamics: a mathematical model

The influence of a resource subsidy on predator-prey interactions is examined using a mathematical model. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). In one version of the model, the predator, prey and subsidy all occur in the same location; in a second version, the predator moves between two patches, one containing only the prey and the other containing only the subsidy. Criteria for feasibility and stability of the different equilibrium states are studied both analytically and numerically. At small subsidy input rates, there is a minimum prey carrying capacity needed to support both predator and prey. At intermediate subsidy input rates, the predator and prey can always coexist. At high subsidy input rates, the prey cannot persist even at high carrying capacities. As predator movement increases, the dynamic stability of the predator-prey-subsidy interactions also increases.     

A mathematical model of the dynamics of granulocytopoiesis in mammals

A mathematical model has been developed for the dynamics of granulocytopoiesis in mammals subjected to chronic irradiation. The model involves a chalones mechanism of haemopoiesis regulation and comprises 12 nonlinear differential equations. The simulation results agree with the experimental data concerning the dynamics of granulocytopoiesis in rats affected by radiation within a wide range of dose rates.     

A mathematical model of the dynamics of odontogenic cyst growth

OBJECTIVE: To formulate a mathematical model of odontogenic cyst growth and establish the dynamics of cyst enlargement and role of osmotic pressure forces throughout its growth. STUDY DESIGN: The model assumed a spherical cyst with a semipermeable lining of living cells and a core consisting of degraded cellular material, including generic osmotic material, fed by the continuous death of epithelial cells in the lining. The lining cells were assumed to have both elastic and viscous properties, reflecting the action of physical stresses by the surrounding cyst capsule, composed of fibroblasts and collagen fibers. The model couples the cyst radius and osmotic pressure differences resulting in a system of 2 nonlinear ordinary differential equations. RESULTS: The model predicts that in all parameter regimens the long-time behavior of the cyst is the same and that linear radial expansion results. CONCLUSION: In the early and intermediate stages of cystic growth, osmotic pressure differences play an important role; however, in very large cysts, this role becomes negligible, and cell birth in the lining dominates growth.     

数学判别模型在预测害虫种群动态上的应用

根据两个总体的Fisher判别准则,建立了预测害虫种群动态的数学判别模型,对山东省惠民县1967～1977年共11年二代棉铃虫发生程度的两类资料进行了数量分析,建立了数学模型：y＝0．0127x1－0．023X2,对历史资料的回代验证与独立样本的预测,符合率在90％以上。     

A population balance model for fish population dynamics

A population balance model of fish population dynamics for batch systems was developed. A growth rate expression was introduced and coupled with the population balance. Solutions of the model provide predictions of such fish size distribution characteristics as average size, standard deviation and coefficient of variation. A growth diffusivity mechanism was found to be inapplicable to systems where a terminal size is reached. A study of the two parameter growth rate expression was conducted, illustrating that conditions conducive to high growth rates also resulted in broadening of size distributions. The model was compared to data found in the literature to demonstrate its predictive capabilities.     

A one-dimensional mathematical model of collecting lymphatics coupled with an electro-fluid-mechanical contraction model and valve dynamics

We propose a one-dimensional model for collecting lymphatics coupled with a novel Electro-Fluid-Mechanical Contraction (EFMC) model for dynamical contractions, based on a modified FitzHugh–Nagumo model for action potentials. The one-dimensional model for a deformable lymphatic vessel is a nonlinear system of hyperbolic Partial Differential Equations (PDEs). The EFMC model combines the electrical activity of lymphangions (action potentials) with fluid-mechanical feedback (circumferential stretch of the lymphatic wall and wall shear stress) and lymphatic vessel wall contractions. The EFMC model is governed by four Ordinary Differential Equations (ODEs) and phenomenologically relies on: (1) environmental calcium influx, (2) stretch-activated calcium influx, and (3) contraction inhibitions induced by wall shear stresses. We carried out a stability analysis of the stationary state of the EFMC model. Contractions turn out to be triggered by the instability of the stationary state. Overall, the EFMC model allows emulating the influence of pressure and wall shear stress on the frequency of contractions observed experimentally. Lymphatic valves are modelled by extending an existing lumped-parameter model for blood vessels. Modern numerical methods are employed for the one-dimensional model (PDEs), for the EFMC model and valve dynamics (ODEs). Adopting the geometrical structure of collecting lymphatics from rat mesentery, we apply the full mathematical model to a carefully selected suite of test problems inspired by experiments. We analysed several indices of a single lymphangion for a wide range of upstream and downstream pressure combinations which included both favourable and adverse pressure gradients. The most influential model parameters were identified by performing two sensitivity analyses for favourable and adverse pressure gradients.     

A mathematical model for dynamics of CD40 clustering

Ligand bound-receptors in a signalosome complex trigger signals to determine cellular functions. Upon ligand binding, the ligand–receptor complexes form clusters on cell membrane. Guided by the previous experimental reports on the cluster formation of CD40, a trans membrane receptor for CD40-ligand, we built a minimal model of the receptor cluster formation. In this model, we studied co-operative and non-co-operative clustering of a maximum of four CD40 molecules assuming a positive mediator of clustering such as cholesterol to be present in both cases. We observed that co-operative interactions between CD40 molecules resulted in more of the largest CD40 clusters than that observed with the non-co-operatively interacting CD40 molecules. We performed global sensitivity analysis on the model parameters and the analyses suggested that cholesterol influenced only the initial stage of the co-operatively clustering CD40 molecules but it affects both the initial and the final stages in case of the non-co-operatively clustering CD40 molecules. Robustness analyses revealed that in both co-operative and non-co-operative interactions, the higher order clusters beyond a critical size are more robust with respect to alterations in the environmental parameters including the cholesterol. Thus, the role of co-operative and non-co-operative interactions in environment-influenced receptor clustering is reported for the first time.