共查询到20条相似文献,搜索用时 62 毫秒
1.
Arino J Brauer F van den Driessche P Watmough J Wu J 《Journal of theoretical biology》2008,253(1):118-130
Compartmental models for influenza that include control by vaccination and antiviral treatment are formulated. Analytic expressions for the basic reproduction number, control reproduction number and the final size of the epidemic are derived for this general class of disease transmission models. Sensitivity and uncertainty analyses of the dependence of the control reproduction number on the parameters of the model give a comparison of the various intervention strategies. Numerical computations of the deterministic models are compared with those of recent stochastic simulation influenza models. Predictions of the deterministic compartmental models are in general agreement with those of the stochastic simulation models. 相似文献
2.
Stochastic differential equations that model an SIS epidemic with multiple pathogen strains are derived from a system of ordinary
differential equations. The stochastic model assumes there is demographic variability. The dynamics of the deterministic model
are summarized. Then the dynamics of the stochastic model are compared to the deterministic model. In the deterministic model,
there can be either disease extinction, competitive exclusion, where only one strain persists, or coexistence, where more
than one strain persists. In the stochastic model, all strains are eventually eliminated because the disease-free state is
an absorbing state. However, if the population size and the initial number of infected individuals are sufficiently large,
it may take a long time until all strains are eliminated. Numerical simulations of the stochastic model show that coexistence
cases predicted by the deterministic model are an unlikely occurrence in the stochastic model even for short time periods.
In the stochastic model, either disease extinction or competitive exclusion occur. The initial number of infected individuals,
the basic reproduction numbers, and other epidemiological parameters are important determinants of the dominant strain in
the stochastic epidemic model. 相似文献
3.
The scarcity of water characterising drylands forces vegetation to adopt appropriate survival strategies. Some of these generate water–vegetation feedback mechanisms that can lead to spatial self-organisation of vegetation, as it has been shown with models representing plants by a density of biomass, varying continuously in time and space. However, although plants are usually quite plastic they also display discrete qualities and stochastic behaviour. These features may give rise to demographic noise, which in certain cases can influence the qualitative dynamics of ecosystem models. In the present work we explore the effects of demographic noise on the resilience of a model semi-arid ecosystem. We introduce a spatial stochastic eco-hydrological hybrid model in which plants are modelled as discrete entities subject to stochastic dynamical rules, while the dynamics of surface and soil water are described by continuous variables. The model has a deterministic approximation very similar to previous continuous models of arid and semi-arid ecosystems. By means of numerical simulations we show that demographic noise can have important effects on the extinction and recovery dynamics of the system. In particular we find that the stochastic model escapes extinction under a wide range of conditions for which the corresponding deterministic approximation predicts absorption into desert states. 相似文献
4.
New stochastic models are developed for the dynamics of a viral infection and an immune response during the early stages of infection. The stochastic models are derived based on the dynamics of deterministic models. The simplest deterministic model is a well-known system of ordinary differential equations which consists of three populations: uninfected cells, actively infected cells, and virus particles. This basic model is extended to include some factors of the immune response related to Human Immunodeficiency Virus-1 (HIV-1) infection. For the deterministic models, the basic reproduction number, R0, is calculated and it is shown that if R0<1, the disease-free equilibrium is locally asymptotically stable and is globally asymptotically stable in some special cases. The new stochastic models are systems of stochastic differential equations (SDEs) and continuous-time Markov chain (CTMC) models that account for the variability in cellular reproduction and death, the infection process, the immune system activation, and viral reproduction. Two viral release strategies are considered: budding and bursting. The CTMC model is used to estimate the probability of virus extinction during the early stages of infection. Numerical simulations are carried out using parameter values applicable to HIV-1 dynamics. The stochastic models provide new insights, distinct from the basic deterministic models. For the case R0>1, the deterministic models predict the viral infection persists in the host. But for the stochastic models, there is a positive probability of viral extinction. It is shown that the probability of a successful invasion depends on the initial viral dose, whether the immune system is activated, and whether the release strategy is bursting or budding. 相似文献
5.
Spatial heterogeneity and host demography have a direct impact on the persistence or extinction of a disease. Natural or human-made landscape features such as forests, rivers, roads, and crops are important to the persistence of wildlife diseases. Rabies, hantaviruses, and plague are just a few examples of wildlife diseases where spatial patterns of infection have been observed. We formulate multi-patch deterministic and stochastic epidemic models and use these models to investigate problems related to disease persistence and extinction. We show in some special cases that a unique disease-free equilibrium exists. In these cases, a basic reproduction number ?(0) can be computed and shown to be bounded below and above by the minimum and maximum patch reproduction numbers ?(j), j=1, …, n. The basic reproduction number has a simple form when there is no movement or when all patches are identical or when the movement rate approaches infinity. Numerical examples of the deterministic and stochastic models illustrate the disease dynamics for different movement rates between three patches. 相似文献
6.
For a system of biochemical reactions, it is known from the work of T.G. Kurtz [J. Appl. Prob. 8, 344 (1971)] that the chemical
master equation model based on a stochastic formulation approaches the deterministic model based on the Law of Mass Action
in the infinite system-size limit in finite time. The two models, however, often show distinctly different steady-state behavior.
To further investigate this “paradox,” a comparative study of the deterministic and stochastic models of a simple autocatalytic
biochemical reaction, taken from a text by the late J. Keizer, is carried out. We compute the expected time to extinction,
the true stochastic steady state, and a quasistationary probability distribution in the stochastic model. We show that the
stochastic model predicts the deterministic behavior on a reasonable time scale, which can be consistently obtained from both
models. The transition time to the extinction, however, grows exponentially with the system size. Mathematically, we identify
that exchanging the limits of infinite system size and infinite time is problematic. The appropriate system size that can
be considered sufficiently large, an important parameter in numerical computation, is also discussed. 相似文献
7.
《Journal of biological dynamics》2013,7(1):63-85
Spatial heterogeneity and host demography have a direct impact on the persistence or extinction of a disease. Natural or human-made landscape features such as forests, rivers, roads, and crops are important to the persistence of wildlife diseases. Rabies, hantaviruses, and plague are just a few examples of wildlife diseases where spatial patterns of infection have been observed. We formulate multi-patch deterministic and stochastic epidemic models and use these models to investigate problems related to disease persistence and extinction. We show in some special cases that a unique disease-free equilibrium exists. In these cases, a basic reproduction number ?0 can be computed and shown to be bounded below and above by the minimum and maximum patch reproduction numbers ? j , j=1, …, n. The basic reproduction number has a simple form when there is no movement or when all patches are identical or when the movement rate approaches infinity. Numerical examples of the deterministic and stochastic models illustrate the disease dynamics for different movement rates between three patches. 相似文献
8.
Density-independent and density-dependent, stochastic and deterministic, discrete-time, structured models are formulated,
analysed and numerically simulated. A special case of the deterministic, density-independent, structured model is the well-known
Leslie age-structured model. The stochastic, density-independent model is a multitype branching process. A review of linear,
density-independent models is given first, then nonlinear, density-dependent models are discussed.
In the linear, density-independent structured models, transitions between states are independent of time and state. Population
extinction is determined by the dominant eigenvalue λ of the transition matrix. If λ ≤ 1, then extinction occurs with probability one in the stochastic and deterministic models. However, if λ > 1, then the deterministic model has exponential growth, but in the stochastic model there is a positive probability of
extinction which depends on the fixed point of the system of probability generating functions.
The linear, density-independent, stochastic model is generalized to a nonlinear, density-dependent one. The dependence on
state is in terms of a weighted total population size. It is shown for small initial population sizes that the density-dependent,
stochastic model can be approximated by the density-independent, stochastic model and thus, the extinction behavior exhibited
by the linear model occurs in the nonlinear model. In the deterministic models there is a unique stable equilibrium. Given
the population does not go extinct, it is shown that the stochastic model has a quasi-stationary distribution with mean close
to the stable equilibrium, provided the population size is sufficiently large. For small values of the population size, complete
extinction can be observed in the simulations. However, the persistence time increases rapidly with the population size.
This author received partial support by the National Science Foundation grant # DMS-9626417. 相似文献
9.
Pengxing Cao Xiahui Tan Graham Donovan Michael J. Sanderson James Sneyd 《PLoS computational biology》2014,10(8)
The inositol trisphosphate receptor () is one of the most important cellular components responsible for oscillations in the cytoplasmic calcium concentration. Over the past decade, two major questions about the have arisen. Firstly, how best should the be modeled? In other words, what fundamental properties of the allow it to perform its function, and what are their quantitative properties? Secondly, although calcium oscillations are caused by the stochastic opening and closing of small numbers of , is it possible for a deterministic model to be a reliable predictor of calcium behavior? Here, we answer these two questions, using airway smooth muscle cells (ASMC) as a specific example. Firstly, we show that periodic calcium waves in ASMC, as well as the statistics of calcium puffs in other cell types, can be quantitatively reproduced by a two-state model of the , and thus the behavior of the is essentially determined by its modal structure. The structure within each mode is irrelevant for function. Secondly, we show that, although calcium waves in ASMC are generated by a stochastic mechanism, stochasticity is not essential for a qualitative prediction of how oscillation frequency depends on model parameters, and thus deterministic models demonstrate the same level of predictive capability as do stochastic models. We conclude that, firstly, calcium dynamics can be accurately modeled using simplified models, and, secondly, to obtain qualitative predictions of how oscillation frequency depends on parameters it is sufficient to use a deterministic model. 相似文献
10.
A model of the gating of ion channels 总被引:4,自引:0,他引:4
T L Croxton 《Biochimica et biophysica acta》1988,946(1):19-24
The gating of ion channels in biological membranes has usually been described in terms of Markov transitions between a few discrete open or closed states. Such models predict that the distributions of open and closed durations decay as a sum of exponential terms. Recent experimental data have indicated that certain channels are not easily described by these models. We show that distributions of open and closed times similar to those seen experimentally are predicted by a model that involves only one open and closed state but that assumes the activation energy of the gating process to be stochastic. This model involves only a few parameters and these have direct physical interpretations. Measurements of the correlation between the durations of successive open or closed events is shown to provide an experimental method for distinguishing between this and other models. 相似文献
11.
The dynamics of deterministic and stochastic discrete-time epidemic models are analyzed and compared. The discrete-time stochastic models are Markov chains, approximations to the continuous-time models. Models of SIS and SIR type with constant population size and general force of infection are analyzed, then a more general SIS model with variable population size is analyzed. In the deterministic models, the value of the basic reproductive number R0 determines persistence or extinction of the disease. If R0 < 1, the disease is eliminated, whereas if R0 > 1, the disease persists in the population. Since all stochastic models considered in this paper have finite state spaces with at least one absorbing state, ultimate disease extinction is certain regardless of the value of R0. However, in some cases, the time until disease extinction may be very long. In these cases, if the probability distribution is conditioned on non-extinction, then when R0 > 1, there exists a quasi-stationary probability distribution whose mean agrees with deterministic endemic equilibrium. The expected duration of the epidemic is investigated numerically. 相似文献
12.
We analyze theoretically the problem of cargo transport along microtubules by motors of two species with opposite polarities. We consider two different one-dimensional models previously developed in the literature: a quite widespread model which assumes equal force sharing, here referred to as the mean field model (MFM), and a stochastic model (SM) which considers individual motor-cargo links. We find that in generic situations, the MFM predicts larger cargo mean velocity, smaller mean run time and less frequent reversions than the SM. These phenomena are found to be the consequences of the load sharing assumptions and can be interpreted in terms of the probabilities of the different motility states. We also explore the influence of the viscosity in both models and the role of the stiffness of the motor-cargo links within the SM. Our results show that the mean cargo velocity is independent of the stiffness, while the mean run time decreases with such a parameter. We explore the case of symmetric forward and backward motors considering kinesin-1 parameters, and the problem of transport by kinesin-1 and cytoplasmic dyneins considering two different sets of parameters previously proposed for dyneins. 相似文献
13.
14.
Luchsinger CJ 《Journal of mathematical biology》2001,42(6):555-581
In a companion paper two stochastic models, useful for the initial behaviour of a parasitic infection, were introduced. Now we analyse the long term behaviour. First a law of large numbers is proved which allows us to analyse the deterministic analogues of the stochastic models. The behaviour of the deterministic models is analogous to the stochastic models in that again three basic reproduction ratios are necessary to fully describe the information needed to separate growth from extinction. The existence of stationary solutions is shown in the deterministic models, which can be used as a justification for simulation of quasi-equilibria in the stochastic models. Host-mortality is included in all models. The proofs involve martingale and coupling methods. 相似文献
15.
Optimal time to emerge from refuge 总被引:1,自引:0,他引:1
WILLIAM E. COOPER JR WILLIAM G. FREDERICK 《Biological journal of the Linnean Society. Linnean Society of London》2007,91(3):375-382
Factors affecting emergence by prey that enter refuges when approached by predators have been studied intensively, but only two theoretical models predict how long prey should remain in a refuge before emerging. We argue that prey can make better decisions than allowed by one model; the other model describes cases in which predators wait for prey to emerge. We present optimality models that permit prey to select a time to emerge that maximizes fitness. When in a refuge, a prey cannot obtain benefits outside; emerging too soon can be catastrophic, but delaying emergence entails loss of fitness. If predators resume foraging quickly rather than engaging in strategic waiting games, current theory suggests that prey emerge when the costs of remaining in a refuge and of emerging are equal. However, prey often can do better by emerging at the time maximizing fitness rather than when benefits equal costs (i.e. when prey break even). Optimal emergence time depends on initial fitness, benefits lost by remaining in refuge, and the decay rate of predation risk. Benefits lost if a prey is killed are modelled separately from benefits that contribute to lifetime fitness, even if the prey is killed (individual reproduction, altruism). Fitness of prey emerging at the optimal emergence time may be greater than, equal to or less than initial fitness. Break-even and optimality models base predictions on the opposing effects of risk and loss of benefits. Thus, many empirically verified predictions are identical at the ordinal level although differing quantitatively. Optimality models provide novel testable predictions for the effects of initial fitness, benefits, and, for ectotherms, the rate of cooling in refuge. They predict earlier emergence for equal retainable benefits than for those lost upon death. © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 91 , 375–382. 相似文献
16.
The transformation of synaptic input into patterns of spike output is a
fundamental operation that is determined by the particular complement of ion
channels that a neuron expresses. Although it is well established that
individual ion channel proteins make stochastic transitions between conducting
and non-conducting states, most models of synaptic integration are
deterministic, and relatively little is known about the functional consequences
of interactions between stochastically gating ion channels. Here, we show that a
model of stellate neurons from layer II of the medial entorhinal cortex
implemented with either stochastic or deterministically gating ion channels can
reproduce the resting membrane properties of stellate neurons, but only the
stochastic version of the model can fully account for perithreshold membrane
potential fluctuations and clustered patterns of spike output that are recorded
from stellate neurons during depolarized states. We demonstrate that the
stochastic model implements an example of a general mechanism for patterning of
neuronal output through activity-dependent changes in the probability of spike
firing. Unlike deterministic mechanisms that generate spike patterns through
slow changes in the state of model parameters, this general stochastic mechanism
does not require retention of information beyond the duration of a single spike
and its associated afterhyperpolarization. Instead, clustered patterns of spikes
emerge in the stochastic model of stellate neurons as a result of a transient
increase in firing probability driven by activation of HCN channels during
recovery from the spike afterhyperpolarization. Using this model, we infer
conditions in which stochastic ion channel gating may influence firing patterns
in vivo and predict consequences of modifications of HCN
channel function for in vivo firing patterns. 相似文献
17.
Stochastic models sometimes behave qualitatively differently from their deterministic analogues. We explore the implications of this in ecosystems that shift suddenly from one state to another. This phenomenon is usually studied through deterministic models with multiple stable equilibria under a single set of conditions, with stability defined through linear stability analysis. However, in stochastic systems, some unstable states can trap stochastic dynamics for long intervals, essentially masquerading as additional stable states. Using a predator–prey model, we demonstrate that this effect is sufficient to make a stochastic system with one stable state exhibit the same characteristics as an analogous system with alternative stable states. Although this result is surprising with respect to how stability is defined by standard analyses, we show that it is well-anticipated by an alternative approach based on the system's “quasi-potential.” Broadly, understanding the risk of sudden state shifts will require a more holistic understanding of stability in stochastic systems. 相似文献
18.
Richard R. Lawler Hal Caswell Alison F. Richard Joelisoa Ratsirarson Robert E. Dewar Marion Schwartz 《Oecologia》2009,161(3):491-504
In this study, we use deterministic and stochastic models to analyze the demography of Verreaux’s sifaka (Propithecus verreauxi verreauxi) in a fluctuating rainfall environment. The model is based on 16 years of data from Beza Mahafaly Special Reserve, southwest
Madagascar. The parameters in the stage-classified life cycle were estimated using mark-recapture methods. Statistical models
were evaluated using information-theoretic techniques and multi-model inference. The highest ranking model is time-invariant,
but the averaged model includes rainfall-dependence of survival and breeding. We used a time-series model of rainfall to construct
a stochastic demographic model. The time-invariant model and the stochastic model give a population growth rate of about 0.98.
Bootstrap confidence intervals on the growth rates, both deterministic and stochastic, include 1. Growth rates are most elastic
to changes in adult survival. Many demographic statistics show a nonlinear response to annual rainfall but are depressed when
annual rainfall is low, or the variance in annual rainfall is high. Perturbation analyses from both the time-invariant and
stochastic models indicate that recruitment and survival of older females are key determinants of population growth rate. 相似文献
19.
The minority cytotype exclusion principle describes how random mating between diploid and autotetraploid cytotypes hinders establishment of the rare cytotype. We present deterministic and stochastic models to ascertain how selfing, inbreeding depression, unreduced gamete production, and finite population size affect minority cytotype exclusion and the establishment of autotetraploids. Results demonstrate that higher selfing rates and lower inbreeding depression in autotetraploids facilitate establishment of autotetraploid populations. Stochastic effects due to finite population size increase the probability of polyploid establishment and decrease the mean time to tetraploid fixation. Our results extend the minority cytotype exclusion principle to include important features of plant reproduction and demonstrate that variation in mating system parameters significantly influences the conditions necessary for polyploid establishment. 相似文献
20.
Wimmer G Dedík L Michal M Mudríková A Durisová M 《Bulletin of mathematical biology》1999,61(2):365-377
Properties of two of the stochastic circulatory models theoretically introduced by Smith et al., 1997, Bull. Math. Biol. 59, 1–22 were investigated. The models assumed the gamma distribution of the cycle time under either the geometric or Poisson
elimination scheme. The reason for selecting these models was the fact that the probability density functions of the residence
time of these models are formally similar to those of the Bateman and gamma-like function models, i.e., the two common deterministic
models. Using published data, the analytical forms of the probability density functions of the residence time and the distributions
of the simulated values of the residence time were determined on the basis of the deterministic models and the stochastic
circulatory models, respectively. The Kolmogorov-Smirnov test revealed that even for 1000 xenobiotic particles, i.e., a relatively
small number if the particles imply drug molecules, the probability density functions of the residence time based on the deterministic
models closely matched the distributions of the simulated values of the residence time obtained on the basis of the stochastic
circulatory models, provided that parameters of the latter models fulfilled selected conditions. 相似文献