STOCHASTIC PREDATION MODEL WITH DEPLETION

1979 ◽  
Vol 111 (4) ◽  
pp. 465-470 ◽  
Author(s):  
Guy L. Curry ◽  
Richard M. Feldman
Keyword(s):  
Stochastic Model ◽  
Deterministic Model ◽  
Expected Number ◽  
Numerical Comparisons ◽  
Prey Depletion

AbstractA stochastic model is developed for the expected number of prey taken by a single predator when prey depletion is apparent. The so-called “random predator equation” with prey exploitation of Royama and Rogers is compared with the stochastic model. The numerical comparisons illustrate situations where the deterministic model provides adequate and inadequate approximations.

scholarly journals Stochastic and deterministic mathematical model of cholera disease dynamics with direct transmission

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Getachew Teshome Tilahun ◽  
Woldegebriel Assefa Woldegerima ◽  
Aychew Wondifraw
Keyword(s):  
Mathematical Model ◽  
Stochastic Model ◽  
Deterministic Model ◽  
Equilibrium Points ◽  
Invariant Solution ◽  
Stochastic Approach ◽  
Disease Dynamics ◽  
Treatment Rate ◽  
Invariant Region ◽  
Contact Transmission

AbstractIn this paper we develop a stochastic mathematical model of cholera disease dynamics by considering direct contact transmission pathway. The model considers four compartments, namely susceptible humans, infectious humans, treated humans, and recovered humans. Firstly, we develop a deterministic mathematical model of cholera. Since the deterministic model does not consider the randomness process or environmental factors, we converted it to a stochastic model. Then, for both types of models, the qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction numbers are obtained for both models and compared. From the comparison, we obtained that the basic reproduction number of the stochastic model is much smaller than that of the deterministic one, which means that the stochastic approach is more realistic. Finally, we performed sensitivity analysis and numerical simulations. The numerical simulation results show that reducing contact rate, improving treatment rate, and environmental sanitation are the most crucial activities to eradicate cholera disease from the community.

Distribution of the number of alleles in multigene families

1992 ◽  
Vol 29 (04) ◽  
pp. 759-769
Author(s):  
R. C. Griffiths
Keyword(s):  
Stochastic Model ◽  
Gene Conversion ◽  
Lower Bounds ◽  
Multigene Families ◽  
Expected Number ◽  
Allele Type ◽  
The Mean

The distribution of the number of alleles in samples from r chromosomes is studied. The stochastic model used includes gene conversion within chromosomes and mutation at loci on the chromosomes. A method is described for simulating the distribution of alleles and an algorithm given for computing lower bounds for the mean number of alleles. A formula is derived for the expected number of samples from r chromosomes which contain the allele type of a locus chosen at random.

The dynamics of a delayed deterministic and stochastic epidemic SIR models with a saturated incidence rate

2018 ◽  
Vol 26 (4) ◽  
pp. 235-245 ◽  
Author(s):  
Modeste N’zi ◽  
Ilimidi Yattara
Keyword(s):  
Stochastic Model ◽  
White Noise ◽  
Incidence Rate ◽  
Deterministic Model ◽  
Contact Rate ◽  
Almost Sure Stability ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Global Positive Solution ◽  
Disease Free

AbstractWe treat a delayed SIR (susceptible, infected, recovered) epidemic model with a saturated incidence rate and its perturbation through the contact rate using a white noise. We start with a deterministic model and then add a perturbation on the contact rate using a white noise to obtain a stochastic model. We prove the existence and uniqueness of the global positive solution for both deterministic and stochastic delayed differential equations. Under suitable conditions on the parameters, we study the global asymptotic stability of the disease-free equilibrium of the deterministic model and the almost sure stability of the disease-free equilibrium of the stochastic model.

scholarly journals A Novel Theoretical Probabilistic Model for Opportunistic Routing with Applications in Energy Consumption for WSNs

Sensors ◽  
2021 ◽  
Vol 21 (23) ◽  
pp. 8058
Author(s):  
Christian E. Galarza ◽  
Jonathan M. Palma ◽  
Cecilia F. Morais ◽  
Jaime Utria ◽  
Leonardo P. Carvalho ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Energy Consumption ◽  
Stochastic Model ◽  
Opportunistic Networks ◽  
Opportunistic Routing ◽  
Opportunistic Network ◽  
Expected Number ◽  
Successful Transmission ◽  
Network Parameters ◽  
Proposed Model

This paper proposes a new theoretical stochastic model based on an abstraction of the opportunistic model for opportunistic networks. The model is capable of systematically computing the network parameters, such as the number of possible routes, the probability of successful transmission, the expected number of broadcast transmissions, and the expected number of receptions. The usual theoretical stochastic model explored in the methodologies available in the literature is based on Markov chains, and the main novelty of this paper is the employment of a percolation stochastic model, whose main benefit is to obtain the network parameters directly. Additionally, the proposed approach is capable to deal with values of probability specified by bounded intervals or by a density function. The model is validated via Monte Carlo simulations, and a computational toolbox (R-packet) is provided to make the reproduction of the results presented in the paper easier. The technique is illustrated through a numerical example where the proposed model is applied to compute the energy consumption when transmitting a packet via an opportunistic network.

Gray-Box Approach for Fault Detection of Dynamical Systems

2003 ◽  
Vol 125 (3) ◽  
pp. 451-454 ◽  
Author(s):  
Han G. Park ◽  
Michail Zak
Keyword(s):  
Neural Network ◽  
Time Delay ◽  
Fault Detection ◽  
Stochastic Model ◽  
Deterministic Model ◽  
Feed Forward Neural Network ◽  
The Neural Network ◽  
Simulated System ◽  
Auto Regressive ◽  
Nonlinear Components

We present a fault detection method called the gray-box. The term “gray-box” refers to the approach wherein a deterministic model of system, i.e., “white box,” is used to filter the data and generate a residual, while a stochastic model, i.e., “black-box” is used to describe the residual. The residual is described by a three-tier stochastic model. An auto-regressive process, and a time-delay feed-forward neural network describe the linear and nonlinear components of the residual, respectively. The last component, the noise, is characterized by its moments. Faults are detected by monitoring the parameters of the auto-regressive model, the weights of the neural network, and the moments of noise. This method is demonstrated on a simulated system of a gas turbine with time delay feedback actuator.

A Dynamic Generalization of Zipf's Rank-Size Rule

1982 ◽  
Vol 14 (11) ◽  
pp. 1449-1467 ◽  
Author(s):  
B Roehner ◽  
K E Wiese
Keyword(s):  
Stochastic Model ◽  
Size Distribution ◽  
Urban Growth ◽  
Simple Form ◽  
Deterministic Model ◽  
City Size ◽  
Zipf’S Law ◽  
Zipf's Law ◽  
City Size Distribution ◽  
Zero Growth

A dynamic deterministic model of urban growth is proposed, which in its most simple form yields Zipf's law for city-size distribution, and in its general form may account for distributions that deviate strongly from Zipf's law. The qualitative consequences of the model are examined, and a corresponding stochastic model is introduced, which permits, in particular, the study of zero-growth situations.

A stability analysis on a smoking model with stochastic perturbation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Anwar Zeb ◽  
Sunil Kumar ◽  
Almaz Tesfay ◽  
Anil Kumar
Keyword(s):  
Stochastic Model ◽  
Stochastic System ◽  
Existence And Uniqueness ◽  
Deterministic Model ◽  
Sufficient Conditions ◽  
Reproductive Number ◽  
Content Type ◽  
Model Form ◽  
The World ◽  
Dynamic Stochastic

Purpose The purpose of this paper is to investigate the effects of irregular unsettling on the smoking model in form of the stochastic model as in the deterministic model these effects are neglected for simplicity. Design/methodology/approach In this research, the authors investigate a stochastic smoking system in which the contact rate is perturbed by Lévy noise to control the trend of smoking. First, present the formulation of the stochastic model and study the dynamics of the deterministic model. Then the global positive solution of the stochastic system is discussed. Further, extinction and the persistence of the proposed system are presented on the base of the reproductive number. Findings The authors discuss the dynamics of the deterministic smoking model form and further present the existence and uniqueness of non-negative global solutions for the stochastic system. Some previous study’s mentioned in the Introduction can be improved with the help of obtaining results, graphically present in this manuscript. In this regard, the authors present the sufficient conditions for the extinction of smoking for reproductive number is less than 1. Research limitations/implications In this work, the authors investigated the dynamic stochastic smoking model with non-Gaussian noise. The authors discussed the dynamics of the deterministic smoking model form and further showed for the stochastic system the existence and uniqueness of the non-negative global solution. Some previous study’s mentioned in the Introduction can be improved with the help of obtained results, clearly shown graphically in this manuscript. In this regard, the authors presented the sufficient conditions for the extinction of smoking, if <1, which can help in the control of smoking. Motivated from this research soon, the authors will extent the results to propose new mathematical models for the smoking epidemic in the form of fractional stochastic modeling. Especially, will investigate the effective strategies for control smoking throughout the world. Originality/value This study is helpful in the control of smoking throughout the world.

Random exchanges of information

1981 ◽  
Vol 18 (3) ◽  
pp. 743-746 ◽  
Author(s):  
John Haigh
Keyword(s):  
The Other ◽  
Expected Number ◽  
Numerical Comparisons

Suppose that n persons each know a different piece of information, and that, whenever a pair of them talk on the telephone, each tells the other all the information he knows at that time. If the calls are made at random, we show that the expected number of calls required for everyone to know all n pieces of information is asymptotically 1.5 n log n + O(n). This sharpens an earlier result of D. W. Boyd and J. M. Steele. Some numerical comparisons are given.

Asymptotic behavior of a generalization of Bailey's simple epidemic

1971 ◽  
Vol 3 (02) ◽  
pp. 220-221
Author(s):  
George H. Weiss ◽  
Menachem Dishon
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Rate Constants ◽  
Deterministic Model ◽  
Stochastic Theory ◽  
Expected Number ◽  
Deterministic Theory ◽  
Mean Values ◽  
Image Position ◽  
Fixed Population

It has been shown that for many epidemic models, the stochastic theory leads to essentially the same results as the deterministic theory provided that one identifies mean values with the functions calculated from the deterministic differential equations (cf. [1]). If one considers a generalization of Bailey's simple epidemic for a fixed population of size N, represented schematically by where I refers to an infected, S refers to a susceptible, and α and β are appropriate rate constants, then it is evident that at time t = ∞, the expected number of infected individuals must be zero provided that β &gt; 0. If x(t) denotes the number of infected at time t, then the deterministic model is summarized by

First-Order Conservative Processes with Multiple Latent Roots

1969 ◽  
Vol 6 (01) ◽  
pp. 186-194 ◽  
Author(s):  
J. Radcliffe ◽  
P. J. Staff
Keyword(s):  
Stochastic Process ◽  
Stochastic Model ◽  
Chemical Reactions ◽  
Equilibrium Distribution ◽  
Deterministic Model ◽  
Multicomponent System ◽  
Mass Action ◽  
Approach To Equilibrium ◽  
First Order ◽  
Gas Molecules

There are now many examples in various fields where the behaviour of ‘particles' as exhibited by their transition from one state to another is described by a multidimensional stochastic process. The linear migration model in which particles move independently of one another through a number of states has been dealt with by Bartlett (1949). This process has been used by Siegert (1949) in considering the approach to equilibrium of non-interacting gas molecules and by Krieger and Gans (1960) and Gans (1960) to examine the distribution of a multicomponent system disturbed from its equilibrium distribution and relaxing by first-order processes to another equilibrium. The correspondence between the deterministic model based on the principle of mass action and the stochastic model has been discussed by Darvey and Staff (1966) in the context of unimolecular multicomponent chemical reactions.

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