The Stochastic and Deterministic Model of the Spread of a Disease in Age-Structured Population

2020 ◽  
Vol 8 (12) ◽  
pp. 290-295
Author(s):  
Yardjouma Yéo
Keyword(s):  
Stochastic Model ◽  
Law Of Large Numbers ◽  
Deterministic Model ◽  
Characteristic Curve ◽  
Structured Population ◽  
The Central Limit Theorem ◽  
Large Numbers ◽  
The Law ◽  
Age Structured ◽  
Age Structured Population

We model the spread of an epidemic which depends on age and time. The behavior of the model obtained was the object of our studies.This studies shown that on each characteristic curve, the central limit theorem and the law of large numbers were satisfied. In this paper, we write a stochastic model to studie a disease which is begin in a population which is not large. we study overall the stochastic model obtained by varying the age and time together. We prove that the law of large numbers is satisfied.

The Law of Large Numbers and the Central Limit Theorem

1996 ◽  
pp. 92-96
Author(s):  
Richard L. Scheaffer ◽  
Ann Watkins ◽  
Mrudulla Gnanadesikan ◽  
Jeffrey A. Witmer
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Law Of Large Numbers ◽  
The Central Limit Theorem ◽  
Large Numbers ◽  
The Law

A Stochastic Age-Structured Population Model of Striped Bass (Morone saxatilis) in the Potomac River

1983 ◽  
Vol 40 (12) ◽  
pp. 2170-2183 ◽  
Author(s):  
Joel E. Cohen ◽  
Sigurd W. Christensen ◽  
C. Phillip Goodyear
Keyword(s):  
Growth Rate ◽  
Stochastic Model ◽  
Population Size ◽  
Striped Bass ◽  
Morone Saxatilis ◽  
Potomac River ◽  
Structured Population ◽  
Age Structured ◽  
Average Population Size ◽  
Age Structured Population

Deterministic age-structured models of fish populations neglect apparently stochastic fluctuations in the catch per unit effort of yearlings and of adult fish. We describe a model of an age-structured population in which the survival of eggs to yearlings fluctuates randomly, but all other age-specific rates of survival and of egg-laying are constant. For such a stochastic model, two measures of the long-term population growth rate are the average growth rate of the population size and the growth rate of the average population size. We compute both measures analytically for a simplified model representing only eggs and reproductive adults. For a model of the striped bass (Morone saxatilis) population spawning in the Potomac River, we compute both point and interval estimates of the growth rate of the average population size. We illustrate some statistical tests of the correctness of our stochastic model.

The Central Limit Theorem and the Law of Large Numbers for Pair-Connectivity in Bernoulli Trees

1989 ◽  
Vol 3 (4) ◽  
pp. 477-491
Author(s):  
Kyle T. Siegrist ◽  
Ashok T. Amin ◽  
Peter J. Slater
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Law Of Large Numbers ◽  
Network Reliability ◽  
Random Variable ◽  
The Central Limit Theorem ◽  
Large Numbers ◽  
The Mean ◽  
The Law

Consider the standard network reliability model in which each edge of a given (n, m)-graph G is deleted, independently of all others, with probability q = 1– p (0 <p < 1). The pair-connectivity random variable X is defined to be the number of connected pairs of vertices that remain in G. The mean of X has been proposed as a measure of reliability for failure-prone communications networks in which the edge deletions correspond to failures of the communications links. We consider deviations from the mean, the law of large numbers, and the central limit theorem for X as n → ∞. Some explicit results are obtained when G is a tree using martingale difference sequences. Stars and paths are treated in detail.

CLTs for Dependent Processes

2021 ◽  
pp. 548-567
Author(s):  
James Davidson
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Law Of Large Numbers ◽  
Strong Mixing ◽  
Mixing Processes ◽  
The Central Limit Theorem ◽  
Large Numbers ◽  
The Law ◽  
Dependent Processes

This chapter deals with the central limit theorem (CLT) for dependent processes. As with the law of large numbers, the focus is on near‐epoch dependent and mixing processes and array versions of the results are given to allow heterogeneity. The cornerstone of these results is a general CLT due to McLeish, from which a result for martingales is obtained directly. A result for stationary ergodic mixingales is given, and the rest of the chapter is devoted to proving and interpreting a CLT for mixingales and hence for arrays that are near‐epoch dependent on a strong‐mixing and uniform-mixing processes.

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