scholarly journals A Stochastic SIVS Epidemic Model Based on Birth and Death Process

2016 ◽  
Vol 04 (09) ◽  
pp. 1837-1848
Author(s):  
Lin Zhu ◽  
Tiansi Zhang
Keyword(s):  
Epidemic Model ◽  
Death Process ◽  
Birth And Death Process ◽  
Model Based

On the asymptotic distribution of the maximum number of infectives in epidemic models by immigration

1994 ◽  
Vol 31 (3) ◽  
pp. 606-613 ◽  
Author(s):  
V. M. Abramov
Keyword(s):  
Asymptotic Distribution ◽  
Epidemic Model ◽  
Epidemic Models ◽  
Death Process ◽  
Birth And Death Process ◽  
Initial Number ◽  
Martingale Approach ◽  
Distribution Of The Maximum ◽  
Non Linear

This paper considers the asymptotic distribution of the maximum number of infectives in an epidemic model by showing that, as the initial number of susceptibles converges to infinity, the process of infectives converges almost surely to a birth and death process. The model studied here is more general than usual (see e.g. Bailey (1975), Bharucha-Reid (1960), Keilson (1979)) in that it incorporates immigration and the limiting birth and death process is non-linear. The main novelty of the present paper is the martingale approach used to prove the above-mentioned convergence.

On the asymptotic distribution of the maximum number of infectives in epidemic models by immigration

1994 ◽  
Vol 31 (03) ◽  
pp. 606-613
Author(s):  
V. M. Abramov
Keyword(s):  
Asymptotic Distribution ◽  
Epidemic Model ◽  
Epidemic Models ◽  
Death Process ◽  
Birth And Death Process ◽  
Initial Number ◽  
Martingale Approach ◽  
Distribution Of The Maximum ◽  
Non Linear

This paper considers the asymptotic distribution of the maximum number of infectives in an epidemic model by showing that, as the initial number of susceptibles converges to infinity, the process of infectives converges almost surely to a birth and death process. The model studied here is more general than usual (see e.g. Bailey (1975), Bharucha-Reid (1960), Keilson (1979)) in that it incorporates immigration and the limiting birth and death process is non-linear. The main novelty of the present paper is the martingale approach used to prove the above-mentioned convergence.

Strong Convergence of Stochastic Epidemics

1994 ◽  
Vol 26 (3) ◽  
pp. 629-655 ◽  
Author(s):  
Frank Ball ◽  
Philip O'Neill
Keyword(s):  
Strong Convergence ◽  
Epidemic Model ◽  
Death Process ◽  
Birth And Death Process ◽  
Initial Number ◽  
Positive Real ◽  
Immigration And Emigration

This paper is concerned with a model for the spread of an epidemic in a closed, homogeneously mixing population in which new infections occur at rate f(x, y) and removals occur at rate g(x, y), where x and y are the numbers of susceptible and infective individuals, respectively, and f and g are arbitrary but specified positive real-valued functions. Sequences of such epidemics, indexed by the initial number of susceptibles n, are considered and conditions are derived under which the epidemic processes converge almost surely to a birth and death process as n tends to infinity. Thus a threshold theorem for such an epidemic model is obtained. The results are extended to models which incorporate immigration and emigration of susceptibles. The theory is illustrated by several examples of models taken from the epidemic literature. Generalizations to multipopulation epidemics are discussed briefly.

Strong Convergence of Stochastic Epidemics

1994 ◽  
Vol 26 (03) ◽  
pp. 629-655 ◽  
Author(s):  
Frank Ball ◽  
Philip O'Neill
Keyword(s):  
Strong Convergence ◽  
Epidemic Model ◽  
Death Process ◽  
Birth And Death Process ◽  
Initial Number ◽  
Positive Real ◽  
Immigration And Emigration

This paper is concerned with a model for the spread of an epidemic in a closed, homogeneously mixing population in which new infections occur at rate f(x, y) and removals occur at rate g(x, y), where x and y are the numbers of susceptible and infective individuals, respectively, and f and g are arbitrary but specified positive real-valued functions. Sequences of such epidemics, indexed by the initial number of susceptibles n, are considered and conditions are derived under which the epidemic processes converge almost surely to a birth and death process as n tends to infinity. Thus a threshold theorem for such an epidemic model is obtained. The results are extended to models which incorporate immigration and emigration of susceptibles. The theory is illustrated by several examples of models taken from the epidemic literature. Generalizations to multipopulation epidemics are discussed briefly.

A Novelty Massive MIMO Channel Model Based on the Birth‐and‐Death Process of Spatial Multipath Cluster

Radio Science ◽  
2020 ◽  
Vol 55 (10) ◽  
Author(s):  
Yanping Lu ◽  
Yongjun Zhang ◽  
Liqin Fu ◽  
Jiahui Qiu ◽  
Kai Liu ◽  
...  
Keyword(s):  
Massive Mimo ◽  
Channel Model ◽  
Mimo Channel ◽  
Death Process ◽  
Birth And Death Process ◽  
Model Based

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

A stochastic process related to language change

1970 ◽  
Vol 7 (01) ◽  
pp. 69-78 ◽  
Author(s):  
Barron Brainerd
Keyword(s):  
Stochastic Process ◽  
Language Change ◽  
Death Process ◽  
Birth And Death Process ◽  
Standard Methods

The purpose of this note is two-fold. First, to introduce the mathematical reader to a group of problems in the study of language change which has received little attention from mathematicians and probabilists. Secondly, to introduce a birth and death process, arising naturally out of this group of problems, which has received little attention in the literature. This process can be solved using the standard methods and the solution is exhibited here.

Multi-Location Inventory Model Considering Bidirectional and Unidirectional Transshipments Simultaneously

2013 ◽  
Vol 694-697 ◽  
pp. 2742-2745
Author(s):  
Jin Hong Zhong ◽  
Yun Zhou
Keyword(s):  
Process Model ◽  
Approximate Calculation ◽  
Inventory Model ◽  
Inventory System ◽  
Death Process ◽  
Birth And Death Process ◽  
Inventory Models ◽  
Continuous Review ◽  
Poisson Demand ◽  
Queue Theory

Abstract. A cross-regional multi-site inventory system with independent Poisson demand and continuous review (S-1,S) policy, in which there is bidirectional transshipment between the locations at the same area, and unidirectional transshipment between the locations at the different area. According to the M/G/S/S queue theory, birth and death process model and approximate calculation policy, we established inventory models respectively for the loss sales case and backorder case, and designed corresponding procedures to solve them. Finally, we verify the effectiveness of proposed models and methods by means of a lot of contrast experiments.

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