The rumour process

1982 ◽  
Vol 19 (04) ◽  
pp. 759-766
Author(s):  
Ross Dunstan
Keyword(s):  
Epidemic Model ◽  
Asymptotic Form ◽  
Deterministic Model ◽  
Final Size ◽  
Stochastic Epidemic ◽  
The Mean ◽  
Stochastic Epidemic Model ◽  
General Stochastic

The general stochastic epidemic model is used as a model for the spread of rumours. Recursive expressions are found for the mean of the final size of each generation of hearers. Simple expressions are found for the generation size and the asymptotic form of its final size in the deterministic model. An approximating process is presented.

The rumour process

1982 ◽  
Vol 19 (4) ◽  
pp. 759-766 ◽  
Author(s):  
Ross Dunstan
Keyword(s):  
Epidemic Model ◽  
Asymptotic Form ◽  
Deterministic Model ◽  
Final Size ◽  
Stochastic Epidemic ◽  
The Mean ◽  
Stochastic Epidemic Model ◽  
General Stochastic

The general stochastic epidemic model is used as a model for the spread of rumours. Recursive expressions are found for the mean of the final size of each generation of hearers. Simple expressions are found for the generation size and the asymptotic form of its final size in the deterministic model. An approximating process is presented.

The transition probabilities of the general stochastic epidemic model

1975 ◽  
Vol 12 (3) ◽  
pp. 415-424 ◽  
Author(s):  
Richard J. Kryscio
Keyword(s):  
Stochastic Model ◽  
Convenient Method ◽  
Epidemic Model ◽  
Transition Probabilities ◽  
Stochastic Epidemic ◽  
General Stochastic Model ◽  
Stochastic Epidemic Model ◽  
Forward Equations ◽  
General Stochastic

Recently, Billard (1973) derived a solution to the forward equations of the general stochastic model. This solution contains some recursively defined constants. In this paper we solve these forward equations along each of the paths the process can follow to absorption. A convenient method of combining the solutions for the different paths results in a simplified non-recursive expression for the transition probabilities of the process.

Study on a susceptible–infected–vaccinated model with delay and proportional vaccination

2018 ◽  
Vol 11 (08) ◽  
pp. 1850102 ◽  
Author(s):  
Shuqi Gan ◽  
Fengying Wei
Keyword(s):  
Positive Solution ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Stochastic Epidemic ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean ◽  
Stochastic Epidemic Model

A susceptible–infected–vaccinated epidemic model with proportional vaccination and generalized nonlinear rate is formulated and investigated in the paper. We show that the stochastic epidemic model admits a unique and global positive solution with probability one when constructing a proper [Formula: see text]-function therewith. Then a sufficient condition that guarantees the disappearances of diseases is derived when the indicator [Formula: see text]. Further, if [Formula: see text], then we obtain that the solution is weakly permanent with probability one. We also derived the sufficient conditions of the persistence in the mean for the susceptible and infected when another indicator [Formula: see text].

The transition probabilities of the general stochastic epidemic model

1975 ◽  
Vol 12 (03) ◽  
pp. 415-424 ◽  
Author(s):  
Richard J. Kryscio
Keyword(s):  
Stochastic Model ◽  
Convenient Method ◽  
Epidemic Model ◽  
Transition Probabilities ◽  
Stochastic Epidemic ◽  
General Stochastic Model ◽  
Stochastic Epidemic Model ◽  
Forward Equations ◽  
General Stochastic

Recently, Billard (1973) derived a solution to the forward equations of the general stochastic model. This solution contains some recursively defined constants. In this paper we solve these forward equations along each of the paths the process can follow to absorption. A convenient method of combining the solutions for the different paths results in a simplified non-recursive expression for the transition probabilities of the process.

scholarly journals Improved Estimation of the Initial Number of Susceptible Individuals in the General Stochastic Epidemic Model Using Penalized Likelihood

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Changhyuck Oh
Keyword(s):  
Epidemic Model ◽  
Likelihood Function ◽  
Hessian Matrix ◽  
Short Note ◽  
Penalized Likelihood ◽  
Initial Number ◽  
Susceptible Population ◽  
Stochastic Epidemic ◽  
Stochastic Epidemic Model ◽  
General Stochastic

The initial size of a completely susceptible population in a group of individuals plays a key role in drawing inferences for epidemic models. However, this can be difficult to obtain in practice because, in any population, there might be individuals who may not transmit the disease during the epidemic. This short note describes how to improve the maximum likelihood estimators of the infection rate and the initial number of susceptible individuals and provides their approximate Hessian matrix for the general stochastic epidemic model by using the concept of the penalized likelihood function. The simulations of major epidemics show significant improvements in performance in averages and coverage ratios for the suggested estimator of the initial number in comparison to existing methods. We applied the proposed method to the Abakaliki smallpox data.

The estimation of the parameters in epidemics

1975 ◽  
Vol 7 (3) ◽  
pp. 463-463
Author(s):  
Kevin Gough
Keyword(s):  
Epidemic Model ◽  
Stochastic Epidemic ◽  
Stochastic Epidemic Model ◽  
General Stochastic

The General Stochastic Epidemic model is extended to allow for outside infection. The likelihood is derived for small households, and the difficulties for larger populations are discussed.

scholarly journals An epidemic model with infector-dependent severity

2007 ◽  
Vol 39 (4) ◽  
pp. 949-972 ◽  
Author(s):  
Frank Ball ◽  
Tom Britton
Keyword(s):  
Vaccination Coverage ◽  
Epidemic Model ◽  
Branching Process ◽  
Infected Individual ◽  
Large Population ◽  
Final Size ◽  
Stochastic Epidemic ◽  
Major Outbreak ◽  
Stochastic Epidemic Model ◽  
The Individual

A stochastic epidemic model is defined in which infected individuals have different severities of disease (e.g. mildly and severely infected) and the severity of an infected individual depends on the severity of the individual he or she was infected by; typically, severe or mild infectives have an increased tendency to infect others severely or, respectively, mildly. Large-population properties of the model are derived, using branching process approximations for the initial stages of an outbreak and density-dependent population processes when a major outbreak occurs. The effects of vaccination are considered, using two distinct models for vaccine action. The consequences of launching a vaccination program are studied in terms of the effect it has on reducing the final size in the event of a major outbreak as a function of the vaccination coverage, and also by determining the critical vaccination coverage above which only small outbreaks can occur.

scholarly journals An epidemic model with infector-dependent severity

2007 ◽  
Vol 39 (04) ◽  
pp. 949-972 ◽  
Author(s):  
Frank Ball ◽  
Tom Britton
Keyword(s):  
Vaccination Coverage ◽  
Epidemic Model ◽  
Branching Process ◽  
Infected Individual ◽  
Large Population ◽  
Final Size ◽  
Stochastic Epidemic ◽  
Major Outbreak ◽  
Stochastic Epidemic Model ◽  
The Individual

A stochastic epidemic model is defined in which infected individuals have different severities of disease (e.g. mildly and severely infected) and the severity of an infected individual depends on the severity of the individual he or she was infected by; typically, severe or mild infectives have an increased tendency to infect others severely or, respectively, mildly. Large-population properties of the model are derived, using branching process approximations for the initial stages of an outbreak and density-dependent population processes when a major outbreak occurs. The effects of vaccination are considered, using two distinct models for vaccine action. The consequences of launching a vaccination program are studied in terms of the effect it has on reducing the final size in the event of a major outbreak as a function of the vaccination coverage, and also by determining the critical vaccination coverage above which only small outbreaks can occur.

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