A Note on the General Time-Dependent Stochastic Compartmental Model

Biometrics ◽  
1976 ◽  
Vol 32 (2) ◽  
pp. 443 ◽  
Author(s):  
M. J. Faddy
Keyword(s):  
Compartmental Model ◽  
Time Dependent ◽  
General Time ◽  
Stochastic Compartmental Model

Stochastic compartmental models as approximations to more general stochastic systems with the general stochastic epidemic as an example

1977 ◽  
Vol 9 (03) ◽  
pp. 448-461 ◽  
Author(s):  
M. J. Faddy
Keyword(s):  
Generating Function ◽  
Compartmental Model ◽  
Stochastic Systems ◽  
Compartmental Models ◽  
Time Dependent ◽  
Simple Argument ◽  
Stochastic Epidemic ◽  
General Time ◽  
General Stochastic ◽  
Stochastic Compartmental Model

A general time-dependent stochastic compartmental model is considered, where particles may move between a set of m compartments or out of the system, and new particles may be introduced into the compartments by immigration. A simple argument not relying on generating function techniques is given for the solution of such a system. It is then demonstrated that this class of compartmental models can be used as approximations to more complex stochastic systems by replacing dependence on certain stochastic variables by dependence on corresponding deterministic variables, with some recent examples being discussed. A compartmental approximation to the general stochastic epidemic is then constructed which appears on the basis of some simulations to compare favourably with the true process, particularly after the infection has got established in the population.

Stochastic compartmental models as approximations to more general stochastic systems with the general stochastic epidemic as an example

1977 ◽  
Vol 9 (3) ◽  
pp. 448-461 ◽  
Author(s):  
M. J. Faddy
Keyword(s):  
Generating Function ◽  
Compartmental Model ◽  
Stochastic Systems ◽  
Compartmental Models ◽  
Time Dependent ◽  
Simple Argument ◽  
Stochastic Epidemic ◽  
General Time ◽  
General Stochastic ◽  
Stochastic Compartmental Model

A general time-dependent stochastic compartmental model is considered, where particles may move between a set of m compartments or out of the system, and new particles may be introduced into the compartments by immigration. A simple argument not relying on generating function techniques is given for the solution of such a system. It is then demonstrated that this class of compartmental models can be used as approximations to more complex stochastic systems by replacing dependence on certain stochastic variables by dependence on corresponding deterministic variables, with some recent examples being discussed. A compartmental approximation to the general stochastic epidemic is then constructed which appears on the basis of some simulations to compare favourably with the true process, particularly after the infection has got established in the population.

GENERALIZED HANNAY ANGLE FOR THE MOST GENERAL TIME-DEPENDENT HARMONIC OSCILLATOR

1993 ◽  
Vol 07 (28) ◽  
pp. 4827-4840 ◽  
Author(s):  
DONALD H. KOBE ◽  
JIONGMING ZHU
Keyword(s):  
Harmonic Oscillator ◽  
Berry Phase ◽  
Time Dependent ◽  
Canonical Momentum ◽  
Gauge Invariant ◽  
Classical Counterpart ◽  
Mass Spring ◽  
Adiabatic Case ◽  
General Time ◽  
Total Angle

The most general time-dependent Hamiltonian for a harmonic oscillator is both linear and quadratic in the coordinate and the canonical momentum. It describes in general a harmonic oscillator with mass, spring “constant,” and friction (or antifriction) “constant,” all of which are time dependent, that is acted on by a time-dependent force. A generalized Hannay angle, which is gauge invariant, is defined by making a distinction between the Hamiltonian and the energy. The generalized Hannay angle is the classical counterpart of the generalized Berry phase in quantum theory. When friction is present the generalized Hannay angle is nonzero. If the Hamiltonian is (incorrectly) chosen to be the energy, the generalized Hannay angle is different. Nevertheless, in the adiabatic case the same total angle is obtained.

scholarly journals Attack rate and the price of SARS-CoV-2 herd immunity in Brazil

2021 ◽  
Author(s):  
Tarcisio Rocha Filho ◽  
José Mendes ◽  
Carson Chow ◽  
James Phillips ◽  
Antônio Cordeiro ◽  
...  
Keyword(s):  
Attack Rate ◽  
Contact Structure ◽  
Compartmental Model ◽  
Total Population ◽  
Herd Immunity ◽  
Age Groups ◽  
Time Dependent ◽  
Contact Matrix ◽  
The City ◽  
Pharmaceutical Interventions

Abstract We introduce a compartmental model with age structure to study the dynamics of the SARS-COV−2 pandemic. The contagion matrix in the model is given by the product of a probability per contact with a contact matrix explicitly taking into account the contact structure among different age groups. The probability of contagion per contact is considered as time dependent to represent non-pharmaceutical interventions, and is fitted from the time series of deaths. The approach is used to study the evolution of the COVID−19 pandemic in the main Brazilian cities and compared to two good quality serological surveys. We also discuss with some detail the case of the city of Manaus which raised special attention due to a previous report of three-quarters attack rate by the end of 2020. We discuss estimates for Manaus and all Brazilian cities with a total population of more than one million. We also estimate the attack rate with respect to the total population, in each Brazilian state by January, 1 st 2021 and May, 23 2021.

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