On the time-dependent reversible stochastic compartmental model—I. The general two-compartment system

1975 ◽  
Vol 37 (5) ◽  
pp. 505-519
Author(s):  
M. Cardenas ◽  
J. H. Matis
Keyword(s):  
Compartmental Model ◽  
Time Dependent ◽  
Compartment System ◽  
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.

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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