SIR epidemics with stages of infection

2016 ◽  
Vol 48 (3) ◽  
pp. 768-791 ◽  
Author(s):  
Claude Lefèvre ◽  
Matthieu Simon
Keyword(s):  
Markov Process ◽  
Stochastic Model ◽  
Poisson Process ◽  
Matrix Analytic Methods ◽  
Analytic Methods ◽  
Epidemic Size ◽  
Semi Markov Process ◽  
Final Epidemic Size ◽  
Simple Matrix

AbstractIn this paper we are concerned with a stochastic model for the spread of an epidemic in a closed homogeneously mixing population when an infective can go through several stages of infection before being removed. The transitions between stages are governed by either a Markov process or a semi-Markov process. An infective of any stage makes contacts amongst the population at the points of a Poisson process. Our main purpose is to derive the distribution of the final epidemic size and severity, as well as an approximation by branching, using simple matrix analytic methods. Some illustrations are given, including a model with treatment discussed by Gani (2006).

Compartmental models with transfer delays: a semi-Markov approach

1985 ◽  
Vol 22 (3) ◽  
pp. 570-582
Author(s):  
Mary G. Leitnaker ◽  
Peter Purdue
Keyword(s):  
Markov Process ◽  
Stochastic Model ◽  
Compartmental Models ◽  
Time Dependent ◽  
Deterministic Case ◽  
Limiting Behavior ◽  
Dependent Behavior ◽  
Quadrature Methods ◽  
Semi Markov Process ◽  
Delayed Arguments

Compartmental models for which transfer from one compartment to another takes a non-negligible time have been studied in the deterministic case. These models rely on the use of differential equations with delayed arguments. In this paper we show how the well-known structure of the semi-Markov process can be used to analyse stochastic compartmental models with transfer delays. Evaluation of the limiting behavior is much simpler in the stochastic model than in previous deterministic formulations. In addition, time-dependent behavior can be analysed using numerical quadrature methods.

Analysis of a discrete semi-Markov model of continuous inventory control with periodic interruptions of consumption

2015 ◽  
Vol 25 (1) ◽  
Author(s):  
Petr V. Shnurkov ◽  
Alexey V. Ivanov
Keyword(s):  
Optimal Control ◽  
Markov Process ◽  
Optimal Control Problem ◽  
Stochastic Model ◽  
Markov Model ◽  
Control Problem ◽  
Extremal Problem ◽  
Inventory Control ◽  
Optimal Policy ◽  
Semi Markov Process

AbstractWe consider a discrete stochastic model of inventory control based on a controlled semi-Markov process. Probabilistic characteristics of the semi-Markov process are found along with characteristics of a stationary cost functional connected with this process. It is proved that an optimal policy of inventory control is a deterministic one. Explicit analitical representation of stationary functional characterising the control quality is obtained. An optimal control problem is reduced to the solution of an extremal problem for a multivariate function.

scholarly journals Stochastic Model on Three-Similar Units Three Phased Mission System with FCFS Repairs Pattern

2021 ◽  
Vol 10 (4) ◽  
pp. 65-70
Author(s):  
Sudesh Kumari ◽  
Rajeev Kumar
Keyword(s):  
Markov Process ◽  
Stochastic Model ◽  
System Performance ◽  
Phase Iii ◽  
Cost Consideration ◽  
Regenerative Point ◽  
Semi Markov Process ◽  
First Come First Serve ◽  
Mission System ◽  
Repair Facility

The paper allocates a stochastic model on threesimilar units three-phased mission system. The developed system consists of units working in parallel, series and parallel configurations respectively. Initially, the three similar units are operational. Each component has only three states: good, degraded and failed. In this case, the single repair facility that repairs the units in first come first serve (FCFS)pattern has been thought of. Using Semi-Markov Process and regenerative point techniques, various measures of the system performance at each phase are obtained. The system has been analyzed graphically taking a particular case. Various conclusions are made regarding the reliability and cost consideration of the system at each phase as well as for the whole system(as combined Phase I, Phase II, Phase III).

Compartmental models with transfer delays: a semi-Markov approach

1985 ◽  
Vol 22 (03) ◽  
pp. 570-582
Author(s):  
Mary G. Leitnaker ◽  
Peter Purdue
Keyword(s):  
Markov Process ◽  
Stochastic Model ◽  
Compartmental Models ◽  
Time Dependent ◽  
Deterministic Case ◽  
Limiting Behavior ◽  
Dependent Behavior ◽  
Quadrature Methods ◽  
Semi Markov Process ◽  
Delayed Arguments

Compartmental models for which transfer from one compartment to another takes a non-negligible time have been studied in the deterministic case. These models rely on the use of differential equations with delayed arguments. In this paper we show how the well-known structure of the semi-Markov process can be used to analyse stochastic compartmental models with transfer delays. Evaluation of the limiting behavior is much simpler in the stochastic model than in previous deterministic formulations. In addition, time-dependent behavior can be analysed using numerical quadrature methods.

Partially observable semi-Markov reward processes

1993 ◽  
Vol 30 (3) ◽  
pp. 548-560 ◽  
Author(s):  
Yasushi Masuda
Keyword(s):  
Markov Process ◽  
Counting Process ◽  
Probabilistic Interpretation ◽  
Real Domain ◽  
Semi Markov Process ◽  
Reward Process ◽  
Markov Reward ◽  
Partially Observable ◽  
Joint Behavior

The main objective of this paper is to investigate the conditional behavior of the multivariate reward process given the number of certain signals where the underlying system is described by a semi-Markov process and the signal is defined by a counting process. To this end, we study the joint behavior of the multivariate reward process and the multivariate counting process in detail. We derive transform results as well as the corresponding real domain expressions, thus providing clear probabilistic interpretation.

Heterogeneity in epidemic models and its effect on the spread of infection

1998 ◽  
Vol 35 (3) ◽  
pp. 651-661 ◽  
Author(s):  
Håkan Andersson ◽  
Tom Britton
Keyword(s):  
Heterogeneous Population ◽  
Epidemic Models ◽  
Homogeneous Population ◽  
Epidemic Size ◽  
Infection Pressure ◽  
Group A ◽  
Final Epidemic Size ◽  
Spread Of Infection ◽  
Very High ◽  
High Infectivity

We first study an epidemic amongst a population consisting of individuals with the same infectivity but with varying susceptibilities to the disease. The asymptotic final epidemic size is compared with the corresponding size for a homogeneous population. Then we group a heterogeneous population into households, assuming very high infectivity within households, and investigate how the global infection pressure is affected by rearranging individuals between the households. In both situations considered, it turns out that whether or not homogenizing the individuals or households will result in an increased spread of infection actually depends on the infectiousness of the disease.

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