Stochastic processes and applications in biology and medicine II

Iosifescu, Marius; Tautu, P.

doi:10.1007/978-3-642-80753-4

Cited by 20 publications

(7 citation statements)

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“…Applications of control theory to these models are of obvious importance but these have usually been restricted to spread through a discrete state space and observation in discrete or continuous time. Some of this work is described by Abakuks (1973), Becker (1970), Iosifescu and Tautu (1973) and Jaquette (1970). When the population is large, models with continuous state space often yield useful approximations to what are in fact discrete phenomena.…”

Section: O Introductionmentioning

confidence: 99%

On the optimal control of a deterministic epidemic

Morton

Wickwire

1974

Advances in Applied Probability

125

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A control scheme for the immunisation of susceptibles in the Kermack-McKendrick epidemic model for a closed population is proposed. The bounded control appears linearly in both dynamics and integral cost functionals and any optimal policies are of the “bang-bang” type. The approach uses Dynamic Programming and Pontryagin's Maximum Principle and allows one, for certain values of the cost and removal rates, to apply necessary and sufficient conditions for optimality and show that a one-switch candidate is the optimal control. In the remaining cases we are still able to show that an optimal control, if it exists, has at most one switch.

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Section: O Introductionmentioning

confidence: 99%

On the optimal control of a deterministic epidemic

Morton

Wickwire

1974

Advances in Applied Probability

125

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“…Assumptions (1.1) express the quite realistic circumstance that new customers are discouraged from joining long queues, and that the server adapts the service speed to the length of the queue. Note the analogy of this model to the infinite-capacity model discussed by Conolly [2] and by Chan and Conolly [1] in which An = A(n + 1)-1 and J.Ln = nu, as well as its analogy to certain population growth processes in environments of finite carrying capacity ( [4], pp. 121 ff).…”

Section: The Queueing Modelmentioning

confidence: 93%

A solvable model for a finite-capacity queueing system

Giorno¹,

Negri²,

Nobile³

1985

Journal of Applied Probability

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Single–server–single-queue–FIFO-discipline queueing systems are considered in which at most a finite number of customers N can be present in the system. Service and arrival rates are taken to be dependent upon that state of the system. Interarrival intervals, service intervals, waiting times and busy periods are studied, and the results obtained are used to investigate the features of a special queueing model characterized by parameters (λ (Ν –n), μn). This model retains the qualitative features of the C-model proposed by Conolly [2] and Chan and Conolly [1]. However, quite unlike the latter, it also leads to closed-form expressions for the transient probabilities, the interarrival and service probability density functions and their moments, as well as the effective interarrival and service densities and their moments. Finally, some computational results are given to compare the model discussed in this paper with the C-model.

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“…A 2‐parameter negative binomial distribution is a generalized form of the Poisson, but it did not provide stable parameter estimates for these data. Second, mechanistic population‐growth models of birth and death processes can lead to a Poisson distribution of population sizes (Iofescu & Táutu 1973).…”

Section: Methodsmentioning

confidence: 99%