Contributions to the mathematical theory of epidemics—I

Kermack, W. O.; McKendrick, A. G.

doi:10.1007/bf02464423

Cited by 462 publications

(531 citation statements)

References 2 publications

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“…These and subsequent models at the very start of the 20 th Century [2]- [5] focused on determining the infectious disease spread and the associated basic and effective reproduction number. Hugo…”

Section: Introductionmentioning

confidence: 99%

Seventy-five years of estimating the force of infection from current status data

et al. 2009

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(g) 75 years of estimating the force of infection 2 SummaryThe force of infection, describing the rate at which a susceptible person acquires an infection, is a key parameter in models estimating the infectious disease burden, and the effectiveness and cost-effectiveness of infectious disease prevention. Since Muench formulated the first catalytic model to estimate the force of infection in 1934, exactly 75 years ago, several authors addressed the estimation of this parameter by more advanced statistical methods, while applying these to seroprevalence and reported incidence/case notification data. In this paper we present an historical overview, discussing the relevance of Muench"s work, and we explain the wide array of newer methods with illustrations on pre-vaccination serological survey data of two airborne infections: rubella and parvovirus B19. We also provide guidance on deciding which method(s) to apply to estimate the force of infection, given a particular set of data.3

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Section: Introductionmentioning

confidence: 99%

Seventy-five years of estimating the force of infection from current status data

et al. 2009

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“…The most celebrated epidemic model was introduced by a medical doctor W.O. Kermack and a statistician A. G. McKendrick [32]. Both researchers modeled disease dynamics under the assumption that transmission depends on the intensity of hosts' interactions (handshakes, kisses, and more) and the frequency of encounters between susceptible and infected individuals.…”

Section: Managing Cancer As a Heterogeneous Consumer-resource Type Symentioning

confidence: 99%

Resource Consumption, Sustainability, and Cancer

2014

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Preserving a system's viability in the presence of diversity erosion is critical if the goal is to sustainably support biodiversity. Reduction in population heterogeneity, whether inter-or intraspecies, may increase population fragility, either decreasing its ability to adapt e ectively to environmental changes or facilitating the survival and success of ordinarily rare phenotypes. The latter may result in over-representation of individuals who may participate in resource utilization patterns that can lead to over-exploitation, exhaustion, and, ultimately, collapse of both the resource and the population that depends on it. Here, we aim to identify regimes that can signal whether a consumer-resource system is capable of supporting viable degrees of heterogeneity. The framework used here is an expansion of a previously introduced consumer-resource type system of a population of individuals classi ed by their resource consumption. Application of the Reduction Theorem to the system enables us to evaluate the health of the system through tracking both the mean value of the parameter of resource (over)consumption, and the population variance, as both change over time. The article concludes with a discussion that highlights applicability of the proposed system to investigation of systems that are a ected by particularly devastating overly-adapted populations, namely, cancerous cells. Potential intervention approaches for system management are discussed in the context of cancer therapies.

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“…Disregarding the stochasticity and the integer property of the individuals, we start with the classical SIR model [14], which is based on deterministic fractions of the population. This gives us the opportunity to demonstrate how stochastics and discreteness are implemented using the Poisson Simulation approach in a following step.…”

Section: A Deterministic Macro-modelmentioning

confidence: 99%

Bringing consistency to simulation of population models – Poisson Simulation as a bridge between micro and macro simulation

Gustafsson

Sternad

2007

Mathematical Biosciences

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Population models concern collections of discrete entities such as atoms, cells, humans, animals, etc., where the focus is on the number of entities in a population. Because of the complexity of such models, simulation is usually needed to reproduce their complete dynamic and stochastic behaviour. Two main types of simulation models are used for different purposes, namely micro-simulation models, where each individual is described with its particular attributes and behaviour, and macro-simulation models based on stochastic differential equations, where the population is described in aggregated terms by the number of individuals in different states. Consistency between micro-and macro-models is a crucial but often neglected aspect. This paper demonstrates how the Poisson Simulation technique can be used to produce a population macro-model consistent with the corresponding micro-model. This is accomplished by defining Poisson Simulation in strictly mathematical terms as a series of Poisson processes that generate sequences of Poisson distributions with dynamically varying parameters. The method can be applied to any population model. It provides the unique stochastic and dynamic macro-model consistent with a correct micro-model. The paper also presents a general macro form for stochastic and dynamic population models. In an appendix Poisson Simulation is compared with Markov Simulation showing a number of advantages. Especially aggregation into state variables and aggregation of many events per time-step makes Poisson Simulation orders of magnitude faster than Markov Simulation. Furthermore, you can build and execute much larger and more complicated models with Poisson Simulation than is possible with the Markov approach.

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Contributions to the mathematical theory of epidemics—I

Cited by 462 publications

References 2 publications

Seventy-five years of estimating the force of infection from current status data

Seventy-five years of estimating the force of infection from current status data

Resource Consumption, Sustainability, and Cancer

Bringing consistency to simulation of population models – Poisson Simulation as a bridge between micro and macro simulation

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