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Journal of the Royal Statistical Society. Series A (Statistics in Society), 1994
"The problems of understanding and controlling disease raise a range of challenging mathematical and statistical research topics, from broad theoretical issues to specific practical ones. In particular, recent interest in acquired immune deficiency syndrome has stimulated much progress in diverse areas of epidemic modelling, particularly with regard ...
D, Mollison, V, Isham, B, Grenfell
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"The problems of understanding and controlling disease raise a range of challenging mathematical and statistical research topics, from broad theoretical issues to specific practical ones. In particular, recent interest in acquired immune deficiency syndrome has stimulated much progress in diverse areas of epidemic modelling, particularly with regard ...
D, Mollison, V, Isham, B, Grenfell
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Biometrics, 1979
This paper is concerned with models formulated to describe the spread of infectious diseases through a community. Some standard epidemic models are introduced and an overview of their uses is provided. The paper includes a discussion of the advantages of simple models over complex ones and the advantages of stochastic models over deterministic ones ...
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This paper is concerned with models formulated to describe the spread of infectious diseases through a community. Some standard epidemic models are introduced and an overview of their uses is provided. The paper includes a discussion of the advantages of simple models over complex ones and the advantages of stochastic models over deterministic ones ...
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International Journal of Bifurcation and Chaos, 2012
A discrete-time deterministic epidemic model is proposed with the aim of reproducing the behavior observed in the incidence of real infectious diseases, such as oscillations and irregularities. For this purpose, we introduce, in a naïve discrete-time SIRS model, seasonal variability (i) in the loss of immunity and (ii) in the infection probability ...
F. Paladini, Ilaria Renna, L. Renna
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A discrete-time deterministic epidemic model is proposed with the aim of reproducing the behavior observed in the incidence of real infectious diseases, such as oscillations and irregularities. For this purpose, we introduce, in a naïve discrete-time SIRS model, seasonal variability (i) in the loss of immunity and (ii) in the infection probability ...
F. Paladini, Ilaria Renna, L. Renna
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An Epidemic Model With a Multistage Vaccine
Bulletin of Mathematical Biology, 2015Many diseases, such as the seasonal flu, tetanus, and smallpox, can be vaccinated against with a single dose of a vaccine. However, some diseases require multiple doses of a vaccine for immunity. For example, Hepatitis B requires three doses of a vaccine, with the second occurring about 1 month after the first and the third occurring about 5 months ...
Delegge, Anthony +3 more
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A Framework for Epidemic Models
Journal of Biological Systems, 2003A framework is developed that enables the modeling of the various mechanisms of epidemic processes. A model within the framework is completely characterized by a set of transmission functions. These functions support the modeling of the infectivity of a new infective as a function of its age-of-infection.
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2000
Summary: A stochastic epidemic model of SIS type has been investigated. For this, the corresponding Fokker-Planck equation has been solved for stationary or equilibrium transition probabilities. The spatial patterns of spread for the infectives for different transition stationary state probabilities have been obtained.
DAS, P., DE, S.
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Summary: A stochastic epidemic model of SIS type has been investigated. For this, the corresponding Fokker-Planck equation has been solved for stationary or equilibrium transition probabilities. The spatial patterns of spread for the infectives for different transition stationary state probabilities have been obtained.
DAS, P., DE, S.
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1984
This general introduction to the ideas and techniques required for the mathematical modelling of diseases begins with an outline of some disease statistics dating from Daniel Bernoulli's 1760 smallpox data. The authors then describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either ...
D. J. Daley, J. Gani
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This general introduction to the ideas and techniques required for the mathematical modelling of diseases begins with an outline of some disease statistics dating from Daniel Bernoulli's 1760 smallpox data. The authors then describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either ...
D. J. Daley, J. Gani
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2006
One of the important areas of real-life applications of stochastic processes is in epidemiology, more specifically, in analyzing the spread of epidemics. Roughly speaking, the situation that we want to look at is as follows. There is a group of individuals, all mixing homogeneously together.
A. Goswami, B. V. Rao
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One of the important areas of real-life applications of stochastic processes is in epidemiology, more specifically, in analyzing the spread of epidemics. Roughly speaking, the situation that we want to look at is as follows. There is a group of individuals, all mixing homogeneously together.
A. Goswami, B. V. Rao
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