444,637 research outputs found
The SIR epidemic model from a PDE point of view
We present a derivation of the classical SIR model through a mean-field
approximation from a discrete version of SIR. We then obtain a hyperbolic
forward Kolmogorov equation, and show that its projected characteristics
recover the standard SIR model. Moreover, we show that the long time limit of
the evolution will be a Dirac measure. The exact position will depend on the
well-know parameter, and it will be supported on the corresponding stable
SIR equilibrium
Spread of Infectious Diseases with a Latent Period
Infectious diseases spread through human networks.
Susceptible-Infected-Removed (SIR) model is one of the epidemic models to
describe infection dynamics on a complex network connecting individuals. In the
metapopulation SIR model, each node represents a population (group) which has
many individuals. In this paper, we propose a modified metapopulation SIR model
in which a latent period is taken into account. We call it SIIR model. We
divide the infection period into two stages: an infected stage, which is the
same as the previous model, and a seriously ill stage, in which individuals are
infected and cannot move to the other populations. The two infectious stages in
our modified metapopulation SIR model produce a discontinuous final size
distribution. Individuals in the infected stage spread the disease like
individuals in the seriously ill stage and never recover directly, which makes
an effective recovery rate smaller than the given recovery rate.Comment: 6 pages, 3 figure
Modeling Super-spreading Events for Infectious Diseases: Case Study SARS
Super-spreading events for infectious diseases occur when some infected
individuals infect more than the average number of secondary cases. Several
super-spreading individuals have been identified for the 2003 outbreak of
severe acute respiratory syndrome (SARS). We develop a model for
super-spreading events of infectious diseases, which is based on the outbreak
of SARS. Using this model we describe two methods for estimating the parameters
of the model, which we demonstrate with the small-scale SARS outbreak at the
Amoy Gardens, Hong Kong, and the large-scale outbreak in the entire Hong Kong
Special Administrative Region. One method is based on parameters calculated for
the classical susceptible - infected - removed (SIR) disease model. The second
is based on parameter estimates found in the literature. Using the parameters
calculated for the SIR model, our model predicts an outcome similar to that for
the SIR model. On the other hand, using parameter estimates from SARS
literature our model predicts a much more serious epidemic.Comment: 8 pages, 1 figure, 7 table
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