MBI Videos
Linda Allen
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Linda AllenHeterogeneity in pathogen transmission is investigated in stochastic multigroup models, with one group representing superspreaders. Superspreaders are characterized as those individuals able to infect a disproportionately high number of susceptible individuals. Recent emerging diseases such as SARS, MERS and Ebola are some examples of outbreaks with superspreading events. We apply continuous-time Markov chains and branching process theory to determine estimates for the probability of a minor or a major epidemic when initiated by a either a superspreader or a non-superspreader. We also examine the time until the outbreak is observed and discuss some applications to emerging and zoonotic infectious diseases.
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Linda AllenIn deterministic epidemic models, pathogen extinction in a population is determined by the magnitude of the basic reproduction number R0. In stochastic epidemic models, the probability of pathogen extinction depends on R0, the size of the population and the number of infectious individuals. For example, in the SIS Markov chain epidemic model, if the basic reproduction number R0>1, the population size is large and I(0)=a is small, then a classic result of Whittle (1955) gives an approximation to the probability of pathogen extinction: (1/R0)a. This classic result can be derived from branching process theory. We apply results from multitype Markov branching process theory to generalize this approximation for probability of pathogen extinction to more complex epidemic models with multiple stages, treatment , or multiple populations and to within host models of virus and cell dynamics.
Work done in collaboration with Yuan Yuan and Glenn Lahodny. -
Linda AllenA brief introduction is presented to modeling in stochastic epidemiology. Several
useful epidemiological concepts such as the basic reproduction number and the nal size
of an epidemic are de ned. Three well-known stochastic modeling formulations are in-
troduced: discrete-time Markov chains, continuous-time Markov chains, and stochastic
di erential equations. Methods for derivation, analysis and numerical simulation of the
three types of stochastic epidemic models are presented. Emphasis is placed on some of
the di erences between the three stochastic modeling formulations as illustrated in the
classic SIS (susceptible-infected-susceptible) and SIR (susceptible-infected-recovered)
epidemic models. In addition, some of the unique properties of stochastic epidemic
models, such as the probability of an outbreak, nal size distribution, critical commu-
nity size, and expected duration of an epidemic are demonstrated in various models of
diseases impacting humans and wildlife. -
Linda AllenRelations between Markov chain models and differential equation models for infectious diseases near the infection-free state are derived. Approximation of the Markov chain model by a multitype branching process leads to an estimate of the probability of disease extinction. We summarize some extinction results for multi-patch, multi-group, and multi-stage models of infectious diseases for epidemics and within-host models. The successful invasion of a pathogen often depends on the conditions of the environment at a specific time and location.
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Linda Allen -
Linda Allen