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Epidemic Models (epidemic + models)

Distribution by Scientific Domains
Life Sciences75%

Selected Abstracts

POPULATION EXTINCTION IN DETERMINISTICAND STOCHASTIC DISCRETE-TIME EPIDEMIC MODELS WITH PERIODIC COEFFICIENTS WITH APPLICATIONS TO AMPHIBIAN POPULATIONS

NATURAL RESOURCE MODELING, Issue 2 2006
KEITH E. EMMERT
ABSTRACT. Discrete-time deterministic and stochastic epidemic models are formulated for the spread of disease in a structured host population. The models have applications to a fungal pathogen affecting amphibian populations. The host population is structured according to two developmental stages, juveniles and adults. The juvenile stage is a post-metamorphic, nonreproductive stage, whereas the adult stage is reproductive. Each developmental stage is further subdivided according to disease status, either susceptible or infected. There is no recovery from disease. Each year is divided into a fixed number of periods, the first period represents a time of births and the remaining time periods there are no births, only survival within a stage, transition to another stage or transmission of infection. Conditions are derived for population extinction and for local stability of the disease-free equilibrium and the endemic equilibrium. It is shown that high transmission rates can destabilize the disease-free equilibrium and low survival probabilities can lead to population extinction. Numerical simulations illustrate the dynamics of the deterministic and stochastic models. [source]

Time series modelling of childhood diseases: a dynamical systems approach

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 2 2000
B. F. Finkenstädt
A key issue in the dynamical modelling of epidemics is the synthesis of complex mathematical models and data by means of time series analysis. We report such an approach, focusing on the particularly well-documented case of measles. We propose the use of a discrete time epidemic model comprising the infected and susceptible class as state variables. The model uses a discrete time version of the susceptible,exposed,infected,recovered type epidemic models, which can be fitted to observed disease incidence time series. We describe a method for reconstructing the dynamics of the susceptible class, which is an unobserved state variable of the dynamical system. The model provides a remarkable fit to the data on case reports of measles in England and Wales from 1944 to 1964. Morever, its systematic part explains the well-documented predominant biennial cyclic pattern. We study the dynamic behaviour of the time series model and show that episodes of annual cyclicity, which have not previously been explained quantitatively, arise as a response to a quicker replenishment of the susceptible class during the baby boom, around 1947. [source]

POPULATION EXTINCTION IN DETERMINISTICAND STOCHASTIC DISCRETE-TIME EPIDEMIC MODELS WITH PERIODIC COEFFICIENTS WITH APPLICATIONS TO AMPHIBIAN POPULATIONS

NATURAL RESOURCE MODELING, Issue 2 2006
KEITH E. EMMERT
ABSTRACT. Discrete-time deterministic and stochastic epidemic models are formulated for the spread of disease in a structured host population. The models have applications to a fungal pathogen affecting amphibian populations. The host population is structured according to two developmental stages, juveniles and adults. The juvenile stage is a post-metamorphic, nonreproductive stage, whereas the adult stage is reproductive. Each developmental stage is further subdivided according to disease status, either susceptible or infected. There is no recovery from disease. Each year is divided into a fixed number of periods, the first period represents a time of births and the remaining time periods there are no births, only survival within a stage, transition to another stage or transmission of infection. Conditions are derived for population extinction and for local stability of the disease-free equilibrium and the endemic equilibrium. It is shown that high transmission rates can destabilize the disease-free equilibrium and low survival probabilities can lead to population extinction. Numerical simulations illustrate the dynamics of the deterministic and stochastic models. [source]

The effects of habitat destruction in finite landscapes: a chain-binomial metapopulation model

OIKOS, Issue 2 2001
Mark F. Hill
We present a stochastic model for metapopulations in landscapes with a finite but arbitrary number of patches. The model, similar in form to the chain-binomial epidemic models, is an absorbing Markov chain that describes changes in the number of occupied patches as a sequence of binomial probabilities. It predicts the quasi-equilibrium distribution of occupied patches, the expected extinction time ( ), and the probability of persistence ( ) to time x as a function of the number N of patches in the landscape and the number S of those patches that are suitable for the population. For a given value of N, the model shows that: (1) and are highly sensitive to changes in S and (2) there is a threshold value of S at which declines abruptly from extremely large to very small values. We also describe a statistical method for estimating model parameters from time series data in order to evaluate metapopulation viability in real landscapes. An example is presented using published data on the Glanville fritillary butterfly, Meltiaea cinxia, and its specialist parasitoid Cotesia melitaearum. We calculate the expected extinction time of M. cinxia as a function of the frequency of parasite outbreaks, and are able to predict the minimum number of years between outbreaks required to ensure long-term persistence of M. cinxia. The chain-binomial model provides a simple but powerful method for assessing the effects of human and natural disturbances on extinction times and persistence probabilities in finite landscapes. [source]