 1997 International Conference on Mathematical Models in Medical & Health Sciences
Announcement page
Other sessions on Epidemic Models: |
Wednesday afternoon, May 28 Special Session on Epidemic Models Organizer: William Fitzgibbon (University of Houston) Index for this page:
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2:45-3:15 Mi-Young Kim
Department of Mathematics
University of Wyoming
mikim@tamdhu.uwyo.edu
Splitting methods for age-structured population dynamics and epidemiology
Operator splitting methods for nonlinear models arising from
population dynamics and epidemiology are described and analyzed. A backward
finite differencing along the characteristic is used in the
approximations. It is shown that the schemes are convergent at
first-order rate in the maximum norm. The stabilities of the methods are
discussed. Several numerical examples are presented.
3:15-3:45 Michael Y. Li
Department of Mathematics and Statistics
Mississippi State University
The Role of Incubation Period: A New Approach in Compartmental Epidemic
Models
Authors: John R. Graef, Michael Y. Li, and Liancheng Wang
The role of incubation period is studied in an SEIR epidemic model. The incidence is of standard form and the disease is assumed to cause death in the infectious fraction so that the total population may vary in time. The key assumption in our study is that the host population has a small intrinsic growth rate compared to the rate of disease caused death. It is shown that a disease with no incubation period always dies out while a disease with a long incubation period can become endemic.
3:45-4:15 Aino K. Takala
National Public Health Institute
Department of Vaccines
Helsinki, Finland
INFEMAT- development of mathematical models for Haemophilus influenzae
type b (Hib) infection, preventive strategies and vaccination programs
Authors: Tapio Takala (Helsinki University of Technology, Espoo, Finland),
Kari Auranen (University of Helsinki, Helsinki, Finland),
Martin Eichner (University of Tubingen, Germany),
Elja Arjas (University of Helsinki, Helsinki, Finland),
Aino K.Takala (National Public Health Institute, Finland)
Before effective vaccinations were available Hib was the single most important bacterium causing life-threatening infections (e.g. meningitis and pneumonia) in children in industrial countries. Studies from the past two decades have lead to a considerable amount of knowledge on Hib bacteria, risk factors for disease and its spread, immunity and vaccination. Hib bacterium is a strictly human pathogen that is carried and spread by (asymptomatic) pharyngeal carriers. Carriage is most frequent among young children (up to 5%) and carriers cluster in families and day-care groups. The carrier state can occasionally proceed to serious infection (1/ 400 of carriers who have an insufficient level of Hib antibodies at start of carriage). By school-age children have developed natural immunity (serum antibodies) against serious Hib diseases, but this immunity does not prevent re-carriage. The new Hib conjugate vaccines were found to be highly effective against serious Hib diseases; these have practically disappeared from Finland. Hib conjugate vaccine was also shown to prevent carriage. Thus, these vaccines may dramatically interfere with natural transmission of Hib bacteria. These results have led to the need to model the effect of large scale vaccinations. Our main approach in modelling Hib disease is an individual-based state-transition model where each individual is in one of the states S, I or R (S=susceptible for infection, I=infective carrier, R= temporarily resistant to infection). We model the spread of infection via contacts appearing in different groups (family, day-care and school). The transition intensities (S-I, I-R or R-S) depend on age and contact groups of the individual. They are estimated from empirical data using Bayes estimation and include information on incidence and duration of Hib carriage and development and decay of Hib antibodies in serum. For simulation we have created a population dynamics model based on demographic data from Finland (birth rate, life expectancy, data on marriage and divorce, family size and structure, day-care attendance, schools, etc.). On this population model we have superimposed the Hib infection dynamics as an S-I-R-S model. For each time step of simulation (1 day) the force of infection to which an individual is exposed is summed up for the different contact groups and the transition probability S-I is calculated. The transition intensities I-R and R-S are estimated based on the individual's age and Hib serum antibody level.Thus far populations in the order of 100,000 have been simulated with promising preliminary results. The main questions currently under study are 1) more accurate estimation of Hib infection parameters based on (sparse) empirical data, 2) refinement of the contact intensity matrix between age groups by matching modelling results to empirical data 3) evaluation of Hib conjugate vaccine effects using the simulation model. The next aim is to evaluate different vaccination strategies in Finland and other populations.
4:15-4:45 Christelle Suppo
University of Bordeaux2.
Dynamics of Two Retroviruses within a Population of Cats
Co-authors : Franck Courchamp, Emmanuelle Fromont, Catherine Bouloux
We present a deterministic model of the dynamics of two microparasites simultaneously infecting a single host population. Both microparasites are feline retroviruses, namely Feline Immunodificiency Virus (FIV) anf Feline Leukemia Virus (FeLV). The host is the domestic cat (Felis Catus). The model has been tested with data generated by a long term study of several natural cat populations. Stability analysis and simulations show that, once introduced in a population, FIV spreads and is maintained, while FeLV can either disappearor persists. Moreover, introduction of both viruses into the population induces an equilibrium state for individuals of each different pathological class. The viruses never induce the extinction of the population. Furthermore, whatever the outcome for the host population (persistence of FIV only, or both viruses), the global population size at the equilibrium state is only slightly lower than it would have been in the absence of the infections (i.e. at the carrying capacity), indicating a low impact of the viruses on the population. Finally, the impact of the diseases examined simultaneously is higher than the sum of the impact of the two diseases examined separately. This seems to be due to a higher mortality rate when both viruses infect a single individual.
Bibliography: Courchamp F., Suppo Ch., Fromont E., Bouloux C., 1997. Population Dynamics of two Feline retroviruses (FIV and FeLV) within one Population of Cats, Proceedings of Royal Society of London, to appear.
4:45-5:15 Beverly Mellen
Department of Biostatistics
School of Medicine
Vanderbilt University
Methods for Measuring Statistical Evidence with Application to Suspected
Nosocomial Spread of Disease
In science, we value the use of objective methods for evaluating data as evidence in relation to our hypotheses. Such methods can be developed in statistics using a framework that takes likelihood functions as representations of evidence. In this framework, likelihood ratios measure the strength of statistical evidence in favor of one hypothesis vis-a-vis another, while probabilities of obtaining weak and strong evidence (ratios close to and far from unity, respectively) measure stochastic properties of the processes that produce evidence. As in the rest of statistics, probability models play a central role. Since our models only imperfectly represent real phenomena, what risks are there for misinterpreting data? This question is explored in the context of the above methods with an example from hospital-based infectious diseases.