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H W Hethcote

Publications and source records attributed to H W Hethcote.

28 records · Page 2Linked to original sources
PubMed1981

Stability analysis for models of diseases without immunity.

A cyclic, constant parameter epidemiological model is described for a closed population divided into susceptible, exposed and infectious classes. Distributed delays are introduced and the model is formulated as two coupled Volterra integral equations. The delays do not change the general nature of thresholds or asymptotic stability; in all cases considered the disease either dies out, or approaches an endemic steady state.

Bacterial Infections↗
PubMed1980

Integral equation models for endemic infectious diseases.

Endemic infectious diseases for which infection confers permanent immunity are described by a system of nonlinear Volterra integral equations of convolution type. These constant-parameter models include vital dynamics (birth and deaths), immunization and distributed infectious period. The models are shown to be well posed, the threshold criteria are determined and the asymptotic behavior is analysed. It is concluded that distributed delays do not change the thresholds and the asymptotic behaviors of the models.

Communicable Diseases↗
PubMed1978

Model for the incidence of embryonal cancers: application to retinoblastoma.

The two-mutation theory of cancer initiation hypothesizes that some cancers originate after two successive mutations, of which the second mutation is always somatic and the first mutation may be germinal (hereditary cases) or somatic (nonhereditary cases). A quantitative model using the Poisson distribution is developed for ages at diagnosis for hereditary and nonhereditary cases. This model relates age-specific incidence data explicitly to the number of divisions of embryonal cells and to rates of somatic mutations per cell division. A good fit is obtained when the model is applied to data on ages at diagnosis for one such embryonal tumor, retinoblastoma.

Age Factors↗
PubMed1975

Mutation and childhood cancer: a probabilistic model for the incidence of retinoblastoma.

The incidences of some childhood cancers have been shown to fit a two-mutation hypothesis for cancer initiation. According to this hypothesis, the first mutation can be either germinal or somatic while the second is always somatic. A probabilistic model involving the mean number of tumors per genetically susceptible individual is developed as a function of age and is compared with age incidence data for retinoblastoma. The change in the mean number of tumors with time is interpreted in terms of the growth of retinal cells. In patients who are not genetically susceptible, the times of occurrence of the first and second somatic mutations can be inferred from a comparison of familial and non-familial unilateral case incidences. The total incidences of hereditary and nonhereditary forms of retinoblastoma are related to germinal and somatic mutation rates. The even distribution of certain childhood cancers throughout the world suggests that their incidences are determined by spontaneous mutation rates rather than by local environmental mutagenic carcinogens.

Child↗
PubMedDate not supplied

Four SEI endemic models with periodicity and separatrices.

Periodic solutions have been found for some infectious disease models of the SI and SEI types. Here four SEI models with either disease-reduced or uniform reproduction are examined to determine the model features that do and do not lead to periodic solutions. The two SEI models with the simple mass action incidence beta XY can have periodic solutions for some parameter values, but the two SEI models with the standard mass action incidence lambda XY/N do not have periodic solutions. For some intermediate values of lambda in the SEI model with incidence lambda XY/N and uniform reproduction, the interior equilibrium is a saddle whose stable manifold separates the attractive regions for the disease-free equilibrium and the susceptible-free equilibrium.

Communicable Diseases↗
PubMedDate not supplied

Dynamics and control of the transmission of gonorrhea.

Calculations revealed that approximately a third of the reported cases of gonorrhea in women during 1973-1975 were discoveries of the screening program. Theoretical models and epidemiologic data showed that the prevalence of gonorrhea adjusts rapidly to changes in social behavior, medical treatment, and control programs, that prevalence oscillates seasonally around an equilibrium state determined by the current social and medical conditions, and that this equilibrium moves as epidemiologic conditions change. The incidence of gonorrhea is theoretically limited by saturation in a sexually active core population, and this core causes gonorrhea to remain endemic.

Female↗