Dieter Schenzle

Bio: Dieter Schenzle is an academic researcher from University of Tübingen. The author has contributed to research in topics: Metaclazepam & Insulin receptor. The author has an hindex of 8, co-authored 13 publications receiving 763 citations.

An age-structured model of pre- and post-vaccination measles transmission.

Abstract: An infection like measles does not spread uniformly in populations from Europe and North America. Of special importance is a pronounced age-dependency in the contact rates, because of increased infection transmission within schools. Therefore an age-structured epidemiologic model is investigated here, which also pays attention to the fact that children are promoted grade-wise into and out of school. Simulation results are contrasted with pre- and post-vaccination measles data from England and Wales and the model is shown to perform better than previous global mass-action models.

Proportionate mixing models for age-dependent infection transmission.

Abstract: We present explicit formulas for the transmission potential of an immunizing infection where the contact rates and the vaccination rates depend on the chronological age of an individual, and the infectivity and the recovery rate depend on the duration of an infection.

Analysis of a Model for the Pathogenesis of AIDS

Abstract: According to a previously proposed mathematical model, the pathogenesis of acquired immunodeficiency syndrome (AIDS) could be explained by two phenomena: direct human immunodeficiency virus (HIV) infection of CD4+ T-cell populations and ongoing generation and selection of HIV mutants with increasing replicative capacity. In the present paper, the results obtained with this model are described in more detail. For different values of biologically interpretable parameters, the model predicts very different patterns of CD4+ T-cell decline after primary infection. With the assumption of a variability of 10% to 25% of three parameters between infected individuals, the model yields a realistic distribution curve of the incubation period to AIDS.

On the intra-host dynamics of HIV-1 infections.

Abstract: An extension of a previously proposed theory for the pathogenesis of AIDS is presented and analyzed using a mathematical modelling approach. This theory is based on the observation that human immunodeficiency virus type 1 (HIV-1) predominantly infects and replicates in CD4 + -T cells, and that the infection process within an infected individual is characterized by ongoing generation and selection of HIV variants with increasing reproductive capacity. This evolutionary process is considered to be the reason for the gradual loss of immunocompetence and the final destruction of the immune system observed in most patients. The extension presented here incorporates the effect of the permanently increasing susceptibility of CD4 + -T cell clones, as a result of the evolutionary process. The presented model reproduces and possibly explains a wide variety of findings about the HIV infection process. Numerical results indicate that the effect of the initial dose is minimal, and restricted to the primary phase of infection. According to the model predictions the impact of the HIV evolutionary speed is crucial for the progression to disease. An important progression determinant is the initial infection rate, being a component of the viral reproductive capacity. An influential role in disease progression seems to be played by the initial CD4 + -T cell count.

The Mathematics of Infectious Diseases

Abstract: Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\sigma$, and the replacement number $R$ are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of $R_{0}$ and $\sigma$ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.

On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations

Abstract: The expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is mathematically defined as the dominant eigenvalue of a positive linear operator. It is shown that in certain special cases one can easily compute or estimate this eigenvalue. Several examples involving various structuring variables like age, sexual disposition and activity are presented.

On the definition and the computation of the basic reproduction ratio : $R_ 0$ in models for infectious diseases in heterogeneous populations

Abstract: The expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is mathematically defined as the dominant eigenvalue of a positive linear operator. It is shown that in certain special cases one can easily compute or estimate this eigenvalue. Several examples involving various structuring variables like age, sexual disposition and activity are presented.

Mathematical Analysis of HIV-1 Dynamics in Vivo

Abstract: Mathematical models have proven valuable in understanding the dynamics of HIV-1 infection in vivo. By comparing these models to data obtained from patients undergoing antiretroviral drug therapy, it has been possible to determine many quantitative features of the interaction between HIV-1, the virus that causes AIDS, and the cells that are infected by the virus. The most dramatic finding has been that even though AIDS is a disease that occurs on a time scale of about 10 years, there are very rapid dynamical processes that occur on time scales of hours to days, as well as slower processes that occur on time scales of weeks to months. We show how dynamical modeling and parameter estimation techniques have uncovered these important features of HIV pathogenesis and impacted the way in which AIDS patients are treated with potent antiretroviral drugs.

Travelling waves and spatial hierarchies in measles epidemics

Abstract: Spatio-temporal travelling waves are striking manifestations of predator-prey and host-parasite dynamics. However, few systems are well enough documented both to detect repeated waves and to explain their interaction with spatio-temporal variations in population structure and demography. Here, we demonstrate recurrent epidemic travelling waves in an exhaustive spatio-temporal data set for measles in England and Wales. We use wavelet phase analysis, which allows for dynamical non-stationarity--a complication in interpreting spatio-temporal patterns in these and many other ecological time series. In the pre-vaccination era, conspicuous hierarchical waves of infection moved regionally from large cities to small towns; the introduction of measles vaccination restricted but did not eliminate this hierarchical contagion. A mechanistic stochastic model suggests a dynamical explanation for the waves-spread via infective 'sparks' from large 'core' cities to smaller 'satellite' towns. Thus, the spatial hierarchy of host population structure is a prerequisite for these infection waves.