The model of an immune system reaction against malignant gliomas proposed by Kronik and co-workers is simplified to the main components of the immune reaction, which are tumor cells and cytotoxic T-lymphocytes. The system has nonlinear terms with three delays, but remains tractable. For...

A pandemic threshold theorem of the Kermack-McKendrick epidemic system with individual heterogeneity is proved from the definition of R_{<italic>0</italic>} by Diekmann, Heesterbeek, and Metz. The early Kermack-McKendrick epidemic model is extended to recognize individual heterogeneity, where the state variable...

The bioenergetic phenomena occurring in green plants are described by three equations for biomass, <italic>ATP</italic> level, and the level of inorganic phosphorus. The well-posedness of the problem is proved. Simulations show that the bioenergetic processes are oscillatory with sunlight.

A logistic equation with delay introduced into net growth describes an initial stage of solid tumor growth. Impulses describe external interference, such as radiotherapy. Examination of different treatment protocols showed that the one with constant dosage is better than with increasing or...

In a special case of the general linear mixed model, one random component obeys a spatial autoregressive process and another a temporal autoregressive process. The population and any affiliations to subpopulations may change in time. The empirical best linear unbiased predictor is derived and...

Mark-resighting constitutes an advanced technology for estimating animal abundance. Joint hypergeometric maximum likelihood, Minta-Mangel and Bowden estimators are usually adopted with mark-resighting data. In presence of any tendency of animals to aggregate into groups, the Bowden estimator is...

The knowledge of first-order inclusion probabilities characterizing a sampling scheme is essential in design-based estimation of finite population totals. Sometimes the scheme is so complex that these probabilities cannot be computed exactly. Instead, both inclusion probabilities and...

In the Fay-Herriot model, a prior distribution for the variance component allows posterior moments to be approximated with the Laplace method, avoiding computer intensive Monte Carlo Markov chains. The extremely skewed posterior distribution of the variance component results from the asymmetry...