Pete Dayananda

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A simple model is given, based on mass conservation of a non-transformed non-absorbed solute or ion (such as the chloride ion), which allows long term trends in the concentration of this solute to be predicted. The method involves solution of an implicit equation for the long term through-drainage flux below the maximum depth of sampling. A knowledge of the(More)
A model is developed to estimate the duration for which malaria antibody levels in the blood remain high in a closed population. This estimate can be used to calculate the transmission rate within a region, in conjunction with the serological information contained in the population. The model is used on data obtained from a study of malaria in the(More)
Breast cancer patients are often at high risk of fragility fractures partly due to adjuvant endocrine therapy such as aromatase inhibitors and chemotherapy. Baseline dual energy X-ray absorptiometry (DEXA) scanning is recommended as a standard of care in identifying patients who are at risk so they can be commenced on bone protective therapy. NICE guideline(More)
This paper is concerned with the development of a stochastic path of prostate-specific antigen (PSA) level after radiation treatment for prostate cancer. PSA is a biomarker for prostate cancer, higher levels of which indicate the seriousness of the cancer progression. Following the deterministic modeling of the data by the previous authors, Cox et al., this(More)
We introduce a continuous stochastic model for the prostate-specific antigen (PSA) levels following radiotherapy and derive solutions for the associated partial differential (Kolmogorov-Chapman) equation. The solutions describe the evolution of the time-dependent density for PSA levels which take into account an absorbing condition along the boundary and(More)
Traditionally, epidemic processes have focused on establishing systems of differential-difference equations governing the number of individuals at each stage of the epidemic. Except for simple situations such as when transition rates are linear, these equations are notoriously intractable mathematically. In this work, the process is described as a(More)
Stochastic population processes have received a lot of attention over the years. One approach focuses on compartmental modeling. Billard and Dayananda (2012) developed one such multi-stage model for epidemic processes in which the possibility that individuals can die at any stage from non-disease related causes was also included. This extra feature is of(More)
An investigation of the downward transport of a solute following a series of alternating irrigation/rainfall and evapotranspiration events is carried out. The principle of conservation of mass, and the concepts of partition chromatography are used in constructing a simple model which enables the peak solute concentration depth to be calculated at any(More)
This paper investigates the partial differential equation for the evolving distribution of prostate-specific antigen (PSA) levels following radiotherapy. We also present results on the behavior of moments for the evolving distribution of PSA levels and estimate the probability of long-term treatment success and failure related to values of treatment and(More)
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