A nonlinear model is developed for an epidemic with contact tracing, and its dynamic is studied. A linear version of the model is presented in both deterministic and stochastic versions. We present the data for the cuban HIV/AIDS epidemic and fit the linear model to the data, we obtain estimates for the size of the Cuban HIV epidemic.

H. De Arazoza

R. Lounes

T. Hoang

Y. Interian

Modeling HIV Epidemic under Contact Tracing — The Cuban Case

The aim of this work is to analyse the proliferation of tumour cells in the treatment gapduring the radiotherapy for head neck cancer.Material and Methods: The clinical material is based on records of head and neck patients treated by radiotherapyalone in our institution. The effect of radiotherapy was assumed to be described by a linearquadratic model. The patient data were fitted directly to the radiobiological model and theparameters were estimated using maximum-likelihood procedures.Results: According to our model results of treatment were significantly correlated with Normalised Total Dose of radiation, the tumour progression (according to TNM), the overall treatment time and the gap duration. The laryngeal cancers had better prognosis then cancers of oroand nasopharynx. When the treatment time is prolonged without treatment interruptions 0.36 Gylday is lost due to the repopulation of tumour cells. During the treatment gap proliferation is faster and 0.67 Gylday is lost.Conclusion: Proliferation of tumour cells is faster during the treatment gap then during the days with irradiation.

Rafal Tarnawski

Krzysztof Skladowski

Andrzej Swienrniak

Andrzej Wygoda

Anna Mucha

Repopulation of Tumour Cells during Radiotherapy Is Doubled during Treatment Gaps

The problern of regulation of the proliferation-differentiation processes is analysed in the framework of the model of unipotential cell clone dynamics, assuming two alternative ways (scenarios) of an every new-born cell development, which in the long run define correspondingly the proliferating or differentiated cell status. The scenario choice is then supposed to be a random event influenced by both the inherent mitotic activity of the cell and the differentiation factors &#8212; special messengers synthesized by the differentiated cells. Differentiation factors being accepted by every-new born cell can change the way of cell development. Taking into account the clonal heterogeneity it was shown that such mechanism of the regulation of proliferation-differentiation processes can result in the selection of actively proliferating and insensitive with respect to differentiation factors action cells (that is to say, the cells with cancer phenotype). In the framework of investigation the cells with cancer phenotype (which is heritable within the variability of mother-daughter correlations)appears through the series of the permanent nonmutational changes in the proliferating cells by autoselection mechanism retaining for the division and generation of the progeny only that actively proliferating cells which are less sensitive with respect to the action of the differentiation factors. The progression of normal cell clone towards the appearance and increase of the number of the cells with cancer phenotype can be considered as a possible mechanism of carcinogenesis which is alternative to the clonal selection theory of cancer origin.

Galina I. Solyanik

Alexander A. Serikov

Autoselection Phenomenon in the Normal Cell Clone Undergoing Differentiation: From Cell Population Heterogeneity to Cancer Phenotype via Nonmutational Changes

Several AIDS cohort studies observe that the incubation period between HIV infection and AIDS onset can be shorter than 3 years in about 10% seropositive individuals, or longer than 10 years in about 10-15% individuals. On the other hand, many individuals remain seronegative even after multiple exposures to HIV. These distinct outcomes have recently been correlated with some mutant genes in HIV co-receptors (e.g., CCR5,CCR2 and CXCR4). For instance, the mutant alleles △32 and m303 of CCR5 may provide full protection against HIV infection in homozygotes and partial protection in heterozygotes; moreover, infected heterozygotes may progress more slowly than individuals who have no mutant alleles. Frequencies of these mutant alleles are not very low in Caucasian populations, therefore, their effects may not be insignificant. Based on available data, we propose a one-sex model with susceptibles classified as having no, partial or full natural resistance to HIV infection, and infecteds classified as rapid, normal or slow progressors. Our goals are to investigate the impact of such heterogeneity on the spread of HIV and to identify key parameters. The basic reproductive number R0 is derived from a simplified model. The relative contributions to R0 from the three groups of infecteds are investigated. We present a rough estimating procedure making use of limited data to estimate some new parameters specific to our model. Finally the rough estimating procedure is applied to an example focusing on CCR5-△32 in San Francisco gay men. The relative contributions to R0 among the three infected groups are compared using two different classifying criteria for infecteds. Under given assumptions, we conclude that, without any intervention, HIV infection will continue to spread in this population and the epidemic is mainly driven by the normal progressors. The transmission rates from infecteds are identified as key parameters.

Shu-Fang Hsu Schmtiz

A Mathematical Model of HIV Transmission in Homosexuals with Genetic Heterogeneity

New logical and statistical methods are used for the analysis of relationships between survivance and immunological variables. These methods are based on the search of the regularities (syndromes) in the multidimensional space. The syndromes are the elements of partitions of allowable areas of variables. To estimate the statistical validity of found regularities the new technique based on Monte-Carlo computer simulation was used.We present some results from immunological research to illustrate the methods of logistical regularities search. Two tasks are described. The broad panel of monoclonal antibodies for differentiation lymphocytic antigens were used for lymphocytes subpopulations analysis. The purpose of the first task was the evaluation of significance of immunological parameters for prediction of 1-year metastasis-free survival in non-metastatic osteosarcoma of extremities. The second task was the construction of the predicting alghorithm for prognosis 2-years survival of patients with stomach cancer. The optimal sets of parameters for prediction of survivance was found for both tasks. We found out the high forecasting informativity of HLA-DR+ cells percentage in the 1st task, and the percentage of adhesion cells (CD50+-lymphocytes) in the 2nd task. Multivariate forecasting alghorithms are developed.

A. V. Kunznetsova

O. V. Sen'ko

G. N. Matchak

V. V. Vakhotsky

T. N. Zabotina

O. V. Korotkova

The Prognosis of Survivance in Solid Tumor Patients Based on Optimal Partitions of Immunological Parameters Ranges

Development in molecular biology have resulted in very significant increase in the volume of data available to scientists. Handling and modelling there data requires electronic tools, for which world-wide access via the internet is essential. This paper summarises contributions on this area to a summer school organiser in magdeling in September 1999.

Ralf Hofest&#xe4;dt

Summer School Bioinformatics &#8212; Information Systems and Network Analysis of Gene Regulation and Metabolism

The proliferation of eukaryotic cells is driven by a process called the cell cycle. Proper regulation of this process, leading to orderly execution of sequential steps within the cycle, ensures normal development and homeostasis of the organism. On the other hand, perturbations of the cell cycle are frequently attributed to cancer cells. Mechanisms that ensure the order and fidelity of events in the cell cycle are called checkpoints. The checkpoints induced by damaged DNA delay the cell cycle progression, providing more time for repair of lesion before DNA replication and segregation. The DNA damage-induced checkpoints can be recognized as signal transduction pathways that communicate information between DNA lesion and components of the cell cycle. Proteins involved in the cell cycle, as well as components of the signal transduction pathways communicating with the cell cycle, are frequently products of oncogenes and tumor suppressor genes. Malfunction of these genes plays a critical role in the development of human cancers. The key component in the checkpoint machinery is tumor suppressor gene p53, involved in either regulation of the cell cycle progression (e.g. Gl arrest of cells treated with DNA damaging factor) or activation of programmed cell death (apoptosis). It is postulated that p53 protein is activated by DNA damage detectors. One of the candidates for this role is DNA-dependent protein kinase (DNA-PK) which recognizes DNA strand breaks and phosphorylates p53 protein.

Piotr Widlak

The DNA Damage-Induced Cell Cycle Checkpoints

Model of HIV pathogenesis in HIV-infected individuals under very general conditions. In this model, we have considered five different types of CD4(+) T cells, two different types of HIV (M-tropic versus T-tropic) as well as infected and un-infected macrophage. This is a 9-dimensional stochastic process. For this process, we have developed stochastic differential equations for different types of cells. By using these stochastic equations, we have generated some Monte Carlo data to study the stochastic behavior of the HIV pathogenesis and the HIV progression.Through Monte Carlo studies, we have revealed an acute infection stage in the early stage of the HIV infection and have confirmed the basic role played by lymph nodes and some long-lived cells such as macrophage in serving as reservoirs of HIV to escape elimination by the immune system during the long asymptomatic stage of HIV infection. The Monte Carlo results have shown that the HIV heterogeneity and diversity may be a major factor to determine the time period since infection for uninfected T cells to drop to below 200/mm3 of blood. The numerical results have also confirmed our previous findings (see [1]) which concluded that the probability distributions of T cells and free HIV can be classified into three periods over time: The latent period, the transition period and the pseudo-steady period.

Wai-Yuan Tan

Zhengzheng Ye

Assessing Effects of HIV Heterogeneity and Macrophage on the HIV Pathogenesis in HIV-Infected Individuals

The Gompertz function was formulated to represent an actuarial curve, yet it often fits growth of organisms, organs and tumors. Despite numerous attempts, no consensus has been forged about the biological foundation of the broad applicability of the model. Here we revisit the Gompertzian notion of the “power to grow” and equate it with growth fraction. Aside from conferring biological interpretability to the model, this approach allows leading to the possibility of exploring the behavior of Gompertzian growth with fractal kinetics. Significantly, we found that empirical models such as the logistic model, the von Bertalanffy model and the von Bertalanffy Richards model, together with the originative Gompertz model, are special cases of Gampertzian growth in fractal space. This finding permits an analysis of the growth kinetics of tumors which might affect model based design of Chemotherapy protocols.

Željko Bajzer

Stanimir Vuk-Pavlovic

New Dimensions in Gompertzian Growth

B. D. Sleeman

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