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A mathematical model for the quantitative analysis of the interaction between cancer cells and cell-mediated immune system with two discrete-time delays, considering the role of antibodies, is studied in this paper. The model is analyzed both analytically and numerically to understand the dynamics of interaction delay and proliferation enhancement effect delay in the eradication of cancer. Hopf bifurcation occurs when one-time delay crosses the critical value in the absence of the other. It is also observed that as we increase any of the delays, it will increase the cancer burden. The analysis shows that a cancer-free state cannot be obtained solely by the killing rate of cytotoxic T-lymphocytes, but humoral response in combination with cell-mediated immune responses plays an important role to eradicate cancer. [ABSTRACT FROM AUTHOR]

In this paper we show how an Artificial Immune System can be used to study pattern recognition processes and learning. In particular we show the ability of the model to discover and maintain coverage of the diverse patterns through mechanism of evolution and mutation. [ABSTRACT FROM AUTHOR]

In this work, we analyse the dynamics of a five-dimensional hepatitis C virus infection mathematical model including the spatial mobility of hepatitis C virus particles, the transmission of hepatitis C virus infection by mitosis process of infected hepatocytes with logistic growth, time delays, antibody response and cytotoxic T lymphocyte (CTL) immune response with general incidence functions for both modes of infection transmission, namely virus-to-cell as well as cell-to-cell. Firstly, we prove rigorously the existence, the uniqueness, the positivity and the boundedness of the solution of the initial value and boundary problem associated with the new constructed model. Secondly, we found that the basic reproductive number is the sum of the basic reproduction number determined by cell-free virus infection, determined by cell-to-cell infection and determined by proliferation of infected cells. It is proved the existence of five spatially homogeneous equilibria known as infection-free, immune-free, antibody response, CTL response and antibody and CTL responses. By using the linearization methods, the local stability of the latter is established under some rigorous conditions. Finally, we proved the existence of periodic solutions by highlighting the occurrence of a Hopf bifurcation for a certain threshold value of one delay. [ABSTRACT FROM AUTHOR]

A computational model of the dynamics of diversity among T-cell receptors and MHC: peptide complex molecules is presented. We propose a method by which individual immune systems may evolve effcient or ineffcient states as a result of T-cell receptor crossreactivity as well as genetic variation among pathogens. By combining shape space and physical space models, valuable insight is obtained into how immune system-wide state is, in large part, determined by localised space dynamics. In the model, system-wide state also informs local dynamics, especially in the lymphatic system during primary immune response. The process by which similar initial infection conditions across individuals may result in highly variable end states (a phenomenon observed in the clinical context) is modelled. Our results show that activity alone is not a good indicator of infection suppression or removal. In this work, we postulate that successful viral clearance is characterised by broad T-cell receptor activation (in shape space), and results in low average concentration levels of activated cytotoxic lymphocyte cells. [ABSTRACT FROM AUTHOR]