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This monograph has the ambitious aim of developing a mathematical
theory of complex biological systems with special attention to the
phenomena of ageing, degeneration and repair of biological tissues
under individual self-repair actions that may have good potential
in medical therapy. The approach to mathematically modeling
biological systems needs to tackle the additional difficulties
generated by the peculiarities of living matter. These include the
lack of invariance principles, abilities to express strategies for
individual fitness, heterogeneous behaviors, competition up to
proliferative and/or destructive actions, mutations, learning
ability, evolution and many others. Applied mathematicians in the
field of living systems, especially biological systems, will
appreciate the special class of integro-differential equations
offered here for modeling at the molecular, cellular and tissue
scales. A unique perspective is also presented with a number of
case studies in biological modeling.
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