By Abdelghani Bellouquid
This booklet describes the evolution of a number of socio-biological structures utilizing mathematical kinetic conception. in particular, it bargains with modeling and simulations of organic systems—comprised of huge populations of interacting cells—whose dynamics persist with the foundations of mechanics in addition to ideas ruled through their very own skill to prepare circulate and organic features. The authors suggest a brand new organic version for the research of pageant among cells of an competitive host and cells of a corresponding immune system.
Because the microscopic description of a organic method is way extra advanced than that of a actual method of inert subject, a better point of research is required to house such complexity. Mathematical types utilizing kinetic idea may well signify the way to care for such complexity, taking into consideration an figuring out of phenomena of nonequilibrium statistical mechanics now not defined through the conventional macroscopic method. The proposed types are on the topic of the generalized Boltzmann equation and describe the inhabitants dynamics of numerous interacting parts (kinetic inhabitants models).
The specific types proposed via the authors are according to a framework on the topic of a approach of integro-differential equations, defining the evolution of the distribution functionality over the microscopic country of every point in a given approach. Macroscopic details at the habit of the method is bought from appropriate moments of the distribution functionality over the microscopic states of the weather concerned. The booklet follows a classical learn procedure utilized to modeling actual structures, linking the commentary of organic phenomena, number of experimental information, modeling, and computational simulations to validate the proposed types. Qualitative research innovations are used to spot the prediction skill of particular models.
The ebook could be a helpful source for utilized mathematicians in addition to researchers within the box of organic sciences. it can be used for complex graduate classes and seminars in organic structures modeling with purposes to collective social habit, immunology, and epidemiology.
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Extra info for Mathematical Modeling of Complex Biological Systems: A Kinetic Theory Approach (Modeling and Simulation in Science, Engineering and Technology)
5) j=1 where ck is the size of the clusters, has been extensively used to analyze a number of problems in population dynamics. The above examples can be regarded as simple particularizations, while those dealt with in the chapters which follow aim at dealing with relatively more complex phenomena. The various examples shown above describe systems in the spatially homogeneous case. 7. Critical Analysis 31 space-dependent phenomena can be dealt with by appropriate techniques, as documented in the book by Arlotti, et al.
A - Macrophage exposing fragments c - T-helper activates B-cell d - B-cell differentiates into Plasma cells b - T-helper is activated e - Plasma cells release antibodies Fig. 5. Humoral immune response. The activated lymphocytes are long-term survivors, thus retaining a “memory” of the infection and allowing a fast response in the case of repetition of the infection, while the innate response lacks of this kind of immunologic memory. Innate and acquired responses work together against the infection; in both cases the defense starts from the recognition of the pathogen agents.
2 Phenomenological Description The immune system, in multicellular organisms, is an organ system that acts as a defense against foreign pathogens (viruses, bacteria, parasites) as well as against internal cellular disorder. 2. Phenomenological Description Lymphoid stem cell B cell B progenitor Thymus T cell T progenitor Dendritic cell Pluripotent stem cell Bone marrow stromal cell Monocyte Macrophage Monocyte progenitor Neutrophil Myeloid stem cell Basophil prog. Mast cell Basophil Eosinophil Eosinophil progenitor Platelets Megakaryocyte Erythrocyte Erythrocyte progenitor Fig.