GENERAL MODEL OF THE INNATE IMMUNE RESPONSE FROM A MECHANICAL ENGINEERING POINT OF VIEW
| Main Authors: | Paul Okpala , Sam Omenyi |
|---|---|
| Format: | Article Journal |
| Terbitan: |
, 2016
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/61111 |
Daftar Isi:
- The continuous fight between bacteria and the phagocytes that belong to the innate immune system has attracted a cross-disciplinary interest. Different authors had developed different models of phagocytosis in the past. This paper extended the mathematical population model of Reed et al (2011) by investigating the dynamic energy flow associated with the neutrophils phagocytosis of bacteria. Reed et al (2011) had studied the stability properties of trivial and nontrivial equilibrium of their population model using the Jacobian matrix. This paper arrived at same conclusion regarding stability by following a different approach that involved expanding the non-linear system in Taylor series and studying the stability properties after the non-linear terms were truncated. Energy equation model of phagocytosis is then derived in this paper to augment the population model of Reed et al (2011). The derivation of the energy equation aims to bridge the gap between biological sciences (immunology) and mechanical engineering. Solution of the energy equation reveals that as time elapses, the graphs for which the engulfment parameter, , is negative gets more negative. This implies progression of phagocytosis. That is to say that more bacteria are being engulfed and more energy released with time (exothermic process). Propensity of engulfment to occur is considered to be higher for more negative final values of energy of engulfment on the real number line.