One obvious thing that can be stated as up-front for this field is that this part of bioscience is different from other close to it by mathematics as, for example, at this moment from this one - the Virology Heterogeneous Scaled.
Still, we don't know finally which world is more complicated?
The world of viruses or bacteria?
Anyway, the live tissue, microorganisms, is of more complicated nature than the viruses as we suggest right now (yes, it is the common knowledge, but we need to say some acceptable axioms).
That is when we regarding to a single "creature," single piece of action - a bacterium or a virus. Meanwhile, it's still remain to be proven that the collective behaviour of virus populations and of bacteria are simpler or subordinate one to another? Accepting and assuming this, we move forward.
The characteristic nature of all these microbiological fields is that they are dealing with the multiscaled and multispecies subjects. Those subjects similarly to in vitro subjects in other (physical) sciences are interacting between themselves through their physical fields, one of those is complicated movements and through the chemical interactions.
That is enough to say that because we are interested not only in the knowledge of each bacterium function, but primary interest is about the functioning of the whole bio-system consisting of the host tissue (tissues) as well as the multiple species interacting with this host within the same spatial volume.
The talk is here not about a qualitative medical, biological description of the substances, organisms, and processes - but we are talking about mathematical modeling and simulation of those issues. This, and only this approach will give us the firm understanding of reasons, actions and consequences.
And this is enough for stating some initial mathematical statements and models of behavior of such a medium and of its properties. We would like to use the tools of HSP-VAT for this purpose.
Meanwhile, it is known that there are already have been published many multiphase theories for bio- human tissues to function.
Their deficiencies at this moment as we pointed out in the - “Fundamentals of Hierarchical Scaled Physics (HSP-VAT) Description of Transport and Phenomena in Heterogeneous and Scaled Media,” are of the same origin - they use the Homogeneous GO theorem to derive the field's one scale governing equations. Meaning, that the media are quite mixed, thoroughly mixed - the homogeneous down to subatomic scales. No matter what is said by authors about that media at the same time.
Then we need to remind to ourselves that the solutions of those mathematical models as have been shown for in vitro physical media and fields are quite different from those Homogeneous models.
The same is true for more complicated media and processes in bacteriology with the in vivo components (bio-spieces) embedded into the in vitro substances (often liquid, or of elastic nature on its own scale) or into another in vivo component of the higher spatial scale.
More to come.