## 5 Discussion  
The proposed model presents a situation in which a healthy cell or organism (where the homeostatic balance equation is kept) can enter the carcinogenesis phase (the homeostatic balance equation is disturbed) because of the external disturbance of the system. However, contrary to the assumption adopted so far, in, for example, radiological protection, the dose-effect curve (here represented by the \(\left[\varepsilon\right]\) parameters) is not the only factor affecting the individual cancer risk. Moreover, the presented model (in particular the damping factor, see Figure 6) shows that the risk resulting from the dose-effect curve can be effectively mitigated or, on the contrary, strengthened due to additional parameters that may be responsible for the state of the immune system of a given organism (e.g., damping factors \(\left\{\mu\right\}\), or, in a more general approach, damping functions, \(\left\{\mu(x_{1},x_{2},\ldots)\right\}\). Of course, the proposed model is quite a general one, and can be applied for different mechanisms connected with carcinogenesis processes. For example, there are three types of biological mechanisms, which can be modeled in the proposed way: the first is a damage-repair competition, the second is a mutated cell irreversible cancer (neoplastic) transformation and the third is a cancer cell multiplication/immunological cage competition [4]. In those three cases, we have some factors which act in one direction (e.g., detrimental), and some factors which act in the opposite way (e.g., beneficial). The most important thing which can be delivered from the presented model is the fact that every living organism has a different level of equilibrium where all negative and positive factors are equal. This is what is called here a balance. Any strong disturbance of that balance can make irreversible changes in the system. So, there is no one application of the model; this depends on what exactly one would like to simulate. Here, a general tool was proposed, but this can be used in many different situations and conditions. A living organism is a physical, complex system which is very hard to model, even for one interacting factor. Indeed, Lotka-Volterra equations are relatively trivial ones and, therefore, are probably too simplified. This was pretty well discussed in the mentioned case of tumor-immune system interactions [4], where the practical case of cancer-immune system interactions is described. In this case, the Lotka-Volterra (predator-prey) equations are too simplified to model the reality, and only some general-level mechanisms can be described by that approach. Anyway, in this paper, the proposed model, which is based on the complex system physics, is able to show major processes in an irradiated cell/organism, like an adaptive response causing homeostasis (system equilibrium), a damping process which drives balance between detrimental and beneficial factors and, finally, a cliff-like effect where the dose is too high and the damping process breaks. This last situation can describe some irreversible change within the cell/organism, like stable mutation, cancer transformation or even death. Indeed, this \"cliff effect\" is analogous to the cancer transformation which can be described by the purely physical equations of phase transition [18,24]. Also, the breaking of the anticancer immune cage can be treated as a \"cliff-like effect\" process as well. Of course, each model, even the most complicated one, is just a simplification of reality. Therefore, one can always model/simulate something in a more detailed way to find a better approximation than the proposed model. The Lotka-Volterra equations are rather simple. However, they are an example of nonlinear dynamics which, in fact, can describe some relationships on some general conceptual level. This means that those equations can properly simulate processes which are averaged over the population of interacting agents.