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The elevation of Canuc above Cabas was hypothesized to be a saturating function of the total synaptic activity.
It is likely to work similarly and give rise to RPS mediated coexistence if only one basic requirement is met with, that is the intra-group fitness advantage needs to be a saturating function.
Since the virus released from one infected cell cannot reach all susceptible tumor cells in the population, the infection rate must be a saturating function of the number of susceptible tumor cells.
Another obvious extension involves introducing VEGF explicitly into the model, allowing the rate of EC proliferation to be a saturating function of the VEGF concentration.
In particular, we take the rate of occlusion to be a saturating function of Michaelis-Menten type of p/v, the ratio of tumour cells per vessel surface area so that the rate of vessel occlusion is given by where the constant K δ denotes the value of p/ v at which the rate of occlusion attains its half-maximal value, δ/2.
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The predator response expands at a rate (frac{cxy}{1+omega x}), which is a saturating function of the amount of pest present.
Secondly, we followed Boenhoeffer et al. [ 15] and assumed a case where spore production is a saturating function of virulence.
This nonlinearity follows from assuming that fitness is a saturating function of common cellular resources, and that these resources are sequestered in proportion to the enzyme concentration.
According to our model, this assumption can significantly change the basic properties of virus dynamics, especially if the infection term is a saturating function of the number of target cells.
The rate of virus infection is a saturating function of the number of target cells, and the number of cells at which this saturation occurs is determined by the parameter ϵ.
Since we expect that the rate at which the tumour population increases by cell division is a saturating function of oxygen [ 21], we assume that the proliferation rate is of Michaelis-Menten type (see e.g. [ 20]), given by where β is the maximum proliferation rate per unit of cell density and s β is the level of oxygen at which the proliferation rate is half-maximal.
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