Later on, we will extend this simple model to more realistic cases with multiple cell types and with multiple compartments, where multiple point mutations can successively accrue to confer resistance to exceedingly high drug concentrations [54].

Let us now specifically incorporate into the simple model a Hill function that describes concentration-dependent killing efficacy of drugs (see Materials & Methods).

We also extend the simple model to more general cases with multiple cell types and with multiple compartments (see detailed mathematical description in 81 Text).

The pre-PCV7 proportion of VT carriage and IPD are the main determinants for the impact of PCV7 on childhood IPD and can be combined in a simple model to provide predictions of the vaccine preventable burden of IPD.

We find that differences in reported disease impact among mature PCV programmes are likely to be unrelated to the differences in the vaccine programme but can be predicted from a simple model based on pre-vaccination epidemiology, in particular the proportion of vaccine serotypes detected among patients With invasive pneumococcal disease and the proportion of vaccine serotypes that are found in the nasopharynX of healthy individuals.

With a growing body of evidence on the impact of different PCV formulation and from low income countries further validation Will be essential to determine the full potential of this simple model .

To understand the biophysical mechanisms and consequences of a voltage-dependent membrane resistance over a large region of subthreshold voltage, we started by studying the effects of fluctuation-based modulation of input-output behavior in a simplified model of spike generation in the form of an exponential leaky integrate-and-fire (eLIF) model [27].

Additionally, the extent and mechanisms of input-output modulation through fluctuations have been explored largely in simplified models of spike generation, and with limited consideration for the role of nonlinear and voltage-dependent membrane properties.

In simple models , realistic spike generation dynamics have been shown to reduce the likelihood of spike response to rapid voltage fluctuations [27,36].

Thus, this simple model indicates that with a high density of target cells, cytokine receptor expression controls the amount of paracrine cytokine signal.

However, the simple models studied above cannot answer the question if effective paracrine signals are possible despite the low bulk cytokine concentrations.

To account for polarized secretion at the immunological synapse, we do not explicitly model synapse formation but consider the effect of discrete IL-2 sources from which IL-2 escapes into the extra-syn-aptic space (with rate qeff, corresponding to Iescape in the simplified model of the previous section).

In our opinion, this meticulous structure of the energy landscape for our simplified model is of general interest to other cell cycle dynamics, and the proposed methods can be applied to study similar biological systems.

In our simplified model describing the essential dynamics of the yeast cell cycle process, we assumed the “domino” mechanism of cell cycle regulation, which is different from the previous Tyson’s model [42] and its landscape [9].

Most of the insights we gained studying this simple model are independent of the number of dimensions and the specific formulation of the model, and therefore will be valuable to other systems and studies.