In this study, we combine mechanistic mathematical models at the cellular level with epidemiological data at the population level to disentangle the respective roles of immune capacity and cell dynamics in the clearing mechanism.

Combining mechanistic mathematical models at the cell-level with population-level data, we disentangle the contributions from immune system and cellular dynamics in the clearance process.

In this study, we combined mechanistic mathematical models at the cellular level with epidemiological data at the population level to disentangle the respective roles of immune capacity and cell dynamics in the clearing mechanism.

While population-level models of HPV transmission and progression are commonly used by epidemiologists and health economists, only few groups have developed mathematical models of HPV infection at the tissue level.

In fact, mathematical models at the tissue-level are often difficult to parametrize because sample sizes in pathology studies are generally small and exhibit large between-patient variation.

Due to the large number of scales involved, ranging from protein binding to diffusion of specific elements throughout the organism, a correct mathematical modeling of differentiation processes and their associated pattern formation demands an integrative approach combining tools from statistical mechanics and the theory of dynamical systems (see [1, 2] for instance).

Let us briefly review the previous studies on the mathematical modeling of heterocyst pattern formation.

In this work, we develop a simple mathematical model by incorporating the recent experimental results on the genetic regulatory network of cyanobacteria into the theoretical machinery of system biology.

The mathematical models for both gene repression and gene induction by GR require the sequential binding of GR monomers as opposed to the binding of preformed dimers.

We strongly suspect that, as in gene induction, the association of GR with the DNA of repressed genes also proceeds via the stepwise binding of GR monomers, as required by our mathematical model .

Mathematical modeling provides one solution; and, a theory has been developed recently to understand the underlying mechanisms of factor action during steroid-regulated gene induction.

Here we use mathematical models to investigate the effect of drug heterogeneity on the probability of escape from treatment and the time to resistance.

Mathematical models of this kind have provided particularly useful insights into understanding evolutionary dynamics of cancer in response to treatment [11, 14—17, 63—66] (see a review in Ref.

Recent mathematical modeling with laboratory test using mice suggests that resistance carries a fitness cost [68].

We create a mathematical model to investigate the emergence probability of a fitter strain if it mutates from a self-limiting strain that is guaranteed to go extinct in the longterm.

Our study outlines novel mathematical modelling techniques that accurately quantify how ongoing immune growth reduces the emergence probability of mutated pathogenic strains over the course of an infection.

Section 1 Setting up the mathematical model .