Dynamics of Helicobacter pylori colonization
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This post is the notes of this paper.
Abstract

A mathematical model that includes the host response, which encompasses both host and microbiological variation.

A key model parameter: the individual capacity of the host response, leading to either transient or persistent colonization, whereas the growth rate of that response has little effect.
Introduction
 A phenomenon
 Such a phenomenon has been postulated for the highly prevalent human gastric（胃） bacterium, Helicobacter pylori, which induces a host response in virtually all carriers but in a subset can augment the risk of peptic ulceration（消化性溃疡）and distal gastric cancers（远端胃癌）。
 during the lag time between the introduction of a microbe and the development of a mature immune response after primary acquisition, the dynamics of the interaction often are markedly different from those in the presence of the fully developed immune response.
 a deterministic mathematical model describing the steadystate pattern of H. pylori colonization. In that model, the ability to induce a host response was considered adaptive.
 new model that incorporates the development of the host response concurrent with H. pylori’s establishment of persistence. Allow us both to examine the initial events following H.pylori introduction into a naive host and the development of the steadystate relationship.
 incorporating a dynamics host response into the model of H. pylori colonization is key if we are to understand the initial features of the relationship between microbe and host, as well as the phenomenon that permit persistence to develop.
The model
Assumption
 no different during the initial and steadystate phases of the infection. That is, the microbial populations behave essentially identically both during the establishment of persistence and during colonization.
Terminology
 the mucusliving population: $M(t)$
 the population adheres to epithelial cells: $A(t)$
 the concentration of bacterial nutrient released via inflammation: $N(t)$
 the concentration of effector molecules: $E(t)$
 the host response: $I(t)$
what’s more, it needs to define values for the parameters and initial conditions.
Biological Analysis of the Host Response

Individuals differ in their ability to recognize and combat a newly introduced microbial pathogen（病原），such differences can be analyzed by examining the effects that varying the parameters $k_1, k_2$, and $k_3$ has on the microbial population.

Two cases:
 persistence
 transient