Mathematical Biosciences and Engineering, 2010, 7(2): 277-300. doi: 10.3934/mbe.2010.7.277.

Primary: 35K57, 92C17 ; Secondary: 65C20, 93A30.

Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

A pressure model of immune response to mycobacterium tuberculosis infection in several space dimensions

1. Istituto per le Applicazioni del Calcolo “M. Picone”, CNR, c/o Dip. di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1; I-00133 Roma

Mycobacterium tuberculosis (Mtb) is a widely diffused infection. However, in general, the human immune system is able to contain it. In this work, we propose a mathematical model which describes the early immune response to the Mtb infection in the lungs, also including the possible evolution of the infection in the formation of a granuloma. The model is based on coupled reaction-diffusion-transport equations with chemotaxis, which take into account the interactions among bacteria, macrophages and chemoattractant. The novelty of this approach is in the modeling of the velocity field, proportional to the gradient of the pressure developed between the cells, which makes possible to deal with a full multidimensional description and efficient numerical simulations. We perform a linear stability analysis of the model and propose a robust implicit-explicit scheme to deal with long time simulations. Both in one and two-dimensions, we find that there are threshold values in the parameters space, between a contained infection and the uncontrolled bacteria growth, and the generation of granuloma-like patterns can be observed numerically.
  Article Metrics

Keywords Internal velocity.; Reaction-diffusion-advection; Multi-dimensional model; Mycobacterium tuberculosis; Chemotaxis

Citation: Fabrizio Clarelli, Roberto Natalini. A pressure model of immune response to mycobacterium tuberculosis infection in several space dimensions. Mathematical Biosciences and Engineering, 2010, 7(2): 277-300. doi: 10.3934/mbe.2010.7.277


This article has been cited by

  • 1. Massimiliano Pio di Cagno, Fabrizio Clarelli, Jon Våbenø, Christina Lesley, Sokar Darsim Rahman, Jennifer Cauzzo, Erica Franceschinis, Nicola Realdon, Paul C. Stein, Experimental Determination of Drug Diffusion Coefficients in Unstirred Aqueous Environments by Temporally Resolved Concentration Measurements, Molecular Pharmaceutics, 2018, 15, 4, 1488, 10.1021/acs.molpharmaceut.7b01053
  • 2. Fabrizio Clarelli, Gabriele Inglese, Reconstruction of a nonlinear heat transfer law from uncomplete boundary data by means of infrared thermography, Inverse Problems, 2016, 32, 11, 115017, 10.1088/0266-5611/32/11/115017

Reader Comments

your name: *   your email: *  

Copyright Info: 2010, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved