Journal of Mathematical Biology

, Volume 48, Issue 2, pp 218–242

# Macrophage response to Mycobacteriumtuberculosis infection

• D. Gammack
• C.R. Doering
• D.E. Kirschner
Article

## Abstract

The immune response to Mycobacteriumtuberculosis (Mtb) infection is the formation of multicellular lesions, or granolomas, in the lung of the individual. However, the structure of the granulomas and the spatial distribution of the immune cells within is not well understood. In this paper we develop a mathematical model investigating the early and initial immune response to Mtb. The model consists of coupled reaction-diffusion-advection partial differential equations governing the dynamics of the relevant macrophage and bacteria populations and a bacteria-produced chemokine. Our novel application of mathematical concepts of internal states and internal velocity allows us to begin to study this unique immunological structure. Volume changes resulting from proliferation and death terms generate a velocity field by which all cells are transported within the forming granuloma. We present numerical results for two distinct infection outcomes: controlled and uncontrolled granuloma growth. Using a simplified model we are able to analytically determine conditions under which the bacteria population decreases, representing early clearance of infection, or grows, representing the initial stages of granuloma formation.

### Key words or phrases

Reaction-diffusion-advection Granuloma Mycobacterium tuberculosis Internal states Internal velocity Immune response

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## Authors and Affiliations

• D. Gammack
• 1
• C.R. Doering
• 2
• D.E. Kirschner
• 3
1. 1.Department of Microbiology and ImmunologyUniversity of Michigan Medical SchoolUSA
2. 2.Department of Mathematics, Michigan Center for Theoretical Physics,University of MichiganUSA
3. 3.Department of Microbiology and ImmunologyUniversity of Michigan Medical SchoolUSA