A Delayed Mathematical Model for the Acute Inflammatory Response to Infection

Authors

Carlo Bianca, Laboratoire de Physique Th´eorique de la Mati`ere Condens´ee, Sorbonne Universit´es, UPMC Univ Paris 06, UMR 7600, 75252 Paris cedex 05, France\\ CNRS, UMR 7600 LPTMC, Paris, FranceFollow
Luca Guerrini, Department of Management, Polytechnic University of Marche, Piazza Martelli 8, 60121 Ancona, ItalyFollow
Julien Riposo, Laboratoire de Physique Th´eorique de la Mati`ere Condens´ee, Sorbonne Universit´es, UPMC Univ Paris 06, UMR 7600, 75252 Paris cedex 05, France\\ CNRS, UMR 7600 LPTMC, Paris, FranceFollow

Author Country (or Countries)

France

Abstract

This paper deals with further developments on a mathematical model recently proposed for the modeling of the acute inflammatory response to infection or trauma. In particular in order to take into account that some interactions have not an immediate effect, we introduce time delays. Specifically the paper deals with the existence of steady states, determining the parameter regimes where the equilibrium points are stable, and the onset of Hopf bifurcation appears. Numerical simulations are performed with the main aim of supporting the analytical results and investigate further dynamics.

Recommended Citation

Bianca, Carlo; Guerrini, Luca; and Riposo, Julien (2015) "A Delayed Mathematical Model for the Acute Inflammatory Response to Infection," Applied Mathematics & Information Sciences: Vol. 09: Iss. 6, Article 3.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss6/3