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BioMed Research International
Volume 2015 (2015), Article ID 504259, 31 pages
Research Article

Mathematical Model of Innate and Adaptive Immunity of Sepsis: A Modeling and Simulation Study of Infectious Disease

1Health Care Operations Resource Center, Department of Industrial and Manufacturing Systems Engineering, Kansas State University, 2037 Durland Hall, Manhattan, KS 66506, USA
2Division of Pulmonary Diseases and Critical Care Medicine, University of Kansas, Mail Stop 3007, 3901 Rainbow Boulevard, Kansas City, KS 66160, USA

Received 5 October 2014; Revised 7 April 2015; Accepted 15 April 2015

Academic Editor: Farai Nyabadza

Copyright © 2015 Zhenzhen Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Sepsis is a systemic inflammatory response (SIR) to infection. In this work, a system dynamics mathematical model (SDMM) is examined to describe the basic components of SIR and sepsis progression. Both innate and adaptive immunities are included, and simulated results in silico have shown that adaptive immunity has significant impacts on the outcomes of sepsis progression. Further investigation has found that the intervention timing, intensity of anti-inflammatory cytokines, and initial pathogen load are highly predictive of outcomes of a sepsis episode. Sensitivity and stability analysis were carried out using bifurcation analysis to explore system stability with various initial and boundary conditions. The stability analysis suggested that the system could diverge at an unstable equilibrium after perturbations if (maximum release rate of Tumor Necrosis Factor- (TNF-) α by neutrophil) falls below a certain level. This finding conforms to clinical findings and existing literature regarding the lack of efficacy of anti-TNF antibody therapy.