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

Abstract

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 resultsin silicohave 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 ifrt2max(maximum release rate of Tumor Necrosis Factor- (TNF-)αby 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.