MATHEMATICAL INSIGHTS INTO THE DYNAMICS OF INNATE IMMUNE RESPONSE DURING INFLAMMATION

Abstract

Innate immune system cells activate in response to infection and trigger an acute inflammatory reaction to restore tissue homeostasis and promote subsequent tissue repair. Their activation and functions must be very well regulated to avoid tissue damage, organ dysfunction, or even death. In this work, a new set of mathematical models is presented to examine the dynamics of the innate immune system response to tissue damage and provide further understanding of the role of the innate immune system during the early stages of an inflammatory response. Different damaged cells production functions are proposed to represent the effect of secondary tissue damage by the innate immune system. The stability and bifurcation analyses of the model reveal that there is an important threshold parameter that can be controlled in order to avoid sustained chronic inflammation and secure a successful healing outcome. A set of numerical simulations is also performed to support the presented theoretical results and demonstrate the medical applicability of the new mathematical model.