The Dynamics of Acute Inflammation

The acute inflammatory response is the non-specific and immediate reaction of the body to pathogenic organisms, tissue trauma and unregulated cell growth. An imbalance in this response could lead to a condition commonly known as "shock" or "sepsis". This thesis is an attempt to elucidate the dynamics of acute inflammatory response to infection and contribute to its systemic understanding through mathematical modeling and analysis.The models of immunity discussed use Ordinary Differential Equations (ODEs) to model the variation of concentration in time of the various interacting species. Chapter 2 discusses three such models of increasing complexity. Sections 2.2 and 2.3 discuss smaller models that capture the core features of inflammation and offer general predictions concerning the design of the system. Phase-space and bifurcation analyses have been used to examine the behavior at various parameter regimes. Section 2.3 discusses a global physiological model that includes several equations modeling the concentration (or numbers) of cells, cytokines and other mediators. The conclusions drawn from the reduced and detailed models about the qualitative effects of the parameters are very similar and these similarities have also been discussed.In Chapter 3, the specific applications of the biologically detailed model are discussed in greater detail. These include a simulation of anthrax infection and an in silico clinical trial simulation. Such simulations are very useful to biologists and could prove to be invaluable tools in drug-design.Finally, Chapter 4 discusses the general problem of extinction of populations modeled as continuous variables in ODEs. The average time to extinction and threshold are estimated based on analyzing the equivalent stochastic processes