|Model, 1. modul, 2008, id:373|
|Findes på RUb:||Ja|
This report investigates a matemathical model for the severe blood poisoning sepsis. The model is developed by Zuev et al. (2006) as a patient specific model with one patient specific, dimensionless parameter, H, which is dependent of the patients BMI. In the paper by Zuev et al. (2006) it is not shown how the model is actually made patient specific by means of only one parameter, which is why the argument is made in the report. We perform an investigation consisting of stability analysis and sensitivity analysis. The stability analysis consists of a primarily algebraic analysis, where steady states and eigenvalues of the Jacobian matrix are investigated, and a numerical analysis where we focus on the general dynamics of the model. We find 3 different dynamics for the model where the patient recovers if H >0.86, while the patients at (XXX) will experience a periodic course of disease without either recovery nor death as an outcome. Finally patients with H < 0.52 will certainly die if treatment is not initiated. By including the sensitivity analysis, we furthermore find, that the model is somewhat accurate for H < 1, but at larger values of H, the output of the model are related with great incertainty. In total we conclude that the model by Zuev et al. (2006) is sufficient to describe sepsis. It will, however, demand further work before it can be implemented. We recommend significantly more empiric evidence and a more biological ivestigation. Our analyses recommend a discussion about whether it is suitable to make a model with only one patient specific parameter. This discussion gain further relevance since this parameter is also a bifurcation parameter, and the parameter which the variables ahs the highest sensitivity too. In the paper by Zuev et al. (2006), H is proposed to be dependent of variuos things; age, lung capacity etc. By means we find criticizable. We also suggest an expansion of the model, to incorporate antibiotic treatments. Finally we give a suggestion to implementation - which will need to wait for further validation of the model to take place.