Mathematical models for treatment time of pathogenic infection in blood after antibiotics administration

Abstract

The objective in this thesis is to create a mathematical model to predict the period of time needed to clear out the pathogens from the bloodstream after the patient receives certain antibiotics. The result will lead to the time where the drug administration can be terminated. This research is to compute the densities of bacteria and malaria in bloodstream at any given time and to compare this level with the actual results of the patient’s blood sampling, which was sent to the laboratory for investigation. The laboratory process of the blood sampling will usually take more than 2-3 days to culture and to calculate the density of pathogens. However, the prediction of treatment duration by using our mathematical model can get the results within few seconds. Therefore, the numerical results can be done faster by entering some certain parameters and running the mathematical program. The research method consists of the formulation of the death rates of bacteria and malaria in the mathematical forms under our assumptions. We assume that the independent variable is the plasma drug concentration and other parameters, based on the probabilistic theory, the relative velocity, the binding mechanism between drug molecules and pathogens by the blood convection, the structure and properties of antibiotics including bacteria and malaria. The dependent variable is the density of pathogens. The results from this research are consistent with the actual clinical data by comparing with the patient pathogen density graph.