Analysis of the Dynamics of MS2 in Escherichia Coli: a Comparison Between the Stochastic Approach and Uncertainty Analysis

A hospital acquired infection is defined as an infection developed during hospital care which was not present or incubating at the time of admission. In addition, it causes a defined clinical pathology secondary to the patient's original condition [1]. This type of infection mainly results from the interaction between a patient -whose immune system is weakened- and a resistant strain of microorganism that does no longer respond to antibiotic treatment. Particularly Escherichia coli (E.coli) has been considered one of the mayor infectious agents in hospitals causing respiratory, gastrointestinal, and urinary infections [1]. While these infections can usually be treated with antibiotics, when dealing with an E.coli resistant strains the use of antibiotics is inefficient and the patient's health is seriously jeopardized. Fortunately, there is an alternative treatment that has been recently considered known as phage therapy. This therapy is described as the use of bacteriophages to treat pathogenic bacterial infections by controlling and, therefore, reducing the growth of bacterial population. In order to get better understanding of the infection dynamics, there is a need to develop models that allow describing the influence of the phage over the pathogen. Numerous models have been published that can be classified in deterministic and stochastic. Stochastic models consider the intrinsic noise and describe its effects on the dynamics while deterministic, based on differential ordinary equations just accounts for the average of the variable. When comparing with experimental results, it can be argued that either the noise or the uncertainty on the parameters, are the sources or the reasons of for the differences between both, experimental and model data. Thus the aim of this work was to determine if the source of error is based on uncertainty or noise expression. For the deterministic model a system of differential equations was found in literature for the E.coli-MS2 system [2], these were solved using the parameters reported in this same reference and a fourth-order Runge Kutta Method. In order to evaluate the effect of parameter uncertainty, interval analysis was implemented to solve the system of differential equations using Krawczyk's method to control the wrapping effect. Both the stochastic and the deterministic models predicted the experimental tendency. However the stochastic model was a better approximation for all of the species in the system and along the different stages of the infection; therefore stochastic noise has less effect in results than parameter uncertainty.

[1] JARAMILLO E. (1996). Vigilancia epidemiológica de infecciones intrahospitalarias. Colombia médica, Vol 27 N° 1

[2] JAIN, R., KNORR, A. L., BERNACKI, J., & SRIVASTAVA, R. (2006). Investigation of Bacteriophage MS2 Viral Dynamics Using Model Discrimination Analysis and the Implications for Phage Therapy. Biotechnology , 1650-1658.