PTF Model for Evaluating the Relationships between the VAC and Antimicrobial Resistance in Human Communities

This paper shows the possibility to create the basis of a computational (mathematical) model for the relationship between the volume of antimicrobial consumption (VAC) and the frequency of antimicrobial resistance in the human communities, based on an analogy with oscillations and wavelets. A heuristic algorithm for generating asymmetrical practical test functions (ie PTF) using MATLAB procedures was elaborated. Based on the fact that differential equations can generate only functions similar to test functions (defined as practical test functions), the invariance general properties suitable for generating symmetrical pulses as related to the middle of the working interval are presented.

Then some possibilities for obtaining asymmetrical pulses as related to this middle of the working interval using the derivative of such symmetrical pulse are studied, for certain differential equations corresponding to second order systems (with unity-step input and for an input represented by a Gaussian pulse). Finally it is shown that we can reach an oscillating system by joining such working intervals and restoring the initial null conditions for a second order system, in an adequate manner.