Eigenvector Approach for Comparing the Probability of an Event under Two Different Pre-conditions

Abstract

Here, a tool has been formulated to quantify the effect of changes occurred in pre- conditions of a probabilistic event. Main underpinning concept is from eigenvectors of a matrix. Perron-Frobenius theorem for positive square matrices is a key result applied in the formulation of the tool. Special feature of this tool is its ability of catering possible population changes exposed under different pre-conditions of an event. Applicability of the tool can be verified by comparing with a classical way and further extensions/ modifications will arise after assimilating practical situations. This tool would be useful in recognizing the effect of pre-conditions in industrial, biological, computational, commercial and social processes. For an example, consider a treatment package for a certain disease in two phases called selective (treating infected individuals) and mass (treating all susceptible individuals). An increment of mass treatment coverage will enhance the awareness among the population to be treated. This additional awareness is infused in our tool