Rational Model and Probability of Infection

Abstract

We generalized the solution to the problem of probability of infection from, (mathforum.org/dr.math?). We derived a model for n hermits. The model was used to generate expectation for some number of hermits and the result tabulated and graphed. Due to computational limitation of the software used to evaluate factorial n where n is greater than 170, the model could be evaluated up to n=170 populations, we then used the curve fitting tool to fit some curves using the data generated by our model. Among all, the Rational function model(R4) performed best with SSE: 0.01654,   R-square: 0.9999,   Adjusted R-square: 0.9999 and   RMSE: 0.0108.

Keywords: Probability, Mathematical model , Series , Infection, Population.