Sensitivity Analysis of Markovian Exact Reproduction Numbers

Abstract

In this investigation a sensitivity analysis is presented by computing the partial derivatives and elasticities of several summary statistics with respect to parameters of the exact reproduction numbers, Re0 and Rp, for the stochastic SVIS model with an external source of infection and imperfect vaccine. These epidemic quantifiers are significant improvements over the basic reproductive number, R0, to study the potential transmission of an epidemic under a stochastic approach. Our research provides theoretical and algorithmic results for understanding the impact of vaccination strategies on the spread of epidemics. We provide efficient tools to evaluate the importance of each model parameters in the propagation of the pathogen which have significant implications for public health policies aimed at controlling and preventing infectious disease outbreaks. We illustrate our methodology in the context of the transmission of the diphtheria virus.