An analysis of the vectorial capacity using moment-generating functions

TL;DR

This paper introduces a mathematical approach using moment-generating functions to analyze the stochastic distribution of vectorial capacity in disease transmission, enabling detailed insights into disease spread dynamics.

Contribution

It presents a novel application of moment-generating functions to derive the distribution and moments of vectorial capacity in infectious disease modeling.

Findings

Derived the generating function for infectious contacts

Enabled calculation of distribution moments

Facilitated sensitivity analysis of disease dynamics

Abstract

This paper describes a technique for analyzing the stochastic structure of the vectorial capacity using moment--generating functions. In such formulation, for an infectious disease transmitted by a vector, we obtain the generating function for the distribution of the number of infectious contacts (e.g., infectious bites from mosquitoes) between vectors and humans after a contact to a single infected individual. This approach permits us to generally derive the moments of the distribution and, under some conditions, derive the distribution function of the vectorial capacity. A stochastic modeling framework is helpful for analyzing the dynamics of disease spreading, such as performing sensitivity analysis.