Presentation Title

Modeling epidemic interventions with probability generating functions

Project Collaborators

Andrea Allen (Collaborator), Nicholas Roberts (Collaborator), Laurent Hébert-Dufresne (Graduate Student Mentor)

Abstract

Infectious diseases, now more than ever, are a critical area of study within the field of public health.Probability generating functions are a common approach used to analyze percolation models on contact networks, which allow for the inclusion of both the stochastic nature of disease spread and the heterogeneous structure of contact networks. One critical limitation of using percolation models to study epidemics, and the generating function approach more specifically, is that they integrate over time, precluding us from studying disease dynamics over time. However, there has been recent work which allows for the application of a time varying generating function approach to study disease spread. We extend the theory of time varying generating functions to study the effect of public health interventions on the spread of infectious diseases within a human population. Our extended model studies the effects of interventions such as vaccination, which reduces transmissibility, on population-level disease dynamics. We perform simulations of disease spread on synthetic contact networks, and find that our results agree with our framework across a range of degree distributions. This agreement validates the use of our model over computationally ex-pensive simulations and paves the way for extensive computational experiments of time-dependent interventions against emerging epidemics.

Primary Faculty Mentor Name

Laurent Hébert-Dufresne

Status

Graduate

Student College

College of Engineering and Mathematical Sciences

Program/Major

Mathematical Sciences

Primary Research Category

Biological Sciences

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Modeling epidemic interventions with probability generating functions

Infectious diseases, now more than ever, are a critical area of study within the field of public health.Probability generating functions are a common approach used to analyze percolation models on contact networks, which allow for the inclusion of both the stochastic nature of disease spread and the heterogeneous structure of contact networks. One critical limitation of using percolation models to study epidemics, and the generating function approach more specifically, is that they integrate over time, precluding us from studying disease dynamics over time. However, there has been recent work which allows for the application of a time varying generating function approach to study disease spread. We extend the theory of time varying generating functions to study the effect of public health interventions on the spread of infectious diseases within a human population. Our extended model studies the effects of interventions such as vaccination, which reduces transmissibility, on population-level disease dynamics. We perform simulations of disease spread on synthetic contact networks, and find that our results agree with our framework across a range of degree distributions. This agreement validates the use of our model over computationally ex-pensive simulations and paves the way for extensive computational experiments of time-dependent interventions against emerging epidemics.