RUI: Applications of a Generalized Differential Equation Compartmental Model of Infectious Disease Transmission

This project concerns a novel class of mathematical models that quantify disease outbreaks by the total number of days people are infected with a disease. The goal of the project is to apply these models to answer open questions in public health and evolutionary biology. The models can provide a simple means to study how the differences in peoples’ recovery time from infection affects the evaluation of public health policies, disease interventions, and disease evolution.

As proof of concept, the project will model historical disease outbreaks, such as measles, whooping cough, and influenza, and compare predictions to classical modeling approaches that are based on tracking the number of infected people. The results of the research are expected to contribute to both the information needed by public health officials to make informed decisions and the state of knowledge on disease evolution.

This project will develop and apply a new class of differential equation compartmental models. This class of models is the first to consider an alternative assumption as to what quantifies the amount of disease in a population. By considering the quantity "person-days of infection" over "disease incidence," the new class of models enables the incorporation of higher statistical moments from latent and infectious period distributions into the rates that govern the dynamics of the model.

The work aims to illustrate the straightforward, accurate, and readily interpretable properties of this new class of compartmental model and its application. The project will analyze questions such as 1) the interplay between health disparities and virulence evolution, 2) the impact of infectious period outliers on the cost-effectiveness of disease interventions, and 3) how host variation affects the evolutionary and epidemiology dynamics of infectious disease transmission.

Essential in tackling these issues will be the use of mean-residual life theory and analysis techniques that include stability, cost-effectiveness, and evolutionary invasion analyses. The research will illustrate the utility of this new class of models, contribute to the information needed by public health officials to mitigate disease outbreaks, and contribute to the state of knowledge on disease evolution.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.