Speaker
Description
Mathematical epidemiologists focus on the numbers of secondary infections per primary, R, but the intervals between primary and secondary infections, T, also determine infected population growth rates, r. Empirical estimates of R from reported cases or hospitalizations approximate T from periods between symptom onsets in paired primary and secondary infections. Mechanistic models typically are systems of ordinary differential equations (ODEs) that may be stratified. In such meta-population models, r and R may be derived from the Jacobian matrix, partial derivatives of the linearized system of ODEs for the infected states at equilibrium with respect to the remaining variables. They are the eigenvalue with largest real part and dominant eigenvalue of the matrix product of the infection and inverse of the transmission terms, respectively. The associated left and right eigenvectors are equilibrium contributions and prevalence of infectious states, respectively. And T is the mean generalized-gamma-distributed sojourn of people following all possible paths among infected states weighted by their respective contributions to R. In this presentation, we describe insights from weekly evaluations of the impact of mitigation measures, via effective values of these analytical quantities derived from our meta-population model of SARS-CoV-2 transmission in the United States, that estimates of R via renewal equations with proxy T would miss even if infections were accurately reported.
Joint work with Troy Day (Queens University) and Zhilan Feng (National Science Foundation).
