Abstract: Mixing among sub-populations, as well as heterogeneity in characteristics affecting their reproduction numbers, must be considered when evaluating public health interventions to prevent or control infectious disease outbreaks. In this talk, we model preferential within- and proportional among-group contacts in compartmental models of disease transmission and derive results for the overall effective reproduction number (Rv) assuming different levels of vaccination in the sub-populations. Specifically, we unpack the dependency of Rv on the fractions of contacts reserved for individuals within one’s own subgroup and show that Rv increases as this fraction increases in a given sub-population. These considerations lead to our proposing the gradient of Rv with respect to subgroup vaccination fractions as a measure by which to evaluate interventions. Examples of applying the results to specific populations and diseases will be discussed.

A Short Bio: Zhilan Feng studied mathematics at Jilin and Arizona State Universities, before joining the faculty in the Department of Mathematics at Purdue University, where she became full professor in 2005. She is currently a program director for the Mathematical Biology program in the Division of Mathematical Sciences at the National Science Foundation. She was elected a Fellow of the American Mathematical Society in 2021. Her research includes mathematical modeling of ecology and epidemiology using ordinary, partial, and integro-differential equations. She has supervised 16 Ph.D. students at Purdue. She has co-authored three books and more than 100 papers on mathematical biology. She served as an editor for Journal of Theoretical Biology, Mathematical Biosciences, SIAM Journal of Applied Mathematics, and Journal of Biological Dynamics. She is currently a member of the Board of Directors of SMB.