An elaboration of theory about preventing outbreaks in homogeneous populations to include heterogeneity or preferential mixing. (7th December 2015)

• Record Type: Journal Article
• Authors: Feng, Zhilan; Hill, Andrew N.; Smith, Philip J.; Glasser, John W.
• Is Part Of: Journal of theoretical biology. Volume 386(2015)
• Page Start: 177
• Page End: 187
• Publication Date: 2015-12-07
• Subjects: Heterogeneity -- Population-immunity threshold -- Vaccine coverage; Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2015.09.006
• Languages: English
• ISSNs: 0022-5193

Abstract

Abstract: The goal of many vaccination programs is to attain the population immunity above which pathogens introduced by infectious people (e.g., travelers from endemic areas) will not cause outbreaks. Using a simple meta-population model, we demonstrate that, if sub-populations either differ in characteristics affecting their basic reproduction numbers or if their members mix preferentially, weighted average sub-population immunities cannot be compared with the proportionally-mixing homogeneous population-immunity threshold, as public health practitioners are wont to do. Then we review the effect of heterogeneity in average per capita contact rates on the basic meta-population reproduction number. To the extent that population density affects contacts, for example, rates might differ in urban and rural sub-populations. Other differences among sub-populations in characteristics affecting their basic reproduction numbers would contribute similarly. In agreement with more recent results, we show that heterogeneous preferential mixing among sub-populations increases the basic meta-population reproduction number more than homogeneous preferential mixing does. Next we refine earlier results on the effects of heterogeneity in sub-population immunities and preferential mixing on the effective meta-population reproduction number. Finally, we propose the vector of partial derivatives of this reproduction number with respect to the sub-population immunities as a fundamentally new tool for targeting vaccination efforts. Highlights: Population-immunity thresholds are useful only in homogeneous, proportionally-mixing populations. Meta-population effective reproduction numbers, ℜ v, and related quantities always are useful. Heterogeneity in variables affecting sub-population reproduction numbers is relevant. Together with preferential mixing among sub-populations, such heterogeneity increases ℜ v . The partial derivatives of ℜ v with respect to sub-population immunities indicates the optimal strategy.