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 overview, we apply a linear algebraic approach to re-derive some well-known results pertaining to preferential within- and proportionate among-group contacts in compartmental models of pathogen transmission. We give results for the meta-population effective reproduction number ([Formula: see text]) assuming different levels of vaccination in the sub-populations. Specifically, we unpack the dependency of [Formula: see text] on the fractions of contacts reserved for individuals within one's own subgroup and, by obtaining implicit expressions for the partial derivatives of [Formula: see text], we show that these increase as this preferential-mixing fraction increases in any sub-population.
Keywords: Dominant eigenvalue; Implicit function; Mixing; Perron-Frobenius; Reproduction number.
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