Abstract
ABSTRACTIn meta-population models for infectious diseases, the basic reproduction number can be as much as 70% larger in the case of preferential mixing than that in homogeneous mixing [J.W. Glasser, Z. Feng, S.B. Omer, P.J. Smith, and L.E. Rodewald, The effect of heterogeneity in uptake of the measles, mumps, and rubella vaccine on the potential for outbreaks of measles: A modelling study, Lancet ID 16 (2016), pp. 599–605. doi: 10.1016/S1473-3099(16)00004-9]. This suggests that realistic mixing can be an important factor to consider in order for the models to provide a reliable assessment of intervention strategies. The influence of mixing is more significant when the population is highly heterogeneous. In this paper, another quantity, the final epidemic size () of an outbreak, is considered to examine the influence of mixing and population heterogeneity. Final size relation is derived for a meta-population model accounting for a general mixing. The results show that can be influenced by the pattern of mixing in a significant way. Another interesting finding is that, heterogeneity in various sub-population characteristics may have the opposite effect on and .
Highlights
Epidemiological models can be used to identify key factors affecting disease outbreaks and to evaluate intervention strategies
Examples Because population heterogeneity in factors such as ai or i may affect the final size and the basic reproduction number in significant ways, we investigate how the model evaluations of intervention strategies may be affected
The results presented in this paper provide another example that incorporation of population heterogeneity and non-homogeneous mixing in epidemic models can generate outcomes that are qualitatively different from that based on models for populations with homogeneous mixing
Summary
Epidemiological models can be used to identify key factors affecting disease outbreaks and to evaluate intervention strategies. One of the most commonly used assumptions in epidemiological models is the homogeneous, or random, mixing in the whole population, which allows the model to ignore heterogeneity in various sub-population factors including activity (pertinent to disease transmission), susceptibility, preference in contact, group size, etc. Results concerning final epidemic sizes can be found in other studies including [1,3,4,10,15,16] None of these studies considered the influence of heterogeneity on the final size or the relationship between F and R0 in a meta-population with preferential mixing.
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