Influence of non-homogeneous mixing on final epidemic size in a meta-population model

Abstract

In meta-population models for infectious diseases, the basic reproduction number $R_0$ 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 ( $F$ ) 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 $F$ 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 $R_0$ and $F$ .

Keywords: Epidemic meta-population models; final epidemic size; non-homogeneous mixing.