Multiscale, resurgent epidemics in a hierarchical metapopulation model

Abstract

Although population structure has long been recognized as relevant to the spread of infectious disease, traditional mathematical models have understated the role of nonhomogenous mixing in populations with geographical and social structure. Recently, a wide variety of spatial and network models have been proposed that incorporate various aspects of interaction structure among individuals. However, these more complex models necessarily suffer from limited tractability, rendering general conclusions difficult to draw. In seeking a compromise between parsimony and realism, we introduce a class of metapopulation models in which we assume homogeneous mixing holds within local contexts, and that these contexts are embedded in a nested hierarchy of successively larger domains. We model the movement of individuals between contexts via simple transport parameters and allow diseases to spread stochastically. Our model exhibits some important stylized features of real epidemics, including extreme size variation and temporal heterogeneity, that are difficult to characterize with traditional measures. In particular, our results suggest that when epidemics do occur the basic reproduction number R 0 may bear little relation to their final size. Informed by our model's behavior, we suggest measures for characterizing epidemic thresholds and discuss implications for the control of epidemics.

Effects of fear factors in disease propagation

“…Inter-community and intra-community links could have different impacts on the disease propagation [29], and such links may be removed in different ways due to fear factor. All these will be of our future research interest.…”

Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: Theory and simulations

“…In particular, the effects due to the finite size of subpopulations and the stochastic nature of the diffusion might have a crucial role in the problem of resurgent epidemics, extinction and eradication (Ball, 1997;Watts et al, 2005;Vázquez, 2007;Cross et al, 2007). Therefore it is important to consider the discrete nature of individuals.…”

The effect of clumped population structure on the variability of spreading dynamics

“…In both the initial phase (i) and the early growth phase (ii), increasing the clump size, while keeping all other factors constant, increases the variance in the process. The enhanced variability arises in the early dynamics through the variability in the lag before the early growth phase begins, and hence gives rise to stuttering behaviour as seen in actual epidemics (Anderson et al, 2004;Watts et al, 2005). Combined with partial detection of cases, this could be mistaken as stochastic fade-out followed by re-introductions of infection.…”

“…It has been noticed for some time that many models of these processes do not capture the noisy behaviour of empirical data. For example many epidemic outbreaks are far noisier than predicted by simple models (Watts et al, 2005), suggesting that some element (or elements) are missing from these.…”