A metapopulation model for cholera transmission dynamics between communities linked by migration

摘要

A metapopulation model is developed to describe the spread of cholera between two communities connected by migratory movement. Disease threshold ratios specific to the communities are given, considering a case when the communities are isolated and when the communities are connected. The connection of the threshold ratios to disease spread and stability is discussed. The disease free equilibrium is globally stable whenever, the corresponding community specific disease threshold ratios are less than one and unstable otherwise. Community specific endemic equilibrium points are unique, locally asymptotically stable, and only exist when the corresponding disease thresholds are greater than unit. Disease spread is explosive in nature at the beginning of the outbreak but more severe in a community with poor facilities relative to a community with more improved facilities. In isolated communities, in the case of endemic cholera, the infection is characterised by a big outbreak, followed by a small episode of the infection. Only one typically big outbreak is observed in the community with improved facilities with no recurrence of the epidemic. In connected communities, movement of individuals across communities not only influences persistence of the infection but also results in more pronounced outbreak in a relatively well facilitated community in the long term. Synchronous fluctuation of the population is observed when there is unrestricted movement of both immunologically naive and infected individuals across the communities. Our results suggest that during times of cholera, movement to and fro cholera endemic areas should be avoided if the outbreak is to be contained. Otherwise, with continued migration, the infection may potentially worsen even in communities with relatively good facilities.