Comparison of smallpox outbreak control strategies using a spatial metapopulation model

Abstract

To determine the potential benefits of regionally targeted mass vaccination as an adjunct to other smallpox control strategies we employed a spatial metapopulation patch model based on the administrative districts of Great Britain. We counted deaths due to smallpox and to vaccination to identify strategies that minimized total deaths. Results confirm that case isolation, and the tracing, vaccination and observation of case contacts can be optimal for control but only for optimistic assumptions concerning, for example, the basic reproduction number for smallpox (R0=3) and smaller numbers of index cases ( approximately 10). For a wider range of scenarios, including larger numbers of index cases and higher reproduction numbers, the addition of mass vaccination targeted only to infected districts provided an appreciable benefit (5-80% fewer deaths depending on where the outbreak started with a trigger value of 1-10 isolated symptomatic individuals within a district).

Individual identity and movement networks for disease metapopulations

“…The traditional method of modeling transmission in full stochastic metapopulation models is to allow subpopulations that are connected to share a proportion of their associated force of infection (10,14,26); we term such methods kernel transmission based, because effectively the movement network defines a spatial transmission kernel between subpopulations. (We note that for commuter movements the interaction between subpopulations is actually based on the convolution of the kernel, because infection can pass from subpopulation A to subpopulation B whenever individuals from these subpopulations meet in location C.) We can conceptualize this kernel model as moving a continuum of infection across network connections-effectively moving the pathogen.…”

“…With concerns over novel or reemerging infections, such networks of movements often form the core of mathematical models that examine the spatiotemporal spread of infections and the associated public health implications. Examples include work movements for the spread of seasonal influenza in the United States (9, 10); aviation traffic for the spread of smallpox (11), sudden acute respiratory syndrome (12), and general epidemics (13); commuting movements for deliberate release of smallpox (14); and trade for the 1918-1919 influenza pandemic (15); a more systematic review of techniques and applications is available from Riley (16). The sensitivity of the epidemic to the topological structure of the movement network has already been shown (13,17); in contrast here, through detailed simulation, we address how such movement networks should be modeled and the biases that occur from making naïve assumptions.…”

A model for the spread of an SIS epidemic in a human population

“…I also expect that by incorporating births and deaths in the model, existence of an endemic equilibrium may be shown by dropping the assumption Λ = H and applying uniform persistence results given for example in [200,217]. A similar approach was used in [210,107] [19,17,34,43,57,61,77,84,91,112,143,161,162,176,194,207,208]. The model studied in this thesis could be generalised by incorporating arbitrarily distributed infectious periods and allowing infectives and susceptibles to follow specified movement processes, which are not necessarily Markovian, by following a similar construction as described by Clancy [52].…”

“…Various other stochastic metapopulation models exist and some were developed to study specific diseases [18,34,55,56,61,91,104,112,114,120]. However, due to the size and complexity of the populations involved, these models needed to be analysed numerically.…”

“…There have been a number of attempts to model the spread of disease in real populations using metapopulation networks. Some were developed considering the type of mobility that individuals make between the subgroups, either long distance travel [104,56,55], commuter movements [34,61,91,112] or mixture of both [18]. Often these models rely on transportation data to estimate mobility.…”