A stochastic SIR network epidemic model with preventive dropping of edges View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03-13

AUTHORS

Frank Ball, Tom Britton, Ka Yin Leung, David Sirl

ABSTRACT

A Markovian Susceptible [Formula: see text] Infectious [Formula: see text] Recovered (SIR) model is considered for the spread of an epidemic on a configuration model network, in which susceptible individuals may take preventive measures by dropping edges to infectious neighbours. An effective degree formulation of the model is used in conjunction with the theory of density dependent population processes to obtain a law of large numbers and a functional central limit theorem for the epidemic as the population size [Formula: see text], assuming that the degrees of individuals are bounded. A central limit theorem is conjectured for the final size of the epidemic. The results are obtained for both the Molloy-Reed (in which the degrees of individuals are deterministic) and Newman-Strogatz-Watts (in which the degrees of individuals are independent and identically distributed) versions of the configuration model. The two versions yield the same limiting deterministic model but the asymptotic variances in the central limit theorems are greater in the Newman-Strogatz-Watts version. The basic reproduction number [Formula: see text] and the process of susceptible individuals in the limiting deterministic model, for the model with dropping of edges, are the same as for a corresponding SIR model without dropping of edges but an increased recovery rate, though, when [Formula: see text], the probability of a major outbreak is greater in the model with dropping of edges. The results are specialised to the model without dropping of edges to yield conjectured central limit theorems for the final size of Markovian SIR epidemics on configuration-model networks, and for the size of the giant components of those networks. The theory is illustrated by numerical studies, which demonstrate that the asymptotic approximations are good, even for moderate N. More... »

PAGES

1-77

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00285-019-01329-4

DOI

http://dx.doi.org/10.1007/s00285-019-01329-4

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112731546

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/30868213


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