Exact solutions and bounds for network SIR and SEIR models using a rooted-tree approximation

In this paper, we develop a new node-based approximate model to describe contagion dynamics on networks. We prove that our approximate model is exact for Markovian SIR (susceptible-infectious-recovered) and SEIR (susceptible-exposed-infectious-recovered) dynamics on tree graphs with a single source...

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Bibliographic Details
Published in:Journal of mathematical biology 2023-02, Vol.86 (2), p.22-22, Article 22
Main Authors: Hall, Cameron Luke, Siebert, Bram Alexander
Format: Article
Language:English
Subjects:
Applications of Mathematics
Approximation
Communicable Diseases - epidemiology
Differential equations
Disease Susceptibility
Exact solutions
Humans
Infections
Mathematical and Computational Biology
Mathematical models
Mathematics
Mathematics and Statistics
Nodes
Probability
Stochastic models
Trees
Upper bounds
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Summary:In this paper, we develop a new node-based approximate model to describe contagion dynamics on networks. We prove that our approximate model is exact for Markovian SIR (susceptible-infectious-recovered) and SEIR (susceptible-exposed-infectious-recovered) dynamics on tree graphs with a single source of infection, and that the model otherwise gives upper bounds on the probabilities of each node being susceptible. Our analysis of SEIR contagion dynamics is general to SEIR models with arbitrarily many classes of exposed/latent state. In all cases of a tree graph with a single source of infection, our approach yields a system of linear differential equations that exactly describes the evolution of node-state probabilities; we use this to state explicit closed-form solutions for an SIR model on a tree. For more general networks, our approach yields a cooperative system of differential equations that can be used to bound the true solution.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-022-01854-9