Poster

Reproduction Numbers for ODE Models of Arbitrary Finite Dimension: An Application of the Generalized Linear Chain Trick

eSMB2020 eSMB2020 Follow 2:30 - 3:30pm EDT, Monday - Wednesday
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Paul J Hurtado

University of Nevada, Reno
"Reproduction Numbers for ODE Models of Arbitrary Finite Dimension: An Application of the Generalized Linear Chain Trick"
The Generalized Linear Chain Trick (GLCT) is a conceptually and practically useful approach for deriving mean field ODE models, since it describes how the structure of mean-field ODE models (and quantities like the basic reproduction number) reflect the assumptions of an often unspecified underlying continuous-time, stochastic state-transition model. In this talk, I will first describe how to generalize an existing ODE model -- such as the SEIR model or Rosenzweig-MacArthur consumer-resource model -- using the GLCT to incorporate non-exponential dwell times (e.g., latent periods in SEIR models, or predator maturation times in consumer-resource models) that are Erlang distributed or, more generally, are phase-type distributed. The phase-type family of distributions are the absorption time distributions for continuous time Markov chains, and include exponential, Erlang, generalized Erlang, and Coxian distributions. Second, I will show how the structure of the resulting ODE model, which is of arbitrary finite dimension, can be exploited to obtain a general expression for the (basic) reproduction number. These results illustrate the utility of the GLCT, not just for model derivation, but also for model analysis and interpretation.
eSMB2020
Hosted by eSMB2020 Follow
Virtual conference of the Society for Mathematical Biology, 2020.