Connecting fields to connect models: A derivation of a viral master equation and the construction of transition rates

Abstract

Viral infections have dynamics that are difficult to understand, but the choice of model can lend a helping hand to understanding an infection. The work here is a continuing effort to understand viral infections for the better of all people, by exploring the connections between models and the connections between the model parameters and the data that that model is intending to replicate. A viral master equation is constructed to show how ODEs are derived from AB models, therefore showing that AB models that use transition rates for the transition rules have a corresponding ODE model. Then, this concept is taken further by exploring the idea that hazard functions from survival analysis can be used as transition rates. This work proposes a method for finding transition rates for AB models that do not have explicitly defined transition rates. Following the results of the methods, Ro values are calculated from the ODE and AB models then compared and Ro dependency on model selection is briefly discussed. The work here is a product of interdisciplinary research, drawing from the subfields of math and physics. This work demonstrates that every field can gain from a change in perspective.