Epidemiological models in semiclassical approximation: an analytically solvable model as a test case

摘要

Stochastic models that can describe real epidemiological processes can become very quickly quite complex. Approximation schemes are a useful tool to understand the qualitative behaviour of such processes. In this paper, we investigate the semiclassical approximation, performed in the context of the Hamilton-Jacobi formalism, for solutions of master equations of stochastic epidemiological systems. In a test case of a previously investigated process, the linear infection model, we can analytically solve Hamilton's equations of motion. This helps to understand generalizations to more complex epidemiological systems as needed to describe realistic cases like multi-strain systems applicable to dengue fever, for example. The connection between the semiclassical approach for epidemiological systems and the Wentzel-Kramers-Brillouin approximation in quantum mechanics is also discussed. Copyright (c) 2016 John Wiley & Sons, Ltd.