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Stochastic effects on the dynamics of an epidemic due to population subdivision

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Bittihn,  Philip
Department of Living Matter Physics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Golestanian,  Ramin
Department of Living Matter Physics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Bittihn, P., & Golestanian, R. (2020). Stochastic effects on the dynamics of an epidemic due to population subdivision. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30, 101102. doi:10.1063/5.0028972.


Cite as: http://hdl.handle.net/21.11116/0000-0007-549C-B
Abstract
Using a stochastic susceptible–infected–removed meta-population model of disease transmission, we present analytical calculations and numerical simulations dissecting the interplay between stochasticity and the division of a population into mutually independent sub-populations. We show that subdivision activates two stochastic effects—extinction and desynchronization—diminishing the overall impact of the outbreak even when the total population has already left the stochastic regime and the basic reproduction number is not altered by the subdivision. Both effects are quantitatively captured by our theoretical estimates, allowing us to determine their individual contributions to the observed reduction of the peak of the epidemic. Simple models for the spread of infectious diseases are useful for the quantitative characterization of an epidemic as well as for forecasting future infection numbers and guiding decision-making for containment. Different extensions and refined versions of these models have been created to extract various factors that may be critical for the dynamics and prevention of epidemics. Although it is well known that stochastic fluctuations can alter the dynamics as well, they are often neglected at higher infection number levels such that the contact rates and basic reproduction number become the central quantities of interest. In contrast, we investigate a situation in which stochastic effects can quantitatively change the course of an epidemic when infection numbers are large and contact rates remain unaltered. We consider an extended Susceptible–Infected–Removed (SIR) model in which a large population is subdivided into a certain number of sub-populations, each containing only a few infected individuals. For the limiting case of perfect isolation, i.e., when the epidemic evolves independently in each sub-population with no cross-infections, we derive analytical estimates for these stochastic effects that together recapitulate the results of extensive numerical simulations. Our central quantity of interest is the peak total number of simultaneously infected individuals, which we compare between the subdivided population and a single large population with an identical reproduction number. Our analysis suggests that regional isolation can resurrect certain stochastic effects and thereby contribute to effective containment, regardless of the initial distribution of infected individuals.