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Closed-form probability distribution of number of infections at a given time in a stochastic SIS epidemic model.pdf
Heliyon (2019)
  • Michael Otunuga, Marshall University
Abstract
We study the effects of external fluctuations in the transmission rate of certain diseases and how these affect the distribution of the number of infected individuals over time. To do this, we introduce random noise in the transmission rate in a deterministic SIS model and study how the number of infections changes over time. The objective of this work is to derive and analyze the closed form probability distribution of the number of infections at a given time in the resulting stochastic SIS epidemic model. Using the Fokker-Planck equation, we reduce the differential equation governing the number of infections to a generalized Laguerre differential equation. The properties of the distribution, together with the effect of noise intensity, are analyzed. The distribution is demonstrated using parameter values relevant to the transmission dynamics of influenza in the United States.
Keywords
  • Infection; Stochastic Model; Differential Equation; Hypergeometric; Laguerre; Fokker-Planck; SIS; Kummer; Probability distribution
Publication Date
Fall September 23, 2019
DOI
https://doi.org//10.1016/j.heliyon.2019.e02499
Citation Information
Michael Otunuga. "Closed-form probability distribution of number of infections at a given time in a stochastic SIS epidemic model.pdf" Heliyon Vol. 5 Iss. 9 (2019) ISSN: 2405-8440
Available at: http://works.bepress.com/michael-otunuga/18/
Creative Commons license
Creative Commons License
This work is licensed under a Creative Commons CC_BY-NC International License.