Applications of the Delay Stochastic Simulation Algorithm (DSSA) in Mathematical Epidemiology

Fan Bai ()
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Fan Bai: Applied Mathematics Program, Department of Mathematical Sciences, Faculty of Science and Technology, Beijing Normal University–Hong Kong Baptist University United International College, Zhuhai 519087, China

Mathematics, 2022, vol. 10, issue 20, 1-15

Abstract: The calculation of the probability of a minor outbreak is crucial in analyzing a stochastic epidemic model. For stochastic epidemic models with fixed delays, the linear chain trick is applied to transform the delayed models into a family of ODE models with increasing shape parameters. We then prove that the well-established results on the probability of a minor outbreak for continuous-time Markov chain (CTMC) epidemic models also hold for the stochastic epidemic models with fixed delays. All theoretical results are verified by numerical simulations implemented by the delay stochastic simulation algorithm (DSSA) in Python. It is shown that DSSA is able to generate exact realizations for underlying delayed models in the context of mathematical epidemiology, and therefore, provides insights into the effect of delays during the outbreak phases of epidemics.

Keywords: delay differential equations; stochastic epidemic models with delays; probability of a minor epidemic outbreak; Markov chain; branching process; numerical methods; delay stochastic simulation algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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