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

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...

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Vydané v:Mathematics (Basel) Ročník 10; číslo 20; s. 3759
Hlavný autor: Bai, Fan
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Basel MDPI AG 01.10.2022
Predmet:
Algorithms
branching process
Computer simulation
delay differential equations
Epidemics
Epidemiology
Food science
Gene expression
Infections
Infectious diseases
Learning models (Stochastic processes)
Markov analysis
Markov chain
Markov chains
Mathematical models
numerical methods
Outbreaks
Population
Probability
probability of a minor epidemic outbreak
Probability theory
Random variables
Signal transduction
Simulation
stochastic epidemic models with delays
Stochastic models
Viral infections
United States
ISSN:2227-7390, 2227-7390
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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.
AbstractList 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.
Audience Academic
Author Bai, Fan
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CitedBy_id crossref_primary_10_1080_10739149_2025_2470134
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Snippet The calculation of the probability of a minor outbreak is crucial in analyzing a stochastic epidemic model. For stochastic epidemic models with fixed delays,...
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SubjectTerms Algorithms
branching process
Computer simulation
delay differential equations
Epidemics
Epidemiology
Food science
Gene expression
Infections
Infectious diseases
Learning models (Stochastic processes)
Markov analysis
Markov chain
Markov chains
Mathematical models
numerical methods
Outbreaks
Population
Probability
probability of a minor epidemic outbreak
Probability theory
Random variables
Signal transduction
Simulation
stochastic epidemic models with delays
Stochastic models
Viral infections
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