Allen, Linda J.S.

Nipa, Kaniz Fatema

English

VCU Scholars Compass

Virginia Commonwealth UniversityVCU Scholars CompassBiology and Medicine Through MathematicsConference 2018May 31st, 6:00 PM - 6:30 PMThe Effect of Environmental Variability andPeriodic Fluctuations on Disease Outbreaks inStochastic Epidemic Models.Kaniz Fatema NipaTexas Tech University, kaniz.fatema.nipa@ttu.eduLinda J.S. AllenTexas Tech University, Linda.J.Allen@ttu.eduFollow this and additional works at: https://scholarscompass.vcu.edu/bammPart of the Life Sciences Commons, Medicine and Health Sciences Commons, and the PhysicalSciences and Mathematics CommonsThis Event is brought to you for free and open access by the Dept. of Mathematics and Applied Mathematics at VCU Scholars Compass. It has beenaccepted for inclusion in Biology and Medicine Through Mathematics Conference by an authorized administrator of VCU Scholars Compass. Formore information, please contact libcompass@vcu.edu.https://scholarscompass.vcu.edu/bamm/2018/thursday/16Title: The Effect of Environmental Variability and Periodic Fluctuations on Disease Outbreaks in Stochastic Epidemic Models. Kaniz Fatema Nipa and Linda J.S. Allen Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA. Abstract: Seasonality and contact patterns due to environmental fluctuations and social behavior affect the dynamics of disease outbreaks. Recent studies applied to deterministic epidemic models with periodic environments have shown that the average basic reproduction number is not sufficient to predict an outbreak.  We extend these studies to stochastic epidemic models with periodic environments to investigate the combined effect of periodicity and variability on disease outbreaks. The deterministic models are extended to continuous-time Markov chain and stochastic differential equations. A numerical study of the dynamics of several stochastic SIR and vector-host models with environmental variability and periodicity are investigated in terms of probability of an outbreak. 

The Effect of Environmental Variability and Periodic Fluctuations on Disease Outbreaks in Stochastic Epidemic Models.

Virginia Commonwealth University
VCU Scholars Compass
Biology and Medicine Through Mathematics
Conference 2018
May 31st, 6:00 PM - 6:30 PM
The Effect of Environmental Variability and
Periodic Fluctuations on Disease Outbreaks in
Stochastic Epidemic Models.
Kaniz Fatema Nipa
Texas Tech University, kaniz.fatema.nipa@ttu.edu
Linda J.S. Allen
Texas Tech University, Linda.J.Allen@ttu.edu
Follow this and additional works at: https://scholarscompass.vcu.edu/bamm
Part of the Life Sciences Commons, Medicine and Health Sciences Commons, and the Physical
Sciences and Mathematics Commons
This Event is brought to you for free and open access by the Dept. of Mathematics and Applied Mathematics at VCU Scholars Compass. It has been
accepted for inclusion in Biology and Medicine Through Mathematics Conference by an authorized administrator of VCU Scholars Compass. For
more information, please contact libcompass@vcu.edu.
https://scholarscompass.vcu.edu/bamm/2018/thursday/16
Title: The Effect of Environmental Variability and Periodic Fluctuations on Disease Outbreaks 
in Stochastic Epidemic Models. 
Kaniz Fatema Nipa and Linda J.S. Allen 
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA. 
Abstract: Seasonality and contact patterns due to environmental fluctuations and social 
behavior affect the dynamics of disease outbreaks. Recent studies applied to deterministic 
epidemic models with periodic environments have shown that the average basic reproduction 
number is not sufficient to predict an outbreak.  We extend these studies to stochastic epidemic 
models with periodic environments to investigate the combined effect of periodicity and 
variability on disease outbreaks. The deterministic models are extended to continuous-time 
Markov chain and stochastic differential equations. A numerical study of the dynamics of several 
stochastic SIR and vector-host models with environmental variability and periodicity are 
investigated in terms of probability of an outbreak. 


https://scholarscompass.vcu.edu/cgi/viewcontent.cgi?article=1226&amp;context=bamm

The Effect of Environmental Variability and Periodic Fluctuations on Disease Outbreaks in Stochastic Epidemic Models.

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