Omar, Almbrok Hussin Alsonosi
(2013)
Uncertainty Quantification In Population Models.
Masters thesis, Universiti Sains Malaysia.
Abstract
Uncertainty in general can be in the form of numeric or non-numeric, where the latter
is qualitative and the former quantitative in nature. In numerical quantities, uncertainty
can be random in nature, in which case probability theory is appropriate, or it can be
as a result of unclear information, whereby fuzzy set theory is useful.
Our concern will be on uncertainty in population models described by differential
equations and solved numerically. We select the predator-prey model and susceptible-
infected-recovered epidemic model to explore the uncertainty in the population models
through the initial states. For randomness, the normal distribution is selected to intro-
duce the uncertainty in the predator-prey model while we use the Beta distribution to
insert the uncertainty in the epidemic model. For the fuzzy approach, we consider a
triangular fuzzy number to treat the lack of information in the both models.
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