Uncertainty Quantification In Population Models - Omar, Almbrok Hussin Alsonosi (2013)
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.