Uncertain Population Model with Jumps

Caiwen Gao, Zhiqiang Zhang and Baoliang Liu
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Caiwen Gao: School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China
Zhiqiang Zhang: School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China
Baoliang Liu: School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China

Mathematics, 2022, vol. 10, issue 13, 1-12

Abstract: The uncertain population model (UPM), which has been proposed and studied, is a kind of population model driven by a Liu process that can only deal with continuous uncertain population systems. In reality, however, species systems may be suddenly shaken by earthquakes, tsunamis, epidemics, etc. The drastic changes lead to jumps in the population and make the sample path no longer continuous. In order to model the dramatic drifts embedded in an uncertain dynamic population system, this paper proposes a novel uncertain population model with jumps (UPMJ), which is described by a kind of uncertain differential equation with jumps (UDEJ). Then, the distribution function and the stability of solution for UPMJ are discussed based on uncertainty theory. Finally, a numerical example related to the transmission of Ebola virus is given to illustrate the characteristics of the distribution function and the stability of solution for UPMJ.

Keywords: uncertain differential equation; Liu process; uncertain renewal process; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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