Open AccessA Simplified Fractional Seir Epidemic Model and Unique Inversion of the Fractional Order
Author(s) -
Yi Zhang,
Gongsheng Li
Publication year - 2022
Publication title -
wseas transactions on mathematics
Language(s) - English
Resource type - Journals
eISSN - 2224-2880
pISSN - 1109-2769
DOI - 10.37394/23206.2022.21.17
Subject(s) - laplace transform , mathematics , monotonic function , nonlinear system , fractional calculus , inverse problem , inversion (geology) , inverse , inverse laplace transform , order (exchange) , algebraic equation , function (biology) , mathematical optimization , mathematical analysis , paleontology , physics , geometry , finance , quantum mechanics , structural basin , evolutionary biology , economics , biology
A simplified linear time-fractional SEIR epidemic system is set forth, and an inverse problem of determining the fractional order is discussed by using the measurement at one given time. By the Laplace transform the solution to the forward problem is obtained, by which the inverse problem is transformed to a nonlinear algebraic equation. By choosing suitable model parameters and the measured time, the nonlinear equation has a unique solution by the monotonicity of the Mittag-Lellfer function. Theoretical testification is presented to demonstrate the unique solvability of the inverse problem.