ABSTRACT
In view of the spread of corona virus disease 2019 (COVID-19), this paper proposes a fractional-order generalized SEIR model. The non-negativity of the solution of the model is discussed. Based on the established threshold R0, the existence of the disease-free equilibrium and endemic equilibrium is analyzed. Then, sufficient conditions are established to ensure the local asymptotic stability of the equilibria. The parameters of the model are identified based on the statistical data of COVID-19 cases. Furthermore, the validity of the model for describing the COVID-19 outbreak is verified. Meanwhile, the accuracy of the relevant theoretical results are also verified. Considering the relevant strategies of COVID-19 prevention and control, the fractional optimal control problem (FOCP) is proposed. Numerical schemes for Riemann-Liouville (R-L) fractional-order adjoint system with transversal conditions is presented. Based on the relevant statistical data, the corresponding FOCP is numerically solved, and the control effect of the COVID-19 outbreak under the optimal control strategy is discussed.
ABSTRACT
Since the vessels in the biological tissues are characterized by low seepage Reynolds numbers and contracting or expanding walls, more attention is paid on the viscous flow outside the porous pipe with small expansion or contraction. This paper presents a numerical solution of the flow and heat transfer outside an expanding or contracting porous cylinder. The coupled nonlinear similarity equations are solved by Bvp4c, which is a collocation method with MATLAB. The effects of the different physical parameters, namely the permeability Reynolds number,the expansion ratio and the Prandtl number, on the velocity and temperature distribution are obtained and the results are shown graphically.
