Kolade M. Owolabi

Numerical solution of diffusive HBV model in a fractional medium.

Evolution systems containing fractional derivatives can result to suitable mathematical models for describing better and important physical phenomena. In this paper, we consider a multi-components nonlinear fractional-in-space reaction–diffusion equations consisting of an improved deterministic model which describe the spread of hepatitis B virus disease in areas of high endemic communities. The model is analyzed. We give some useful biological results to show that the disease-free equilibrium is both locally and globally asymptotically stable when the basic reproduction number is less than unity. Our findings of this paper strongly recommend a combination of effective treatment and vaccination as a good control measure, is important to record the success of HBV disease control through a careful choice of parameters. Some simulation results are presented to support the analytical findings.

Mathematical and computational studies of fractional reaction-diffusion system modelling predator-prey interactions

Abstract This paper provides the essential mathematical basis for computational studies of space fractional reaction–diffusion systems, from biological and numerical analysis perspectives. We adopt linear stability analysis to derive conditions on the choice of parameters that lead to biologically meaningful equilibria. The stability analysis has a lot of implications for understanding the various spatiotemporal and chaotic behaviors of the species in the spatial domain. For the solution of the full reaction–diffusion system modelled by the fractional partial differential equations, we introduced the Fourier transform method to discretize in space and advance the resulting system of ordinary differential equation in time with the fourth-order exponential time differencing scheme. Results of numerical experiments are presented.