Control and simulation impact on nonlinear Hepatitis-B model by using Pade-approximation based Differential Evolution

Abstract

Hepatitis B is the main public health problem of the whole world. In epidemiology, mathematical models perform a key role in understanding the dynamics of infectious diseases. This paper proposes Pade approximation (Pa) with Differential Evolution (DE) for obtaining solution of Hepatitis-B model which is nonlinear numerically. The proposed strategy transforms the nonlinear model into optimization problem by using Pade approximation. Initial conditions are converted into problem constraints and constraint problem become unconstraint by using penalty function. DE is obtained numerical solution of Hepatitis-B model by solving the established problem of optimization. There is no need to choose step lengths in proposed Pade-approximation based Differential Evolution (PaDE) technique and also PaDE converges to true steady state points. Finally, a convergence and error analysis evidence that the convergence speed of PaDE is greater than Non-Standard Finite Difference (NSFD) method for different time steps.