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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 Padé approximation ( ) with Differential Evolution ( ) for obtaining solution of Hepatitis-B model which is nonlinear numerically. The proposed strategy transforms the nonlinear model into optimization problem by using Padé approximation. Initial conditions are converted into problem constraints and constraint problem become unconstraint by using penalty function.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 Padéapproximation based Differential Evolution ( ) technique and also converges to true steady state points. Finally, a convergence and error analysis evidence that the convergence speed of is greater than Non-Standard Finite Difference ( ) method for different time steps.

This paper proposes a novel hybrid algorithm called Genetic Algorithm based Simplex Adaptive Hooke and Jeeves (GA-SAHJ) method for solving equality constrained non-linear optimization problems. The proposed hybrid technique uses Genetic Algorithm (GA) as the global optimizer and a modified Hooke and Jeeves method for further refinements of the current solution within the landscape of a feasible region. The convergence proof of the modified approach is also provided. The effectiveness of the proposed GA-SAHJ method is demonstrated by applying it on six test instances each involving at least one equality constraint. The results witness that the proposed hybrid approach is capable of producing highly accurate and fully feasible solutions of the considered problems.