Modeling the dynamics of Hepatitis E with optimal control

The present paper shows the dynamics of Hepatitis E with optimal control. The paper is analyzed by two different aspects: first, we explore the dynamics of Hepatitis E model and then applying the optimal control analysis. Secondly, we use the most appropriate and recent fractional order derivative called the Atangana-Baleanu derivative for the dynamical analysis of Hepatitis E model. The proposed model considered is locally asymptotically stable when the threshold quantity less than one. Further, we explore the stability analysis of the model when R0>1. Then, we choose some appropriate control to formulate the optimality system. The results associated to the optimal control are obtained and discussed with different strategies. Moreover, we apply Atangana-Baleanu derivative to the proposed model and obtain the required results necessary for the fractional order model. Numerical results for the optimal control problem and Atangana-Baleanu derivative are obtained and discussed in detail. The results suggest that control variables chosen should be properly applied to get rid of the infection of Hepatitis E. The Atangana-Baleanu derivative results suggest that at any time t we can check the disease status and make a useful strategy for the early elimination of Hepatitis E from the community.